E.P. Wohlfarth Volume 1 Handbook of Magnetic Materials, Volume 1986

Handbook of Magnetic Materials, Volume1North-Holland Publishing Company, 1980 Edited by: E.P Wohlfarth ISBN: 978-0-444-85311-0 by kmno4 PREFACE This Handbook on the Properties of Magnetically Ordered Substances, Ferromagnetic Materials, is intended as a comprehensive work of reference and textbook at the same time. As such it aims to encompass the achievements both of earlier compilations of tables and of earlier monographs. In fact, one aim of those who have helped to prepare this work has been to produce a worthy successor to Bozorth's classical and monomental book on Ferromagnetism, published some 30 years ago. This older book contained a mass of information, some of which is still valuable and which has been used very widely as a work of reference. It also contained in its text a remarkably broad converage of the scientific and technological background. One man can no longer prepare a work of this nature and the only possibility was to produce several edited volumes containing review articles. The authors of these articles were intended to be those who are still active in research and development and sufficiently devoted to their calling and to their fellow scientists and technologists to be prepared to engage in the heavy tasks facing them. The reader and user of the Handbook will have to judge as to the success of the choice made. One drawback of producing edited volumes is clearly the impossibility of having all the articles ready within a time span sufficiently short for the whole work, once ready, to be up-to-date. This is an effect occurring every time an editor of such a work engages in his task and has been found to be particularly marked in the present case, as might have been expected. Hence a decision was made to edit the first two volumes of the projected four volume work on the basis of the articles available about the end of 1978. Again, the reader must judge whether on balance the lack of a complete logical order of the articles in these two volumes is outweighed by their immediacy and topicality. The future of the work is in the hands of the remaining authors. The projected remaining two volumes will complete a broad and comprehensive coverage of the whole field. Each author had before him the task of producing a description of material properties in graphical and tabular form in a broad background of discussion of vi PREFACE the physics, chemistry, metallurgy, structure and, to a lesser extent, engineering aspects of these properties. In this way, it was hoped to produce the required combined comprehensive work of reference and textbook. The success of the work will be judged perhaps more on the former than on the latter aspect. Ferromagnetic materials are used in remarkably many technological fields, but those engaged on research and development in this fascinating subject often feel themselves as if in a strife for superiority against an opposition based on other physical phenomena such as semiconductivity. Let the present Handbook be a suitable and effective weapon in this strife! I have to thank many people and it gives me great pleasure to do so. I have had nothing but kindness and cooperation from the North-Holland Publishing Company, and in referring only to P.S.H. Bolman by name I do not wish to detract from the other members of this institution who have also helped. In the same way, I am deeply grateful to many people at the Philips Research Laboratory, Eindhoven, who gave me such useful advice in the early stages. Again, I wish to mention in particular H.P.J. Wijn and A.R. Miedema, without prejudice. Finally, .I would like to thank all the authors of this Handbook, particularly those who submitted their articles on time! E.P. Wohlfarth Imperial College. TABLE OF CONTENTS Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V T a b l e of C o n t e n t s L i s t of C o n t r i b u t o r s vii ix 1. Iron, C o b a l t and N i c k e l E.P. W O H L F A R T H . . . . . . . . . 2. Dilute T r a n s i t i o n M e t a l A l l o y s : Spin G l a s s e s J.A. M Y D O S H a n d G.J. N I E U W E N H U Y S 3. R a r e E a r t h M e t a l s a n d A l l o y s S. L E G V O L D . . . . . . . . . . . 4. R a r e E a r t h C o m p o u n d s K.H.J. B U S C H O W . . . . . . . . . . 5. A c t i n i d e E l e m e n t s a n d C o m p o u n d s W. T R Z E B I A T O W S K I . . . . . . . . 6. A m o r p h o u s F e r r o m a g n e t s F.E. L U B O R S K Y . . . . . . . . . . 7. M a g n e t o s t r i c t i v e R a r e E a r t h - F e 2 C o m p o u n d s A.E. C L A R K . . . . . . . . . . . . Author Index Subject Index Materials Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 71 183 297 415 451 531 591 621 629 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii chapter 1 IRON, COBALT AND NICKEL E.P. WOHLFARTH Department of Mathematics Imperial College of Science and Technology London SW7 UK Ferromagnetic Materials, Vol. 1 Edited by E.P. Wohlfarth © North-Holland Publishing Company, 1980 CONTENTS 1. S u m m a r y of theoretical background . . . . . . . . . . . . . . . . . . . l.l. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2. Calculation of energy bands a n d Fermi s u r f a c e . . . . . . . . . . . . . 1.3. T h e Stoner model, origin of splitting energy . . . . . . . . . . . . . . 1.4. Results b e y o n d the Stoner model, m a n y body effects . . . . . . . . . . . 1.5. Spin w a v e s . . . . . . . . . . . . . . . . . . . . . . . . . . 2. F u n d a m e n t a l properties . . . . . . . . . . . . . . . . . . . . . . . 2.1. Magnetization at 0 K and at finite temperatures . . . . . . . . . . . . . 2.2. Hyperfine fields . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Curie temperature . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Susceptibility at T > Tc; C u r i e - W e i s s c o n s t a n t . . . . . . . . . . . . . 2.5. High magnetic field effects; high field susceptibility . . . . . . . . . . . . 2.6. Critical e x p o n e n t s near the Curie point . . . . . . . . . . . . . . . . 2.7. D y n a m i c susceptibility; spin w a v e dispersion and stiffness . . . . . . . . . 2.8. Spin densities f r o m neutron m e a s u r e m e n t s . . . . . . . . . . . . . . . 3. Secondary magnetic properties . . . . . . . . . . . . . . . . . . . . . 3.1. g and g' factors . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Linear magnetostriction . . . . . . . . . . . . . . . . . . . . . . 3.3. Magnetocrystalline anisotropy . . . . . . . . . . . . . . . . . . . 3.4. Magnetoelastic effects . . . . . . . . . . . . . . . . . . . . . . 3.5. T h e r m a l properties . . . . . . . . . . . . . . . . . . . . . . . 3.6. T r a n s p o r t properties . . . . . . . . . . . . . . . . . . . . . . . 3.7. Optical properties . . . . . . . . . . . . . . . . . . . . . . . . 4. Relevant electronic properties . . . . . . . . . . . . . . . . . . . . . 4.1. Solid state s p e c t r o s c o p y . . . . . . . . . . . . . . . . . . . . . 4.2. T h e Fermi surface, especially de H a a s - V a n Alphen technique . . . . . . . . 4.3. Miscellaneous techniques . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 4 10 15 17 19 19 22 23 24 26 28 29 34 34 34 35 38 43 47 51 56 57 57 62 64 65 1. Summary of theoretical background 1.1. Introduction The magnetism of the three ferromagnetic transition metals iron, cobalt and nickel is archetypal to the whole subject of metallic magnetism. It would seem necessary, if not sufficient, to understand the properties of these pure metals before attempting to understand those of the ferromagnetic transition metal alloys. As a result of this evident expectation great controversy has surrounded the three metals for many decades. The question used to be whether the magnetic carriers were localized or itinerant. Each of these views had its eminent proponent, such as Van Vleck on the one hand and Slater on the other. These heated arguments have died down since the 1950's, but even now it is by no means the case that iron, cobalt and nickel are fully understood. In fact, the magnetic properties of a considerable number of alloys are, surprisingly, more readily amenable to a reasonably simple interpretation than those of the pure metals. The reasons for this situation include the following: (1) The three metals are either strong (nickel, cobalt), or almost strong (iron) itinerant electron ferromagnets. Hence the exchange splitting between the + and - spins is relatively large (see section 1.3). The application of one-electron, or Stoner theory is thus less certain than for the more weakly itinerant alloys and is even then algebraically and computationaily less clear since no Landau expansion of the free energy is possible. (2) The influence on the magnetic properties of collective and many body effects, such as spin waves and spin fluctuations, is not only likely to be more important than for the weakly itinerant alloys but also to be itself less amenable to theoretical treatment. (3)The challenge of iron, cobalt and nickel is so clear that more attention has been paid to these materials than to others, so more experimental facts have to be explained. Nevertheless, the controversy is now less heated and is more concerned with the relative importance of itinerancy and localization and of single particle and many body effects below the Curie temperature and with the apparent degree of order present above. Slater's emphatic belief that the Curie temperature itself is unrelated to the exchange splitting, although slowly being accepted as being true by some, continues to arouse some opposition from others. For all these reasons the ferromagnetism of iron, cobalt and nickel continues to provide the major 4 E.P. WOHLFARTH challenge in the field of metallic magnetism, in the same sense as before that any advance in understanding this difficult subject of the pure metals will surely help in understanding the more weakly itinerant alloys. In this summary of the theoretical background a brief discussion of the calculation of energy bands and the Fermi surface is followed by the basics of one-electron or Stoner theory. The central parameter in this theory is the Stoner-Hubbard parameter I and a brief account is given of factors contributing to this energy (exchange and correlation), which in turn determines the exchange splitting between + and - spins. Theoretical values of these parameters for iron, cobalt and nickel are listed here while a summary of the experimental values obtained by the various possible measurements is given in later parts of this article. Since Stoner theory is too simple in some respects a brief discussion is given of results beyond this model, particularly those concerning spin waves and spin fluctuations. The theory of spin waves in metals is briefly outlined and calculated values of the spin wave stiffness D are tabulated. Experimental values are given later in section 2.7. This summary is kept deliberately brief in view of the nature of this Handbook which militates against an extensive theoretical treatment in favour of a more descriptive discussion of the physics of magnetic materials which serves as a background to the tabulation and graphical representation of their actual properties. 1.2. Calculation of energy bands and Fermi surface There have been very many energy band calculations for iron and nickel, but fewer for cobalt. References to some of these are given by Callaway and Wang (1977a) for the former, including those carried out by themselves using the local exchange model of itinerant electron magnetism. Two approximations to the exchange potential were used, namely the so-called Kohn-Sham-Gaspar (KSG) potential which is basically derived from Slater exchange (Xa) here with a close to 2, and the so-called yon Barth-Hedin (vBH) potential which includes correlation. These methods are regarded at the time of writing as the most reliable for these metals. Table 1 summarizes the results for nickel. Detailed comparison with experiment is possible by reference to the later discussions. It suffices to note that (i) the magnetic moment as calculated by either method is reasonable, TABLE 1 Band calculations for Ni (Callaway and Wang 1977a) Potential KSG(a = 32) vBH Moment (/is) 0.65 0.58 AE 0.88 0.63 N(Ev) 22.9 25.4 - 69.7 -57.4 AE, exchange splitting at top of band (eV). N(EF), density of states at Fermi energy (states/atom/Ry). Hh difference in + and - spin densities at the nucleus, expressed as an effective hyperfine field (kG). IRON, COBALT AND NICKEL 5 although better for vBH. (ii) The exchange splitting LiE is sensitive to the potential and may be considerably larger than some but not all experimental values, discussed later; the explicit questions regarding the magnitude of AE remain central to the theory of the properties of the ferromagnetic transition metals. (iii) The density of states N(EF) lies below that obtained from the specific heat (see below) by a factor corresponding to an electron-phonon enhancement factor A---0.60, which is very reasonable. (iv)The effective hyperfine field Hi is also reasonable when compared to experiment (see §2.2). Wang and Callaway (1977) calculated the density of states curve for nickel on the basis of these two potentials, and the result for the vBH potential is shown in fig. 1 where the curve applies to both spin directions. Figure 2 shows crosssections of the Fermi surface of nickel in a (100) plane. The agreement with experiment is generally good, although the d ~ heavy hole pocket shown by contour b has not been observed and may be an artifice of the potentials which are suggested to be insufficiently anisotropic. Another band calculation on Ni has been reported by Marshall and Bross (1978), using an interpolation scheme and the Hubbard (1963) Hamiltonian for the ferromagnetic metal. The results agree better with experiment than those of Wang and Callaway (1977), e.g. the absence of the heavy hole pocket. The gap A defined by eq. (9), comes out smaller at 175 meV, though still twice as large as given by the spin polarized photoemission data discussed in section 4.1. and the neutron data, section 2.7. The authors feel they can account for this remaining difference. 64.0 56.0 ' I I = | ' I i F.E. Both spins (vBH) Ni 48.0 0 "~ 40.0 tO 32.0 ~ 24.0 • ~ 16.0 8.0 O.C -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 Energy (Ry) Fig. 1. Density of states curve for both spin directions of nickel using vBH potential (Wang and Callaway 1977). 6 E.P. WOHLFARTH Ni / 1 I IO 0 o o o 0 O O 0 O O O it x w Fig. 2. Cross-sections of the Fermi surface of nickel in the (100) plane (Wang and Callaway 1977). Dashed lines KSG potential, solid lines vBH potential. Triangles, squares, dotted line, experimental data of Stark (see Gold 1974) and Tsui (1967). (a)Xst hole pocket; (b)X2~ hole pocket; (c)major d ~ hole surface; (d) sp 1' surface; (e) sp ~ surface. For iron similar results are shown in table 2. C o m p a r i s o n with experiment, where possible, is given later. The question of the exchange splitting A E is e v e n m o r e critical for iron than for nickel; as before the calculated values are sensitive to the potential and tend to be s o m e w h a t a b o v e those given, without too m u c h confidence, b y the various possible observations described below. The e l e c t r o n - p h o n o n e n h a n c e m e n t factor A is about 0.70. TABLE 2 Band calculations for bcc Fe (Callaway and Wang 1977a,b) Potential KSG(a -- ~) vBH Moment (#s) 2.30 2.25 AE 2.68 2.21 N(EF) 15.4 16.0 Hi -343 -237 IRON, COBALT AND NICKEL t I 7 I i 60 f~c Fe 50 A > o'= 40 ~ 30 / I ~ a 20 10 0 - I .2 -1.0 -0.8 -0.6 Energy (Ry) -0.4 -0.2 Fig. 3. Density of states curve for both spin directions of bcc iron using vBH potential (CaUaway and Wang 1977a,b). N bcc Fe ////# f / F ¢" H Fig. 4. Cross-section of the Fermi surface of bcc iron in the (100) plane (Callaway and Wang 1977a,b), using vBH potential. Solid lines, majority spin; dashed line.s, minority spin. See original papers for notation. See also fig. 23. Figure 3 shows the density of states curve for iron and fig. 4 a cross-section of the Fermi surface in the (100) plane. Comparison with experiment is given in the original publications (Callaway and Wang 1977a,b). Brief reference only need be made here to energy band calculations for fcc 8 E.P. WOHLFARTH iron (Dalton 1970, Madsen et al. 1975) and to those for hcp iron, a phase which is produced at high pressures of the order of 100 kbar (Madsen et al. 1975, Fletcher and Addis 1974). Although the calculations for the latter do not contain the exchange and correlation potentials as in the Callaway calculations the location of the Fermi energy at a very pronounced dip in the density of states curve leaves little doubt that this high pressure phase of iron has no spin ordering at all, in agreement with observation (Williamson et al. 1972). There is no comparably accurate band calculation for hcp cobalt. Two calculations (Wong et al. 1969, Wakoh and Yamashita 1970) based on different philosophies which both use the KKR method, were compared and contrasted by Wohlfarth (1970). Due to differences in the potential the values of the exchange splitting come out as 1.35eV and 1.71eV for the two respective calculations. Reference to the 1970 paper shows why both these values should be regarded as too large; a "best" estimate of 1.05 eV was thus proposed. Later Ishida (1972) reported a band calculation for hcp cobalt using again a K K R based method. The result of a rigid splitting of the paramagnetic energy bands, which is surely too simple, leads nevertheless to an exchange splitting of 1.13 eV, in excellent agreement with this best value. Figure 5 shows the paramagnetic density of states curve of hcp cobalt (full curve). Due to the fact that both crystal structures are close packed the density of states curves are very similar. The hcp curve is in good agreement with that of the earlier calculations. The electron-phonon enhancement factor A comes out anomalously low at 0.14 in both calculations. Figure 6 shows the calculated Fermi surface of the majority spin band of hcp cobalt. c 35 "~- 30 ~. hcp + fcc Co t t/~ll~ e o . o* 12 £ -~ / / j,,,..\.;, ~ . . j,, .pI t r °°1 8~= "~ 1 o - - • "~ " ~ 'IX - C U ~, - "( ~ | n',.l'f '1 ~1o Z ~ t -° 4 2 , ~. " . • - "" " " " " " " " " I I Ef min ~ Ef I o --0.1 --- ISo.~ 2 0.3 0.4 Energy (Ry) 0.5 E maj 0.6 Fig. 5. Density of states curve of paramagnetic hcp cobalt (Ishida 1972), full curve; the density of states curve of paramagnetie fcc cobalt is shown by the dashed curve. 4 ..-" . ' J ". b~Taken from Wohlfarth (1970) and Ishida (1972).C'--~Y'-v--z-z/-~-"'T4.F ~ I N I \ ±L'~. I i~ - ~Xl-"~./ / / I _~i I F i g .65 Ni 0 . / / ." / / ) i i ix \ \ \ \ \ \ \ \ ".. 2 *) 1.-I I I i ". 6 ¢) 1.~ I ¢1I I I / "t I I . \ .--I l i "~T~-~-"~ ~">-~-~4~'---/-4"~// -" . .0 Co 1. The origins of I are briefly discussed in the next section.'FY.0 AE ( e V ) I (eV) "~raken from table 2.:/ Il" " i I / I / / / .~ / / / I a J \ \ ~ / f / ~ R I / J " ' E l ' ~ i " ~ I/b I" I I b. C~aken from table 1. "~A 71. 6. it seems clear that I varies relatively little for these three metals. I b) 0." . Fermi surface of the majority spin band of hcp cobalt (Ishida 1972). It also gives the resulting values of the Stoner-Hubbard parameter I = A E / ~ s . ".. Even considering that the values of A E and I for iron and nickel are probably too high when considering the later experimentally derived values. where ~s is the saturation magnetization in ~B.//" ""\ \ \ \ \ i f / / \ \ \ . \ d/ ~ .IRON. d)An alternative compilation is clue to Eastman (1979).. Table 3 collects the values of A E regarded as most reasonable on the basis of these band calculations for iron. . \ \ ~"~ ~ "-:4='7-~--7 . cobalt and nickel.L. vBI-I potential. COBALT AND NICKEL 9 hcp Co / / . TABLE 3 Values of AE and I derived from band • d) calculations Metal Fe 2 .-" ./ / / . v B H potential..... 2) and it is .~nI~)/kT} + 1]-1 0 (4) where N(E) is the density of states and ~ the chemical potential.1 and 2. there are significant and serious differences in detail (see sections 2. It is found that curves of ~(T) are rather insensitive to N(E) and have a close resemblance to the observed curves of the ferromagnetic transition metals. W O H L F A R T H 1. Wohlfarth (1951) and by Shimizu et al. (2) The spontaneous magnetization below the Curie temperature To depends on the temperature T through the Stoner equations oo ½n(1 -+ ~') = f N(E) dE[exp{(E . (2) The interactions between the itinerant electrons may be described by a molecular field approximation.s = n~'0 (3) expressed in Bohr magnetons per atom. Solutions of (4) for differing N(E) curves have been obtained by Stoner (1938). (1) with an associated molecular field energy per atom Em = (2) Here n is the number of holes per atom. Section 1. (1) The saturation magnetization at 0 K is given by P. cobalt and nickel are the holes in these 3d bands. The Stoner model.3. with a molecular field Hm proportional to the magnetization.P. (1965). The carriers of magnetism in iron.10 E. However. Equations (4) can be solved numerically or analytically for the quantity ~(T) after /z is eliminated.2. ~"is the relative magnetization and I is the Stoner-Hubbard parameter whose origins are to be discussed below. Specifically Sm = ½nI~/l~B -~n2I~2.4 describes briefly some approximations going beyond the Stoner model and 1. Co) and is less than one for a weak itinerant ferromagnet (Fe). Other consequences of the model will be discussed in later sections.5 concentrates specifically on spin waves which were not a part of the original philosophy. On this basis a number of physically significant results is derived by very elementary means and the most basic of these will now be summarized./ ~ 7. origin of splitting energy The Stoner model as applied to ferromagnetic metals and alloys is the basis of a simple scheme for correlating their magnetic properties. Here ~'0 is the relative magnetization at 0 K which equals 1 for a strong itinerant ferromagnet (Ni. (3) At finite temperatures the distribution of particles among the energy levels is given by Fermi-Dirac statistics. The model is based on the following assumptions: (1) The itinerant electrons are distributed among the energy levels described by density of states curves which are given by the band calculations of the type given in section 1. as discussed in sections 2. on values of I determined by Tc through (6) and on constant additional susceptibilities (of orbital and other origins) also introduced to fit T~.1. Unfortunately. For a more detailed discussion see Shimizu (1977): (i)The molecular field energy Em is a more complicated function of the magnetization ~ than given by (1). T curves for these metals by no means obey a Curie-Weiss law by showing that dx-lldT.2.b shows the calculated X-1. nickel and cobalt is at present impossible to assess.1 and 2. 2/~2. These excitations contribute to the magnetization reduction at finite temperatures although. Shimizu (1977) requires values of B which are inordinately large to bring about agreement for the observed ~(T) curve of iron and cobalt. The measured points are taken from reliable measurements. (3) The Curie temperature Tc is given by 0 where f is the Fermi function given in (4) but with ~"= 0. 0 (7) Although it has just been surmised that T~ (corresponding to X-1= 0) is not apparently given by this formalism the calculations of X reported by Shimizu (1977) are impressive. cobalt and nickel is discussed below (see table 4). in contrast the Curie temperature of weak itinerant ferromagnets was suggested (Wohlfarth 1977a) to be more closely represented by (6) in its low temperature form. fcc Fe. Shimizu makes the valid point that the observed X-I. His discussion of this anomaly is still open to argument. As such it has been . (5) The coefficient A was first introduced by Hunt (1953) to the same end and was later estimated theoretically by Wohlfarth (1953) and Bradbury and Edwards (1969) for nickel where its value is of the order 0. The validity of this formula in giving the Curie temperature for iron. (ii) The Stoner model as used here does not contain the effect of spin wave excitations although these are a natural consequence of the itinerant electron model as such (see section 1.5). specifically Em= -)n2I~2(1 + ~A~2 + 4tB~4 + ' " "). C O B A L T A N D N I C K E L I1 proposed to summarize here possible reasons for these differences.IRON. Figures 7a. The origin of the electron interaction I is of course central to the whole discussion of the ferromagnetism of the transition metals. T curves for Ni. T curves show a very pronounced temperature dependence. the relative importance of spin wave and Stoner excitation in iron. bcc Fe and fcc Co based on reasonable N(E) curves. Although there is by no means any certainty it seems that Tc may be given more in terms of spin wave excitations than by this relationship in the case of the ferromagnetic transition metals. (4) The paramagnetic susceptibility X at T > Tc is given by . for two localized wave functions q~m. what remains an issue is how best to approximate these effects so as to make them amenable to actual calculation. Experimental values will be given where appropriate in later sections. and interatomic nearest . the subject of intense study for several decades. Herring (1966) and Edwards (1977). Paramagnetic susceptibility for (a) Ni and fcc Fe.P. 7. Only a brief account can be given here which summarizes the theoretical background and the resulting numerical values of I and the exchange splitting AE. For these the most important interaction is the intra-atomic Coulomb interaction Im.4.12 (a) E. WOHLFARTH Ni ~-n2 E "5 E ¢o "7 X 0600 S (b) 800 1000 1200 T(K) I . (b) bcc Fe and fcc Co (Shimizu 1977). Reviews of the origins of I are given by Wohlfarth (1953). There is agreement that I is determined by exchange and correlation arising from many body interaction effects. 1400 I 1600 . For a simple discussion the tight binding approximation is felt to be appropriate for metals such as nickel with nearly filled 3d bands. / % 0 ±TS- I I 1000 1200 1400 T(K) 1600 1800 Fig. Measured data are indicated and are discussed further in section 2. Other contributions regarded as important are intra-atomic exchange interactions (Hund's rule) Ira. this formula shows that the effective interaction is determined only by G -t. G = 0. 5 eV. namely again the effect of conduction electron screening and. In the limit Ib~o0. The Hund's rule term is particularly important in iron and cobalt where the large number of holes per atom allows this interaction to take place freely.4 eV. 3 and 5). The correlation problem is one of great theoretical difficulty especially since the interaction is of the order of the width of the 3d band (see figs. For nickel the Hund's rule (intraatomic exchange) contribution to the molecular field is small due to the small number of holes. say.5 eV. is also severely reduced by two effects. The step-by-step reduction of the intra-atomic Coulomb interaction from 20eV to 0. the effect of correlation which is not included in this (Hartree-Fock) estimate of Imm. secondly.IRON. 1.5eV is reasonable though very rough at all steps. If lb = 5 eV.5 eV -! then lee = 1. estimated at about 20 eV. in its original form. Table 4 gives the values of I and IN(EF) for the local spin density functional formalism . 1977) applied this formalism to the ferromagnetic transition metals using various reliable band calculations. this dependence was absent. i.2 holes/atom each so that an average value of I for use in the Stoner model would be about 0. This effect has not been fully investigated.e. For cobalt and iron this semiquantitative discussion is not justified since the Kanamori formalism only applied at low densities and since the Hund's rule contribution will be relatively large. by the band structure. For nickel where the low density limit is reasonable there are three energy bands containing about 0. as discussed by Wohlfarth (1953) the parameter A in (5) also represents a weak wave vector dependence. In order of increasing importance Herring's rough estimate of this last contribution (about 1 eV) is surely much too large since the influence of conduction electron screening would act so as to reduce it drastically. Gunnarson (1976. Kanamori (1963) (see also Hubbard 1963) showed that for the low density limit the ground state properties of the itinerant electron ferromagnet may be treated in the Hartree-Fock approximation if the bare interaction Ib is replaced by an effective interaction lee given by IJ(1 EF (8) and where N ( E ) is the density of states for the holes in the 3d band. He finds that the exchange splittings AE and the corresponding parameter I are only weakly dependent on the wave vector thus giving a justification for the Stoner model in which. For all three ferromagnetic metals the local spin density functional formalism underlying the band calculations of Callaway (1977) has been used explicitly to estimate the Stoner-Hubbard parameter I. COBALT AND NICKEL 13 neighbour Coulomb interactions. This agrees well with some estimates based on experiment and on band calculations as shown in table 3. Hence no estimates of I have been made along these lines. A very rough estimate for the screening effect by Edwards (1977) leads to a modified intra-atomic Coulomb interaction of. The intra-atomic Coulomb term. 01 2.8 - TcK (calc. this problem is discussed below. Ni and also Pd. the difference is dramatically obvious.72 for Fe.6-1. 1977) Metal I (eV) IN(Ev) Fe Co Ni 1.1 2900 Pd 0. (1977) give the followingvalues of I I (eV) 0. since this method does not contain the correlation effects which militate against ferromagnetism. may still be too large when it comes to explaining some properties of these metals.8 4400-6200 3300-4800 Note that similar calculations by Andersen et al. if I is indeed as large as given in table 4 then Tc would clearly have to be determined by causes other than those underlying the Stoner model which involves single particle excitations. however.63 eV from the vBH potential and this calculation also gives A . The values of I agree well with those of table 3 for Fe and Ni but not so well for Co. However.E~ (9) where E~ is the Fermi energy for the + spins.99 1.5-1. The value of A E determines that of the energy gap A of strong itinerant ferromagnets. given by A = AE . respectively.7.P. The spin polarized photoemission data and the neutron data.91 0. From (7) the Stoner criterion for ferromagnetism I N ( E F ) >I 1 (7)* involves the density of states at the Fermi energy EF. This uncertainty may be particularly relevant when considering the Curie temperature on the basis of these calculations and relation (6).1 and 2. demand. WOHLFARTH TABLE 4 Values of I derived from the local spin density functional formalism (Gunnarson 1976.99 0. The calculated values are also given in table 4 and those observed in table 5. On the other hand. it is still possible that all 3 values of I given in tables 3 and 4.92 0.) 0. especially that for nickel. By contrast. In agreement with this criterion the table makes the first three metals ferromagnetic and Pd paramagnetic. Gunnarson's calculation of this product using the Xa method makes Pd ferromagnetic (!) and gives much larger values of I for all four metals.14 E. . Some indication of the correctness of estimates of the exchange splitting A E is given as follows. If I is really too large its reduction would then reduce To. actually more rapidly than linearly as shown by relation (6).3 0 0 meV. presumably since this was obtained in table 3 by rather less reliable and less consequent methods. discussed in sections 4. Co. Using the band calculations of Callaway and Wang (1977a) for nickel table 1 gives A E = 0.7 1.70 0. that A ~< 100 meV as was pointed out by Wohlfarth (1971. 5) stresses that the calculation of the spin wave stiffness D for nickel and its alloys demand the large values of ! and A E obtained from band calculations and given in tables 1. the neutron measurements which are discussed in section 2.7 seem to show that spin waves exist a long way above T~ in nickel and iron. as discussed in section 1.63 . 3 and 4 rather than a smaller value A E ~ 0. an estimate of A E for nickel which had been suggested in an earlier analysis (Wohlfarth 1965) and which leads to a better value of Tc than is given in table 4.(0.4. much larger due to the larger number of holes. However. the problem is this: Is A E ~ 0.0.4 eV? If Tc is not given by the Stoner model it would have to be that temperature where the other principle elementary excitation of the system of itinerant electrons. in fact.4. This is. It is therefore difficult to understand Tc itself in terms of spin wave softening. so that a distinct problem exists. Either all band calculations discussed are thus wrong to this order or they demand for some physical problems the influence of the many body effects discussed in this connection by Edwards (1978) and summarized below. (ii)spin fluctuation effects. In this model the band structure enters explicitly. Further discussion of these quantities follows below with reference to the actual experimental observations.3 . and the various methods of estimating the parameter I which occur were described.4 eV which would be crudely demanded by the photoemission and neutron measurements.1) . COBALT AND NICKEL 15 1977b). Further developments would be concerned with the possibility of applying this model to bee iron where ordinary spin waves also exist above Tc and where Hund's rule effects are. These will again be discussed in the appropriate sections with reference to the experimental values. The model was applied specifically to fee nickel where the Hund's rule term is small. 1. these being the basic observables. Edwards (1976b) proposed that the elementary excitations which soften at Tc are not the usual spin waves but rather other more low lying modes. for many other fundamental properties of the ferromagnetic transition metals. Results beyond the Stoner model. This coupling breaks down at T¢ and long wavelength two-dimensional spin waves are then thermally excited within sub-bands. (iii) . It was shown that these estimates are still rather uncertain. therefore. In this section the Stoner model has been discussed.0. The model itself was used to obtain the temperature dependence of the magnetization and of the susceptibility from 0 K to temperatures above To. the spin waves or magnons. For nickel.6 eV o r . together with numerical estimates of this central quantity of the model. 3 two-dimensional ferromagnetic sub-bands are regarded as coupled by an effective intraatomic Hund's rule exchange interaction to give long range magnetic order.0. This discussion (see section 1. go soft. such observations are available together with similarly based theoretical discussions.IRON. m a n y body effects Among several attempts to go beyond the Stoner model for the ferromagnetism of the transition metals the following three will be mentioned here: (i) The direct influence of the Hund's rule interaction. However. The direct influence of I-Iund's rule exchange interaction. The presence of these fluctuations clearly acts so as to make it easier for the magnetization to vanish when the temperature is raised in comparison with the situation where these fluctuations are absent as in the Stoner model. an estimate of this integral for iron is roughly 50 meV.r and r states per atom.n electrons per atom (n < 1) may be described as having n itinerant holes in the lower band and r holes on each atom in the upper band. the lower and upper bands containing 1 0 .b. A metal with 1 0 .3. Gumbs and Griffin 1976. explicit calculations for quasi-free electrons are necessary for obtaining numerical results.6 eV. Application is made both to w e a k and strong itinerant ferromagnets. The effective exchange integral giving the energy of interaction between the localized spins and the itinerant holes is Jo~= J-~0W. In section 1. Yamada 1974. The validity of this description would require further consideration of the properties of alloys of these metals. The same goes for the result of the theory that the susceptibility above Tc approximately follows a Curie-Weiss law and that it predicts the observed persistence of spin wave like modes above To.b). 1964a. In applying this theory to nickel as an example of a strong itinerant ferromagnet it is found that the spin fluctuations here behave like a set of localized moments.6 eV.b) had proposed a strong interaction model for d bands of width W if II W ~> 1. Although the theory is developed generally. Hence the Curie temperature is lower than is given by relation (6). The problem of the magnetism of this system of localized and itinerant electrons is the same as that of giant moment systems like Fe in Pd (Doniach and Wohlfarth 1967) and using this formalism the following parameters for cobalt are needed for interpreting the properties of this metal: Ie~ ~ 0. WOHLFARTH electron-magnon interactions. For cobalt and iron. The value of Je~ is close to that for Fe in Pd. Application of this theory to weak itinerant ferromagnets was also made by these authors (see also Ramakrishnan 1974.5 spin waves themselves will be discussed. involving I. The fact that such a decrease is demanded by the facts of table 4 may or may not be explicable in this way. The itinerant electrons themselves interact via the mechanisms discussed in section 1. A E ~ 0. has been discussed by Edwards (1970) who recalls that Hubbard (1963. Jar ~ 0. see section 1. The spin fluctuations considered have the same character as paramagnons in strongly enhanced paramagnetic metals (Doniach and Engelsberg 1966) and spin waves in ferromagnetic metals. these having localized spins coupled by Hund's rule.c) and reviewed by Moriya (1977a. here the direct superexchange between the localized spins is also included although it has a value of only about 10 meV. A description of iron and cobalt involving respectively 2 and 1 localized spins is clearly beyond Stoner. r = I and 2. respectively. This model was discussed in detail by Moriya and Kawabata (1973a.16 E.2 eV. Another theoretical description of the ferromagnetism of itinerant electrons involves the effect of spin fluctuations.P. respectively.r . For an atomic d 10-r configuration the band is split into two. for nickel this mechanism does not occur. Sakoh and Edwards (1975) applied it to a calculation of the magnetization and susceptibility of iron and cobalt. Dzy- .5. called J. for example its quasi-two-dimensional character (see section 1. is needed to be sure. This sharper rise also seems to be demanded by the photoemission data. As was mentioned in section 1. Spin waves enter the physics of the ferromagnetic transition metals in the .IRON. For nickel the suspicion remains that the complicated band structure. also for cobalt. The energy of the magnons involved may be estimated as (Edwards 1977) about 90 meV so that A ~ 90 meV. For small values of q. As for paramagnons (de Chatel and Wohlfarth 1973) the band structure may well act so as to attenuate the fluctuation effects in the strong itinerant ferromagnets. This estimate agrees excellently with the estimates based on the above two sets of measurements (Wohlfarth 1971.1 and the neutron date of section 2.5.spin hole self energy increases its effective mass compared to its band structure value so that there is some reason for having the normalized density of states at the band edge rising more sharply than is given in the absence of this many body effect. is not sufficiently a part of the analysis. COBALT AND NICKEL 17 aloshinsky and Kondratenko 1976) but is outside the present scope. The third discussion beyond Stoner concerns electron-magnon interactions. whatever the band calculation may give. at least. and the results have been summarized by Edwards (1978) in referring to the apparently small energy gap A demanded by the spin polarized photoemission data discussed in section 4.(q) = D q 2 (10) where D is the spin wave stiffness.7.e.3). are the elementary excitations of ferromagnetic metals which arise in addition to the single particle excitations of the Stoner model. Much further theoretical and experimental work. the dispersion relation for ferromagnets is ho. and a bound state splits off below the scattering states. or magnons. This characteristic quantity is as fundamental in specifying the magnetism of the transition metals as is the saturation magnetization and the Curie temperature. 1977b). The excitations are of bound electron-hole pairs and are characterized by the dispersion relation giving the energy hop(q) as a function of the wave vector q. i.3 the band calculations imply much larger values of A for nickel and this difference may arise from a many body effect of this sort which the band calculations referred to do not encompass. the frequency dependence of the . 1. Edwards and Hertz consider a hole in the . In addition. This sophisticated many body effect (see also Celasco and Corrias 1976) is thus apparently relevant in discussing the actual physical properties of nickel. long wavelength magnons. This many body problem was discussed with reference to nickel by Edwards and Hertz (1973). The energy of the scattering states is the Fermi energy plus the magnon energy.spin band making a virtual transition to the + spin Fermi level during which process a magnon ig emitted. S p i n w a v e s Spin waves. at least in part. (5) Spin wave scattering of electrons also enters the electrical resistance (see section 3. (4) Proper high frequency excitation of metallic films produces spin wave resonance effects (see the chapter by Hoffmann. As was discussed in section 1. o~) -.Y_ a self energy for the . Calculations of D have been made on several levels of sophistication. For metals the band structure gives rise to severe complications. the Curie temperature may be determined. see section 2. e~ the band structure. Experimental results are given in section 2.3. by X .18 E.O. Experimental results are given in section 3. these enable the spin wave stiffness D to be measured most accurately (see section 2. For shorter wavelengths the electron-hole pairs dissociate into independent particles on entering the continuum of single particle excitations. . (2) The specific heat. rising initially parabolically as given by relation (10). WOHLFARTH following ways: (1) The magnetization decreases as a function of the temperature according to the famous law ~'(r) = ~(0){1 .I ( q .6). The resulting approximations are reflected in the theoretical expressions for spin wave energies. also goes as T 312.a T 31" . the exact nature of the electron interactions is not established.7 with reference to theoretical calculations and to the neutron measurements on nickel and iron. linearly to lowest order. as was discussed in sections 1. This decrease adds. to that given by the Stoner equations. Eventually it will meet the downward going single particle excitations and this occurs at a characteristic wave vector qmax. The wave vector qma~ is also observable by neutron scattering.7).e. again additive to that from the itinerant electrons. (12) This function will be discussed in section 2.5.4.1. The dispersion curve. i.P. Most generally the spin wave energy h~o is given by the pole of the dynamic susceptibility. For a strong itinerant ferromagnet (Ni.7.3 and 1. Co) but with a single band and cubic crystal symmetry Edwards (1967) found that 1 1 Here n is the number of electrons. has been found theoretically and experimentally to deviate from this initial variation at shorter wavelengths. by spin wave excitations.o(rS~)} (11) where a ~ D -312. Theoretical calculations of the spin wave dispersion relation and of the stiffness are much more difficult than for the Heisenberg model where only a direct exchange integral enters to determine the energy scale. (3) Spin waves can scatter neutrons and are thus best observable by neutron techniques. volume 3/4). In addition. 2. use of another parameter is clearly not too satisfactory especially since the RPA itself may be at fault in causing the differences between theory and experiment. 2. and the summation is over occupied + spin states. For nickel more sophisticated calculations of D have been reported by Wang and Callaway (1976) which are based on the local density functional formalism referred to in section 1. smaller values of A E are required. as already pointed out in section 1. On the other hand. George and Thompson (1970) and Thompson and Myers (1967) also reported RPA multiband calculations for iron. further aspects of the theory will be discussed by reference to specific results. respectively. (1968) whose . Further discussions of spin waves are given in the appropriate sections below. cobalt and nickel. lower than the value of table 3.e. The arguments are based on the use of different expressions for ~o in relation (13).spins taken at energies hta depending on the approximation. but with an exchange splitting A E about 0.~ is replaced by the exchange splitting AE.8-0. as given as the larger value in table 1. Where necessary. For nickel. Magnetization at 0 K and at finite temperatures For iron and nickel. Again. Agreement of D with experiment was only attained by including interatomic exchange integrals (of the order of 16 meV for iron and cobalt). Edwards (1978) expresses the belief that different values of A E should in fact be sensibly used for a quasi-static quantity like spin wave stiffness and for such dynamic effects as photoemission where.9 eV. For the more reasonable multiband case and for weak itinerant ferromagnets the problem becomes considerably more difficult and reference may be made to the following publications: Wakoh (1971). COBALT A N D NICKEL 19 . For iron and cobalt the calculated values of D are much lower than those measured. F u n d a m e n t a l properties 2.5 eV. The random phase approximation was used for a multiband model.3.1. iron. i. Thompson and Mook (1970). cobalt and nickel. the exchange splitting is the key quantity in describing spin wave dispersion in the ferromagnetic metals. Since Riedinger and Nauciel-Bloch (1975) also require a large A E value of this order to obtain the experimental value of D for nickel. The calculated value of D is within a few percent of that observed.IRON. This very brief summary of the theoretical background should suffice to indicate the grave complications which arise in trying to establish a fully meaningful description of the experimental and empirical facts which will be the subject of the rest of this chapter. therefore. Their inclusion would also improve agreement in the calculations of Wakoh just referred to since this interaction is clearly one which acts towards stable ferromagnetism and thus increases D. In the random phase approximation and still for a single band strong itinerant ferromagnet . measurements of the saturation magnetization at 0 K with the greatest claim to accuracy were summarized by Dan~-n et al. agreement with experiment is within a factor about 2 using an exchange splitting of about 0. ~2. T) going as T 2 but this is apparently too small to be observed.I ---0. (16) The values of D(0). No such detailed analysis is available for hcp cobalt and the data in table 5 are based on the results of Myers and Sucksmith (1951).72 455 .29 qo/qs 1. cobalt and nickel Fe Saturation magnetization emu/g 221.29 1.4 ± 0.20 E.80/~B.71 ± 0. are in good agreement with those obtained by Stringfellow (1968) from neutron measurements (see also section 2. see also Edwards (1974) and the TABLE 5 Fundamental magnetic properties of iron. qo 2. O) = g~[ kT .8) x 10-4 meV A~K -2.216 Curie temperature Tc K 1044 ± 2 kTo meV 90.7).03 0.715 1388 ± 2 119. T) .616 627.6 2.0 Number of magnetic carriers from Curie-Weiss law. 311 -+ 10 meV .55 1. i.M(O. t) is given by F(n. The latter is discussed in section 3.3 54. These values of the saturation magnetization at 0 K are determined by the number of holes in the d-band. The temperature dependence of the magnetization M ( T ) of iron was measured by Aldred and Froehle (1972) up to room temperature and in fields up to 14 kOe.46 1.57 ± 0.11 510 Ni 58. The change of the magnetization of cobalt resulting from the crystal structure transformation between the two close packed phases must follow similar principles.e. the temperature dependent spin wave stiffness.1. and of DI = (6. The data were best fitted as follows M(H. are given in e m u / g and in ?zB as in table 5.08 Saturation magnetization/-~B(qs) 2. and by the g-factor. with methods of measurement and analysis.1 0. The basis of this analysis is that the low temperature magnetization of iron is determined by spin wave excitations with a temperature dependent spin wave stiffness D(T) determined by the itinerant model.DIT 2.7 [ ~ J "r"p(3 kT --\5' g~s-sH/" (14) Here p is the density. an increase of about 5%. Although fcc cobalt is not stable at 0 K a rough estimate of its saturation magnetization at that temperature may be made by a linear extrapolation of the data for the fcc Ni-Co alloys (Wohlfarth 1949). is given by D(T) = D(O) . F(n. WOHLFARTH best values. The Stoner excitations contribute a term to M(H.34 2. t) = ~ m-" e -~/t mffil (15) and D(T).90 1. by the band structure and the exchange splitting.P.03 Value of qc for liquids 3. giving about 1.42 Spin wave stiffness D m e V ~ 2 (at room tern280 perature) Co 162. (c) heating of a single crystal specimen. respectively. In any case. Magnetization.5 x 10-4 meV 7t" K -2.IRON. 0) coming from spin waves is only about half that observed when T = 300 K. The results differ from those for iron since the change of the magnetization with temperature appears not to be given only by spin wave excitations with a stiffness determined from neutron scattering. 555 meV A 2 and 11. going as T 3t2. the change of magnetization M ( 0 . the value of D and of the coefficients of T 5t2 and thus of q4 disagree with those measured by neutrons (Stringfellow 1968. T) was given by Thompson et al. Aldred and Froehle (1972) also fitted their data for iron on the basis of spin wave theory but with (i) D independent of T and (ii) a term in T sr2 in addition to that. T ) . The coefficient of T m is related to the coefficient of q4 in the spin wave dispersion relation. Mook et al.M(0. (1964) and by Mathon and Wohlfarth (1968). A discussion of these two contributions to M(H.2. 1969). Using these measurements (Minkiewicz et al. where A is the energy gap discussed in section 1. . The change of M(T) of a strong ferromagnet such as nickel varies as e -~/kT (Thompson et al. COBALT AND NICKEL 21 discussion of de Haas-Van Alphen measurements in section 4. larger values of A are suggested ~ b hcp-fcc Co ~ a I I t I I 300 400 Temperature (°C) 500 Fig. (a) Heating. 1973) and the resulting values of D(0) and DI in relation (16). (b) cooling. 1968. 1964). temperature curve of cobalt on passing through the hcp--fcc phase transition (Myers and Sucksmith 1951). 1969. Aldred (1975) thus analyzed his data in terms of additional Stoner excitations. Although a fit of the magnetization data is again possible. Hence this analysis is less satisfactory. For nickel similar measurements were carried out by Aldred (1975). Collins et al. although a more detailed discussion reveals this analysis to be unsatisfactory. in (14). 8. Shirane et al. A value of A = 14meV is required to give some agreement with the neutron data. Hyperfine fields Hyperfine fields of the ferromagnetic transition metals may be measured using nuclear magnetic resonance and M6ssbauer techniques. . later measurements by Riedi (1973. A review (one of many!) of the measurements and their interpretation was given by Feldmann et al. The temperature dependence of the hyperfine fields is usually expressed in terms of that of the magnetization M(T). The review gives a useful summary of the various contributions to the hyperfine field and this is reproduced in table 6. 8 (Myers and Sucksmith 1951). 1977) are also included. 1964) and this seems unlikely. vary with T. Between this range of temperatures and the Curie point the M(T) curves for iron and nickel vary without special features. Typical values of the hyperfine fields of the three metals are given in table 6. The existence of so many contributions clearly makes it difficult to estimate the hyperfine fields accurately.P. nevertheless.M(T) I. as shown in fig. however. The final disappearance of M(T) occurs at the Curie temperature which will be discussed in section 2. For cobalt special features of M(T) do arise and these are related to the crystal structure change from hcp to fcc. such calculations have been performed. Further results based on NMR measurements are discussed in section 2. 2.2. Hence the problem of the temperature dependence of the magnetization of nickel remains unsolved. Even then it would not be clear how the relative weights of spin wave excitations and of Stoner excitations. since roughly the two quantities should vary similarly Y_ZT= .o AT ~ (17) where AT is called the hyperflne coupling constant. The measurements of M(T) just discussed refer to low temperatures.3. WOHLFARTH by all the other measurements. implies that nickel is a weak itinerant ferromagnet (Thompson et al. For iron Riedi (1973) showed that below 32 K vr follows a T 3n law with a coefficient in good agreement with that from static and spin wave measurements. this clearly shows secondary effects having their own intrinsic interest. expressed as a resonance frequency VT. (1971). where T is the temperature.22 E. For cobalt there exists no such detailed analysis and this would clearly be welcome.2. This variation can clearly not be interpreted satisfactorily before the low temperature variation is fully understood. The values of these fields at a given temperature and their temperature variation are both of interest. NMR techniques would provide a much more accurate way of measuring the temperature dependence of the magnetization than static measurements of M(T). A somewhat better agreement is obtained if the contribution to M(T) from the Stoner excitations goes a s T 2 which. If AT were really a constant. where these arise to any extent. as shown in tables 1 and 2. (iv) Closed inner shells Contact interaction with polarized s-electrons. i.216 TK 300 297.4 23 Summary of contributions to the hypefline field (Feldmann et ai. Between 32 and 400 K.58 × 10-9 T 5r2)+ O(T712).6 45. AT varies with temperature according to the relation A T = 1 -. compared to the value 311-_-10 reported in section 2. however.) Ni (Feldmann et al.): (i) Local field (a) external. H e n c e in this temperature range A T = 1 to within the experimental accuracy.IRON.T h e discrepancy between the neutron and static measurements of the magnetization discussed in section 2. For nickel Riedi (1977) showed that A T = 1 to within the experimental error up to 300 K ( ~ 21To). (d) contact interaction of s-electrons hybridized with the d-band.(6. COBALT AND NICKEL TABLE 6 Hyperfine fields of the ferromagnetic transition metals (taken from Feldmann et al. (ii) Conduction electrons (a) Contact interaction due to polarization by 3d electrons via RKKY.1 was confirmed by the hyperfine field measurements.3. (b) demagnetizing.468 210-215 217-223 26. (c) Lorentz. F o r cobalt there are no recent measurements o f the temperature d e p e n d e n c e but earlier ones (Feldmann et al. 1971. (iii) Electrons in unfilled shells (a)Electronic spin-dipole contribution from surrounding ions.) (Riedi 1973) Co hcp (Feldmann et al.1.+ 5 m e V A 2 on this basis. (18) The f o r m of this relationship was given b y Edwards (1976a) as arising f r o m spin wave excitations and the action of the important contributions to the hyperfine field given in table 6. A further difficulty in all cases is that measurements of the hyperfine field have to be corrected for constant volume/constant pressure effects at higher temperatures. (b) intrinsic electronic spin-dipole contribution.096 26. 1977) vr (frequency MHz) Fe (Feldmann et al. Riedi 1973. still without being able to describe these satisfactorily.) fcc (Feldmann et al. these continue to point to important single particle excitations in nickel. 1971) point to a constant A r up to 400 K. 2.e. (b)dipole interaction with orbital momentum of non-s electrons.6 298--398 298-398 300 292. (c) dipole interaction with the orbital momentum. Curie t e m p e r a t u r e T h e Curie temperature Tc o f the ferromagnetic transition metals has often been measured and table 5 shows one reliable measurement in each case. namely iron . thus D(0) equals 3 1 6 .) (Riedi 1977) 45. necessitating accurate high pressure N M R measurements. Curie-Weiss constant The paramagnetic susceptibilities of fcc and bcc Fe. Nevertheless. and clearly is so for weak itinerant ferromagnets. Nevertheless. taken from Arajs and Colvin 1963 and Nakagawa 1956). It was argued. fcc cobalt (Colvin and Arajs 1965) and nickel (Kouvel and Comly 1968). Attempts to do so (for example. the alternative interpretation of T~ in terms of spin wave softening may appear to be more likely. 3) but that the observed curves may be explained on the basis of the itinerant model plus an additional constant susceptibility. it seems clear that there is little certainty in any attempt to estimate the Curie temperatures for these three metals on any reliable theoretical basis. AEJ2kT~ is less than for iron and the high field data discussed in section 2. for example. Indeed. 1977) estimates of T~ given in table 4 are clearly much larger than those observed. q. fcc Co and Ni are given in fig. Moriya (1977a. is not incompatible with this model. WOHLFARTH (Arajs and Colvin 1964). by Capellmann 1979) continue. it is convenient to characterize these curves by a Curie-Weiss constant. perhaps of orbital origins. 2.P. Susceptibility at T > To. indeed. see. 7 (Shimizu 1977. The point is made by Shimizu that these curves do not obey the Curie-Weiss law (see his fig. For nickel. 09) On the basis of comparisons of this number of carriers with that obtained from the saturation magnetization at low temperatures. (see table 5). to be made. the significant ratio AE/2kTc is about 12 for iron and about 5 for cobalt and nickel. given by p~f = qc(qo + 2). If the law is observed even if only over limited temperature ranges. Hence. There is no reliable estimation of Tc for hcp Co which is normally unstable there. the Gunnarson (1976. although an interpretation of Tc in terms of single particle excitations is not impossible. Alternatively.b). Although this ratio can easily be well above 1 in the itinerant electron model. The whole question of the status of the Curie-Weiss law in the framework of this model was also discussed by Wohlfarth (1974). a resulting effective moment Peg and a resulting number of magnetic carriers qc. Maybe the absence of this correlation for nickel alloys is significant in pointing to a single particle origin of Tc in nickel after all. such large values are not so easy to understand in the present cases in particular for iron.5 may also be relevant. there is a qualitative correlation between T~ and the spin wave stiffness D in iron alloys (Wohlfarth 1966) which may also point in this direction.24 E. that the law. For example. however. Rhodes and . as is the case for the curves shown in fig. in some agreement with Simizu. observed over limited or extended temperature ranges. 7.4. The values of kT~ also shown in table 5 demonstrate clearly the difficulty of interpreting the origin of this critical temperature. namely its small value compared to other key energies such as the exchange splitting or the interaction energy ! or the band width. the controversy continues to bedevil the theory of the magnetic properties of the transition metals. and if the Curie temperature T~ is above about 500 K the whole scheme can not be used to distinguish between itinerancy or localization of the magnetic carriers. On the basis of this systematic discussion it was concluded that if qJqs is as close to 1 as is the case here. as is of course well known. that this ratio is greater than 1 but not as excessively so as for the weak itinerant ferromagnets discussed in the above papers. were able to give a systematic discussion of the magnetic properties of ferromagnetic metals and alloys. cobalt and nickel on passing through the melting point. . Measurements are available by Nakagawa (1956). Ni) and the 3.8 E 2. The discussion is only meaningful on a much more fundamental basis.4 TTM 1600 T(K) 1800 2000 Fig. For iron the susceptibility increases by 5% compared to the value for the y-phase extrapolated to the melting point and decreases by 31% compared to the 8-phase which is stable just below the melting point. and qJq~ are given in table 5 from which it appears..temperature curve of nickelabove and belowthe meltingpoint (Miiller 1978. Hence the Curie-Weiss constant and thus q¢ can only be regarded as formally convenient parameters for these metals. 9. COBALTAND NICKEL 25 Wohlfarth (1963) (see also Wohlfarth 1978a)..6 0 . Briane (1973) and Miiller (1978). Briane 1973). Co." I x : 2.o[ Ni 2. The values of qo q. For cobalt the decrease of the susceptibility at the melting point is 6% and for nickel there is an increase of 2%. The changes of the susceptibilities on melting are thus small compared to those of solids with the same structure (TFe. as shown in fig. Apart from these data it is of interest to discuss briefly the susceptibility behaviour of iron. 9. Inverse susceptibility.IRON. Gersdorf 1962) Xo' = (4tt~)-l{N(E+) -1 + N(E-)-'} .1/21~. The Van Vleck orbital susceptibility has been discussed by Place and Rhodes (1971) and by Mori (1971) as well as by Rebouillat (1972) and Fekete et al.P. (20) For strong ferromagnets N(E+)~-O (only a small contribution from the selectrons remains) and )¢0 will be small.26 E. The contribution X0 arises from the itinerancy of the d-electrons and is given as a generalization of the usual exchange enhanced paramagnetic susceptibility (7) by the relation (Wohlfarth 1962. A later analysis for cobalt was given by Fekete et al. high field susceptibility At high magnetic fields H the magnetization of the itinerant ferromagnets iron. seems very reasonable and Briane showed that it can explain quantitatively his measurements on Fe-Ni alloys. The following contributions to the resulting high field susceptibility Xhf have been considered: Pauli spin paramagnetism of d-electrons.5. The inverse susceptibility. The differences from the qc values of the solid metals are large for iron and nickel. Rebouillat (1972) has given an extensive account of his own. WOHLFARTH sign of the changes is not systematic. This approach. XP (---X0 at 0 K) Van Vleck orbital paramagnetism Xvv Pauli spin paramagnetism of s-electrons Diamagnetism. cobalt and nickel continues to increase with H. At low temperatures only the first two contributions are significant in practice. High magnetic 11eldeffects. and others' measurements and also of the results of various theoretical estimates. (1976) on the basis of Knight shift measurements. 2. a phenomenon known as the paraprocess (this term is particularly popular in Germany and Russia but not in the Anglo-Saxon countries!). There is no deep going theory of these two effects (small change of absolute value and larger change of temperature derivative). of several origins Susceptibility due to spin-orbit coupling Susceptibility due to spin wave excitations. temperature curves of the liquid ferromagnets obey the Curie-Weiss law and the corresponding values of qc are shown in table 5. The temperature dependence of the high field susceptibility was discussed by Shimizu (1977) but the effects are complicated partly due to the growing importance of spin wave excitations. a similar situation also occurs for palladium (Miiller 1978). Table 7 gives a summary of these results. which has also been suggested for amorphous ferromagnets (Wohlfarth 1978b). (1976). This susceptibility is largest for metals such as chromium and vanadium near the . as is clear on physical grounds. Briane (1973) appeals to a very simple model calculation of Adachi and Aisaka (1973) which involves a smoothing out of the fine structure of the density of states curve on melting. For weak ferromagnets larger values of X0 are expected. 1976) Fe Xo 69 93 98 86 84 133 110 131 159 202 203 229 245 266 231 305 Co 0 23 30-40 114 27 Ni 0 55 76-114 80 82 48-45 80 137 124-159 116 129 110 Xvv Xo+ Xvv Xu(obs. On the whole X0 tends to be larger for Fe than for Co and Ni since the latter are.IRON. The f o r m e r report meas~urements in fields up to 320 kOe and find that between 550 and 700 K the magnetization M as a . 1977). etc. cobalt and nickel (Rebouillat 1972. so that the several complications do not allow a clear decision to be reached on this point. exchange splittings. The experimental and theoretical results are rather complicated since the measurements are not easy and since the theoretical estimations rely on m a n y other factors (densities of states. COBALT AND NICKEL TABLE 7 High field susceptibility of iron. The data are taken from the two references given which tabulate estimated and observed values from several sources. fully quoted. for iron. the observed values agree surprisingly well with those estimated as the sum of X0 + Xw at 0 K so that this seems to be well established as a reasonable explanation of the observations. (1976) point out for cobalt (where they have X0 = 65. H o w e v e r .) 65 240 240 240 129 202 240 263 270-280 243 267 265 All susceptibilities are in units emu/mol x 106. High field magnetization m e a s u r e m e n t s for nickel near the Curie point have been reported by P o n o m a r e v and T h y s s e n (1977) and for iron and nickel by Hatta and Chikazumi (1976. centre of the periodic table but is certainly also important. Again. as shown in table 7. The precise methods of estimation are too complicated to be given here. Nevertheless. Xvv seems to be larger for cobalt than for nickel and iron. strong itinerant ferromagnets. from other evidence. H e n c e it is not easy to discern clear trends. this metal seems f r o m their evidence to be a weak itinerant ferromagnet. cobalt and nickel. as Fekete et al. Xvv = 202 as s h o w n in table 7).). Fekete et al. going as T z in a temperature interval both above and below T¢ which would imply important and significant effects due to single particle excitations.T) ~ M ( H ) at T = T~ ~ H ua Specific heat Cn at T <> T c ./3.r -(d-2+n) sionality) Spin wave stiffness D at T < T~ ~ ( T ~ .24. for example.Tel-a Correlation length ~ at T X T~ ~ IT . two ~ values and two a values for T <> T~ and (21) is debatable) but it suffices for the present context. 2.28 E. This is in contrast to other measurements in lower fields and is ascribed to the influence of the high fields in removing the effects of short range order near T¢. (1975) and Ahlers and Kornblit (1975). d = dimen- Values of T.6. Stanley's book (1971).g. 1977) also fit their high field data (up to 180 kOe) with a Landau theory and discuss these data on the basis of a localized model of ferromagnetism.T~I-~ Pair correlation function at T = T ~ . All these values are given here in table 8. The value of 8 is given by the scaling law a = 1 + ¢]3.6) deduced from these data for both iron and nickel were found to be close to the classical values. ~/ and v are well related by a scaling law) several features of these data are still not clear. some of which will now be defined and tabulated. Critical exponents near the Curie point Near the Curie point the magnetic properties are characterized by a set of critical exponents. Glinka et al. The values are mean values weighed subjectively and no errors are given. Hatta and Chikazumi (1976.T) ~. (1977) on the basis of their own and others' measurements. The critical exponents (see section 2.To)-~ Magnetization M at T < T~ ~ (To . (r = distance. WOHLFARTH function of H and T follows the Landau theory of phase transitions previously applied by Edwards and Wohlfarth (1968) to weak itinerant ferromagnets. /3. The Landau coefficients were found to vary systematically with temperature. v. (1977) give a very useful review of the data tabulated here and conclude that although some features are reasonable from the point of view of scaling (e. for further details see. 1. From an analysis of the data the exchange splitting came out as 0. Note that this discussion is not fully rigorous (there are strictly two y values. a reasonable result since M is also small near the Curie point of nickel. Thus it does not seem clear why the value of y for (cubic!) cobalt is close to that.33 eV and the high field susceptibility as 570 x 10-~ emu/mol.P.IT . This last value is about 5 times the experimental values given in table 7 since it refers to a fictitious paramagnetic nickel. (21) The values of a have been tabulated by Barmatz et al. ~ and x have been given for all three metals by Glinka et al. for the three-dimensional Ising model while . Susceptibility X at T > Tc ~ ( T . (1969) and b y M o o k and Nicklow (1973).lO 0.47 -0.37 Co 1. to) to be measured. for the isotropic Heisenberg model. Of immediate interest is the spin w a v e stiffness D defined by (10). calculations of D w e r e described in section 1. Ahlers and Kornblit 1975) Exponent y /3 ~$* a v n x Fe 1. characterized by x.39 Ni 1.50 -0. the Rushbrooke inequality is used as an equality (Rocker and Schfpgens 1969).5. was also given but Windsor (1977) cautions against the use of such an expansion.21 0.12 0.65 O. **See section 3. COBALT AND NICKEL TABLE 8 Critical exponents (Glinka et al. going as q4. the values for iron and nickel are closer to that. An excellent s u m m a r y of the present situation has been given by Windsor (1977) who s u m m a r i z e s the techniques of neutron scattering and what m e a s u r e m e n t s are possible by each of these. 2. Spin w a v e stiffnesses m a y also be m e a s u r e d by the spin w a v e resonance m e a s u r e m e n t s on thin films described more fully in the chapter by H o f f m a n n (volume 3/4). The 1969 r o o m t e m p e r a t u r e data are given in table 5 and agree excellently with those of 1973.39 29 *Values of 8 from eq.88 -0. F o r iron triple axis m e a s u r e m e n t s of D have been given by Collins et al.38 4.38.70 0.33 0. spin wave) to be investigated and the dynamic susceptibility x(q. (22) This result follows immediately f r o m r a n d o m phase approximations used in discussing spin w a v e energies.07 0. Dynamic susceptibility. seems exceedingly close to that of M.42 3. 1977. The . (21).IRON. Barmatz et al.38 4.07** 0.094 0. All the evidence points to the fact that these values are less reliable than those obtained by neutron m e a s u r e m e n t s which will now be further discussed.32 0.5. 1. in the earlier m e a s u r e m e n t s the coefficient of the next term in the expansion of htoq. the t e m p e r a t u r e d e p e n d e n c e of the spin w a v e stiffness constant D. so as to lead one to s u c c u m b to the temptation to postulate D(T) ~ M(T) ( T ~ To). characterized by fl. 1975.7. spin wave dispersion and stiffness The use of neutron scattering techniques allows the e l e m e n t a r y excitations of the ferromagnetic metals (single particle. Although there is no absolute theoretical certainty. WOHLFARTH measurements of Mook and Nicklow were taken to higher wave vectors corresponding to spin wave energies about 110 meV. below).5.5 0.30 E. 10. 10. Lynn (1975) reported similar measurements for an Fe(12% Si) crystal and less detailed for pure Fe as a function of temperature. Spin wave intensity against energy at 295 K and 1240 K = 1. are extremely surprising since on a simple basis no excitations should persist so far above T. Outside the long wavelength.28To for Fe (Si) (Lynn 1975). The measurements to show this result were obtained at 1. t\ \ Fe (Si) 20 40 60 80 t=(meV) 100 120 \ 0. A band theoretical estimate of this energy was reported by Thompson and Mook (1970) and others (of. These data. about 110 meV for Fe). hardly changed at all on increasing the temperature from 295 K to 1240 K = 1. (ii) spin waves exist as excitations up to and above the Curie temperature To. where the entry was said to occur at a spin wave energy h¢%~. The spin wave intensity was found to fall off slowly with increasing energy until about 80 meV where the intensity decreased rapidly by about an order of magnitude. but that this critical energy hcoq~.4T=.E 1 e o 0 ~ 1240K °° e ~.1 0 140 Fig. (i) the spin wave dispersion does not fit a quadratic + quartic dependence on q very well.P. as discussed in section 1. shown in fig..2 0. with no further renormalization with T > T¢. For hcp cobalt there are several reported values of D and a value obtained by 10 o 2 . where D(T) varies as I T . It was proposed that this sudden decrease is caused by the entry of the spin wave mode into the continuum of single particle excitations. It was also found that the spin wave intensity dropped off sharply at an energy about 100 meV (for Fe-Si. . low q range.Tc[x with x given in table 8. el.28T=. IRON.4 and a third is a theory of Korenman et al. it was also found that this energy did not decrease as the temperature was raised to over 700 K (Mook (1978) reports that spin wave modes persist up to 2To in Ni which are broadened and somewhat lower in energy than for the modes below To).2 ~--.~ o 2 9 5 K • 504 K 0.1 where it is shown to be in good agreement with some other estimations. In the last there is short range magnetic order above T¢ on a scale characterized by an inverse length about 0. As for iron (Lynn 1975) there are two interesting results. as shown in fig. 11. In spite of Windsor's caution it may be mentioned that the coefficient of q4 is considerably larger than is implied by a localized model of ferromagnetism (this point was still worth making in 1968!).3. 1973).~-i so that a 2 1 . There are several possible interpretations of the surprising persistence of spin waves above T= occurring in iron and nickel.3. . One of these is the model of Edwards (1976b) discussed in section 1.~ 0. Spin wave intensity against energy at various temperatures for Ni (Mook et al.o. also measured the temperature dependence of the spin wave dispersion through the Curie temperature.5 c .05 0 I 10 20 I a 568K • 673 K 30 I I 40 50 60 Spin-wave energy (meV) 70 80 90 Fig. another the spin fluctuation model of Moriya and Kawabata (Moriya 1977a. There is also a report of D for fcc Co(+8% Fe).~ ~ '~.25 . 3. This energy is significant as being roughly a measure of the energy gap A discussed in sections 1.1 . For nickel there are several and differing values of D which have b e e n analyzed carefully by Aldred (1975) who gives the room temperature value deduced from the triple axis data of Minkiewicz et al. (1973) and shown in table 5 as the most reliable. 11. The spin wave intensity at room temperature drops very rapidly at an energy about 80 meV. COBALT AND NICKEL 31 triple axis measurements is given in table 5 (Shirane et al. namely 371 meV/~2 using the triple axis spectrometer..7 and 4. However. (1977). e- 0. Mook et al.b) discussed in section 1.~. 1968). which is explained as the entry of the spin wave mode into the continuum of single particle excitations. (1969) and Mook et al. The calculations of X(q.5. The calculation was based on a Slater-Koster interpolation scheme for the paramagnetic metal and a rigid splitting of 1. (1975). Lowde and Windsor show how for any region in the space away from the origin the passage of the Curie temperature is much less catastrophic than for the static limit. The former reported a rather monumental research programme where the dynamic susceptibility of nickel was investigated by the neutron time-of-flight technique and by a band calculation based on a tight binding interpolation method and the random phase approximation. These were in good agreement with observation (Mook and Nicklow 1973) including a drop of intensity at about 120 meV. However. The agreement with the neutron data is again good. . In the calculation the effective intra-atomic Coulomb interaction was taken to be slightly wave vector dependent. ~o) since its pole leads to the energy of spin waves as already pointed out in section 1.P. again a wave vector dependent effective interaction but covering only low temperatures. Cooke and Davis (1973) (see also Cooke 1973) reported similar calculations for nickel using better band calculations. deduce that the itinerant model gives a good account of spin wave excitations in iron well below T. o~) were carried out using standard numerical procedures and the results were used to calculate the neutron crosssection and spin wave energies.4. The agreement with experiment is quantitatively not perfect. It seems hard to believe in such large regions of coherence at 2 To. Nevertheless. Perhaps the later neutron data focussing attention on the persistence of spin waves above Tc should be reconsidered on this earlier basis. As mentioned in section 2. Although the calculation and the measurements were carried out several years ago they represent the only such analysis ever reported for an itinerant ferromagnet.5 there is evidence from high field measurements that the magnetization of Ni near Tc follows closely a temperature and field dependence given by single particle excitations. the splitting of states other than d-states are themselves wave vector dependent. in good agreement with experiment. as discussed in § 1.94 eV for the d-states resulting from screened wave vector dependent Coulomb interactions which differ for states of different symmetry (cf. Hence Cooke et al. This conclusion is surprising in view of the suspicion that Hund's rule terms are highly important for Fe. It remains to correlate these two sets of data but it should be noted that the spin wave excitations would in any case be removed in these high fields. For iron calculations of this function have been given by Cooke et al. The more general way of systematically regarding spin wave excitations is via the dynamic susceptibility X(q. For nickel the dynamic susceptibility was discussed by Lowde and Windsor (1970) and Cooke and Davis (1973). AE for iron in table 2). Capellmann (1979) has claimed to have calculated Tc for Fe and Ni on the basis of a similar model. an RPA calculation was able to describe the broad features of the neutron data including the Curie point passage. Figure 12 shows contours for the calculated and measured spin correlation function given by the imaginary part of the dynamic susceptibility. above and below T~.32 E.. WOHLFARTH typical wavelength of the fluctuation is as much as 25 ]~. . q\L O t~ O r~ "E o O u o Fo iO O {2 t- t~ i- d~ O E- -• 0 >~ 0 o >~ O . . . COBALT AND NICKEL 33 0 0 u F--.o u / .IRON. . . Thus Wakoh and Yamashita (1966) obtained a negative value of -0. cobalt and nickel reveals a wealth of experimental information and a limited success in understanding these observations. (23) .99 -0. Mook 1966) Fe Co Ni Moment of 3d electrons (/~B) Moment of 4s electrons (t~B) 2.P. cobalt and nickel from neutron measurementsof spin densities(Shuiland Yamada 1962. More detailed discussions of some data are given in Landolt-B6rnstein (1962) and in the excellent article of Carr (1966). Moon 1964.073/~B for iron but Duff and Das (1971) obtained a positive value for the same metal.105 Note: The total momentsdiffersomewhat from those in table 5 but the differenceis within the experimentalerror. g and g' factors The gyromagnetic ratio g' is measured by direct magnetomechanical experiments (Einstein-de Haas) and g by ferromagnetic resonance. This last result is rather unexpected and has been found difficult to interpret theoretically. WOHLFARTH TABLE 9 Magnetic moments of iron. 3. 3. Spin densities from neutron measurements Spin densities of iron. both from the experimental and theoretical point of view. I.28 0. 2.8. cobalt and nickel. Secondary magnetic properties It is impossible to give here a complete treatment of the very many secondary magnetic properties of iron.34 E.620 -0. The future will undoubtedly add new results in both directions. cobalt and nickel nor to give complete tabulations of the relevant numerical values. Mook 1966).39 -0. (Shull and Yamada 1962. This review of the fundamental properties of iron. The resulting form factors were found to agree with calculated free atom form factors provided the magnetic moments are distributed among the 3d and 4s electrons as shown in table 9. The negative 4s magnetizations are relatively large. Instead a fairly subjective approach is taken in tabulating and discussing selected quantities regarded as relevant and as reasonably reliable.21 1.Moon 1964. have been measured using polarized neutron diffraction. They are related by the Kittel-Van Vleck formula I/g'+ 1/g = 1. For cobalt Ishida (1972) estimates g to be 2. 1966). COBALTAND NICKEL 35 Scott (1962.22 _-4-0. This also contains average values of g given by the above authors and by Meyer and Asch (1961) and the corresponding values of g/(g . For iron and nickel Singh et al.916 1. according to the papers of Scott (1962. Reck and Fry (1969).0507 . If. compared to the best estimate of table 10.091 2. 3. 1966). Using magnetic resonance studies on a nickel crystal it has been reported by Rodbell (1965) that g is independent of temperature and frequency. only hi and h2 are significant.11. g.183 1.1) and orbital magnetizations.86 and 2. and Meyer and Asch (1961) g' Fe g g / ( g .06 and for nickel 1. Values of g and g' have been calculated several times on the basis of the itinerant electron model including spin-orbit coupling effects.03.~) + 2h2(ala2[3d32 + -~) +) for nickel for iron +h4(a~+ + 2 2 2 +~a1~2+ +)-]) (24) + 2hs(alaza]fllfl2 + + ).919 1.187 2. Scott and Sturner (1969).845 0. Scott and Sturner (1969). L i n e a r m a g n e t o s t r i c t i o n For cubic crystals the linear strain introduced by the appearance of magnetization is written in a standard notation as follows (Becker and D6ring 1939) in terms of the direction cosines ai of the magnetization and Bi of the strain A l l ! = ho + h l ( a ~ 2 + + h3(a~a22+ + h3(a~a~ + + +) + .95 and 2.0918 0.1472 0.16.2.1) which must be compared with g' according to (23). then the usual magnetostriction coefficients Al00 and Am are given in terms of these coefficients by )[100=2hi . Reck and Fry (1969) and related papers summarize measurements of g' for the metals and their alloys and those for the metals are given in table 10.1) ~orb(~B) Co Ni 1. It is seen that (23) holds excellently and that the orbital magnetizations are relatively large. the agreement for nickel is better than for iron. gl(g . as seen from table 10. TABLE 10 Values of g'. although this constant value is equal to 2.IRON.835 2. as is usual.838 1. AIII = 2h2. The table also contains Reck and Fry's estimates of the orbital magnetizations.842 1. (1976) obtained for g' and g the values 1. A5 = hs). A3= h3. Magnetostrietion coefficients Ai. The various data for iron were compared and contrasted by du Plessis et al. WOHLFARTH Alternative representations of this expression have been given by Gersdorf (1961) and by du Tr6molet de Lacheisserie (1970). The agreement between the data of table 11 is within the experimental uncertainty. For cobalt several notations for the magnetostriction coefficients exist (du Tr6molet de Lacheisserie 1970) and one proposed by Bozorth (1954) is used here since the measurements of Hubert et al. A4 = h4. these being due to Gersdorf (1961) who did not obtain values of h4 and h5 although these were small (~ 1 x 10-6) for dilute iron alloys. Table 11 gives values of hi. Note Aj = hi. A3 = h3. 13. A theoretical interpretation of this peak in a general framework of localized electrons.~ 40 2O F ~ • 0 -20 ~ -40 -60 -80 I i I i 200 400 600 Temperature (K) 800 Fig. For nickel there are again several measurements and those of Lee and Asgar (1971) and Bower (1971) (see also Franse and Stop 1970) can be quoted here with confidence. (1969) are given in terms of this 60 - A1 -.36 E. 14. A2 = 2h2..P. A s = hs. could not be tested using the available experimental data. • A5 for iron (Williams and Pavlovic 1968). 13. (1971) who concentrated on the high temperature peak in A~ = hj shown in fig. A2 = 2h2. due to Callen and Callen (1963). Values of hi to h5 have frequently been obtained for iron and nickel. . The room temperature values are given in table 11 and the temperature variation of all five coefficients in fig. Figure 13 gives results of measurements by Williams and Pavlovic (1968) over a wide temperature range (note the slightly different notations At = h~. A4 = h4. h2 and h3 at room temperature. For iron two sets of measurements using strain gauges are considered here. Both Lee and Asgar and Bower state categorically that the temperature dependence of the hi coefficients can not be explained on the basis of Callen and Callen's localized model. 2 -1.3 +0.2 37 Magnetostriction coefficients for Co at room temperature (Hubert et al.K 0 Ioo 200 300 Fig. h5 for nickel (Lee and Asgar 1971).IRON.7 -0.4 +3.2 +0.1 h3 2 -0.5 -43. .5 +1.0 -42.1 h4 +0. . . .2 -94. COBALT AND NICKEL TABLE 11 Magnetostriction coefficients for Fe and Ni at room temperature 106 x Fe Ni Ni Ni (Gersdorf 1961) 1 (Lee and Asgar 1971) 2 (Lee and Asgar 1971) (Bower 1971) hi 36.3 -93. 14.5 h2 -34.9 -98. Magnetostriction coefficients h.7 -43.4 hs +1. 1969) 106 × A^ --50 AB --107 A¢ +126 AD --105 x l 0 -6 -110 Ni 8 x10-6 4 -105 100 -100 200 3~0 12' ' x l 0 -6 I 80 160 240 320 -60 _ x10-6 100 200 300 -50 8 I 80 160 240 320 Ternperature. P. The calculation was based on that of a band structure of nickel with spin-orbit interactions treated by second order perturbation. a3 the direction cosines of the magnetization with respect to the crystal axes.( a l / 3 1 4 .38 E. there is no very reliable calculation at 0 K. In view of the importance of this property of ferromagnetic materials there are many measurements for the three metals Fe. 3. Usually at most K~. . (1969) and is again shown not to follow that predicted by Callen and Callen. Magnetocrystalline anisotropy Magnetocrystalline anisotropy may be measured by several different techniques. This inability of a localized model of ferromagnetism to explain the temperature dependence of these magnetostriction coefficients is natural. K 2 and K 3 a r e considered. there exist as yet no band theoretical calculations of this dependence and.6 x 10 -6 which agree as well as could be expected with the values of table 11. but Franse and de Vries (1968) and Franse (1969) considered the influence of higher order terms for nickel. for the cubic metals the anisotropy energy may be written Ea = K l s + K2p + K3s 2 + K4sp where s = 0t20/244+ K553 + K6p 2 +" • • ~. such as torque curves. Co and Ni. in particular in the construction of transducers for the conversion of electrical to mechanical energy at ultrasonic frequencies.Ot2/32)2] + Ac[(1 . W O H L F A R T H notation.0 x 10 -6 h2 = -16.(0/1/314. the x or 1 axis the a-axis and y or 2 is perpendicular to x and z. Aubert et al. Probably the largest single application is that of echo-sounding and underwater detection (Anon.AA[(al/31+ a2/32) 2 .AB[(1 -. This is AI/I -. especially the last. 1961). for which they are vitally important at low temperatures (~ 100 K). • • AD at room temperature are given in table 11. However. The temperature dependence of these four coefficients is given by Hubert et al.a2)/32 .ot2/32)o~3/33] 4. (1976) and Gersdorf and Aubert (1978) very carefully produced a series of coefficients to describe the anisotropy at 4 K. after a correction (Fletcher 1961). Values of A A .(al/31 + ot2/32)of3/33] + 4AD[(al/31 + 0t2/32)O/3/33] (25) where the z or 3 axis is the hexagonal c-axis. obtained the following values hi = -70.a 32)(1-/32) . The high values of h~ and h2 for nickel have led to the use of this metal in several applications.2 . The data in table 12 refer to room temperature where the usual representation continues to apply. indeed. Fletcher (1955) (see also Gersdorf 1961) reported a calculation of h~ and h2 for nickel and.2~ 2_.3. In a standard way. p = ¢Xlt~2tx3 (26) with al. a2. magnetization curves and ferromagnetic resonance. In both papers the influence of higher order terms is carefully analyzed. in particular. and of Kz(T) and K3(T) by Escudier (1973).47 × -2.43x 103 liP liP~ lip/ lip K3 -1.) 0. These two sets of data lead to the well-known result that K~(T) varies much more rapidly than M(T) and a brief discussion of this result is given below.26 x 106 erg/cm 3 whereas Franse and de Vries (1968) give . that K2 is virtually undetermined for iron. Escudier (1973) concludes that K2 and K3 are very small compared to KI and that a single anisotropy constant suffices to describe the anisotropy energy between 4 K and room temperature with good accuracy.781 0. L o w temperature values of K3(T) are given by Amighian and Corner (1976) and Birss et al.12 x 106 M1 e m u / c m 3 K2 1.2 × lip -0. measurements above room temperature.Mioo)lMo Iron Nickel 0. showing.7 x liP 4. again. (1977). It is impossible to assess accuracy and table 12 gives the values of KI.3 × 103 0 (K. .2 x -2.015% 0. T h e temperature d e p e n d e n c e of K! due to Escudier (1973) o v e r the range 4 to 300 K agrees very well with that given in Bozorth (1951) over the wider range 0 to 800 K and Escudier's data are given in fig. however.IRON. covering.1 . The value of K! at 4 K is here -1. COBALT AND NICKEL 39 For iron. Measurements by Sato and Chandrasekhar (1957). in agreement with the earlier literature.50) x 103. Thus KI(T) is well established (ferromagnetic resonance measurements of K~ for nickel by Rodbell (1965) are in good agreement with these static measurements) and.81 x 10~ -5. TABLE 12 Anisotropy constants at room temperature in erg/cm3 Ki Iron Nickel Nickel Cobalt 4. the older literature is given by Bozorth (1951) and in LandoltB6rnstein (1962).48 × 104 -5.31 x 106 Author Escudier (1973) Escudier (1973) Franse and de Vries (1968) Sievert and Zehler (1970) (Mm . The temperature d e p e n d e n c e of K~ for nickel given by Escudier from 4 to 300 K is shown in fig.3 x -2.6 x 1. More recent measurements seem to have concentrated more on room temperature and below.246 -0. 16.017% Room temperature values due to Escudier (1973). 15. the variation is very rapid compared to that of M(T). 2 2 x 106 at the same temperature. give Kz = 71 x 103 at room temperature. For nickel there are considerably more measurements and Escudier's and Franse and de Vries' (1968) room temperature data are given in table 12. K2 and K3 of Escudier (1973) at room temperature. The agreement between these two sets of data is excellent. The value o f Kt agrees excellently with an earlier one by Graham (1958) who also gives K2 = (0 . 0 200 Temperature (K) Fig. WOHLFARTH k 1 and K 1 105 erg/cm 3 5. 100 \ 30~ ~k 1 and K 1 105 erg/cm 12 11 1 -.9 4.P. Temperature dependence of K~ for iron (Escudier 1973).3 5. . Ni 7 I I 100 Temperature (K) 200 300 Fig. 15.40 E. Temperature dependence of K~ for nickel (Escudier 1973). 16.2 5.0 4.1 5.8 i I \.4 5. As shown by Barnier et al. . 17. Temperature dependence of K~ and K2 for bcp cobalt (Barnier et al. (1961b). At K 1 • 10 6 K 2 • 10 6 ergs/cm 3 Js 1600 8 Js(T) emu 1200 Co 800 400 • v II -2 200 400 T(K) 600 800 Fig. above which temperature the c-axis ceases to be easy. These values agree reasonably well with those of H o n d a and Masumoto (1931) reanalyzed by Sucksmith and T h o m p s o n (1954) and those of Barnier et al. (1961a). . is shown in fig. 17.IRON. K2 and K ] due to Sievert and Zehler (1970). T h e temperature d e p e n d e n c e of K1 and K2 due to Barnier et al. 41 (27) (Smit 1959) where 0 and d~ are polar angles with respect to the c and a axes. 1961a). It is seen that KI(T) vanishes at 516 K. = Kj sin 2 0 + / ( 2 sin 4 0 + K~ sin 6 0 + K3 sin 6 0 cos 6d~ + . between 518 K and 598 K the easy axis lies along the generator of a cone of semivertical angle sin-l(-Kl/2K2) v2 (Smit 1959) and this interesting behaviour is fully analyzed. . There are several measurements of K1 and K2 and table 12 gives the room temperature values of K1. COBALT AND NICKEL For hcp cobalt the anisotropy energy is written as E . . As was first pointed out qualitatively by Fletcher (1954) and Fletcher and Wohlfarth (1962) large contributions to K~. and obtained the temperature dependence of M1 for these two metals. 1961). however. Kondorsky and Straube (1973). He represented the anisotropic part of the magnetization as A M = M~s + Mzp + M382 +" " " (28) analogous to (26).b) have since extended. are expected where there is a band degeneracy and these would be rapidly reduced by raising the temperature. . The room temperature values are given in table 12 which also contains the corresponding values of the ratio of the change of the magnetization between the two crystal directions noted to the magnetization itself. In view of the strong itinerancy of the d-electrons in these metals this result is not surprising. Here calculations of the anisotropy coefficients have frequently been carried out (for a review for nickel. see Kondorsky 1974). Aubert (1968) has discovered an anisotropy in the magnetization of nickel crystals and Escudier (1973) continued this work for nickel and iron. (The later trend "beyond Stoner" has clearly not yet reached this difficult problem. This prediction was later verified by the several calculations quoted above.b) found none of the several localized models representative of the experimental data of fig. WOHLFARTH even higher temperatures cobalt becomes fcc (see fig. The calculations include the following representative ones: Fletcher (1954. . 8) and values of KI and K2 between about 750 K and 1200 K have been given by Sucksmith and Thompson (1954). Furey (1967). Mori et al. The agreement with experiment of the several formula given was analyzed for iron by du Plessis (1971) who plotted the exponent n(T) to which the reduced magnetization M(T)/M(O) has to be raised to yield K~(T)/Kt(O) (this tortuous procedure is historically based). it cannot be claimed that this very complicated problem has yet been fully solved using the itinerant model. the work of Furey is particularly remarkable but has never been published r The calculations are based on the following concepts: Magnetic anisotropy is a result of spin-orbit coupling as is the case for the g-shift and linear magnetostriction.b). also see Carr 1966). (1974a.42 E. 17. The agreement is poor with all the versions of a localized model but also with one band model calculation (Mori 1969) which. Slonczewski (1962). Gersdorf (1978) and others. The temperature dependence is thus clearly not immediately related to a power of the magnetization and needs to be computed by direct methods of perturbation theory with temperature included by Fermi statistics. . (1961a.P. However. Mori et al. Both K1 and K2 are negative over this temperature range as is the case for fcc Ni (table 12) (see the relevant graphs in Landolt-B6rnstein 1962. The theory of the anisotropy and its temperature variation has been given in terms of localized models (Cart 1966) which relate the K1 coefficients directly to the magnetization M ( T ) . For cobalt Barnier et al. For cubic crystals calculations of K! require 4th order perturbation by the spin-orbit coupling of the unperturbed energy bands.) Another way to smear . The effect is seen to be small. (1974a. Pressure dependence of fundamental properties The Curie temperature of the three metals under pressure has been measured several times and reference is made to the results of Leger et al. respectively. I. The effects are in general small compared to the observations on Invar alloys (Nakamura. The pressure dependence of the saturation magnetization is important in its own right and also by reference to the volume magnetostriction. 0. For iron and cobalt the calculated values. (1972). since O M Oto where to is the volume strain.60 K/khar which agrees as well as can be expected with the above observations at zero pressure. Tc = 652 K. This topic is discussed further by Hoffmann (volume 3/4).4.03 K/kbar for Fe at 0 kbar and 0 -+0. Direct measurements of OMIOP have frequently been carried out and reference is made here to the measurements on nickel and iron by Tatsumoto et al. as well as Franse et al. w h i c h introduces mean free path effects.IRON. 3. For nickel at 0 kbar dTc/dP is quoted as 0. The only simple theoretical formula for these three metals which is based on the itinerant model is that of Lang and Ehrenreich (1968) which is easily obtained by relating Tc to the energy band structure under pressure.4. q u o t e 0 -+ 0. For nickel the calculated value is thus 0.05 for Co at 0 and 60 kbar). i. 3.2 K/kbar.17-+ 0.02 at 80 kbar. as shown by reference to the calculations quoted. (1974). volume 3/4). It reads d TddP = ~KTc (29) where K is the compressibility. Magnetoelastic effects There is a variety of elastic properties of the ferromagnetic transition metals which are influenced by their magnetism. disagree with the observed null results. and there is at present no theoretical interpretation of the null data for these two metals. found this verified by experiment. The perturbation calculations at 0 K and at finite temperatures require an independent knowledge of the spin-orbit coupling parameter. Hausmann and Wolf (1971) thus proposed a relationship between KI and residual resistivity and they. the energy band structure and the temperature dependent exchange splitting. The increase of Tc of nickel at this high pressure is 25 K compared to the value at zero pressure. (1962). For iron and cobalt it was found that dTddP is essentially zero (Leger et al. (1976). They obtained for the room temperature values .e.02 K/kbar at zero pressure and 0. The agreement of these calculations with experiment is good on the whole. COBALTAND NICKEL 43 out the Fermi distribution is by alloying. Finally reference only is made to energy band calculations of the surface anisotropy of nickel by Bennett and Cooper (1971) and Takayama et al.36 _+0.96 and 1. Nevertheless the results are significant and will now be briefly discussed. there being no clear reason for these two quantities being of the same order and sign for a strong itinerant ferromagnet.5). The temperature dependence of dto/~H has been studied particularly for nickel (Stoelinga 1967. Franse and Buis also give values of #hl/#P for Ni and Fe. Values of the pressure derivative of the saturation magnetization for cobalt were obtained by Kouvel and Hartelius (1960).44 E. Saturation for a polycrystailine specimen was achieved in 13 kOe and for a single crystal already in 3 kOe.2.2 quoted above. 1965) and by Fawcett and White (1968) for iron. is discussed in the above publications and by H61scher and Franse (1979). Co and Ni by Stoelinga (1967) (see also Stoelinga et al. This quantity decreases from the above positive value. 7. Anderson (1966) gives values of the hyperfine field of Fe.4. 5 0 x 10-2kbar -~. Co and Ni. compared to the directly observed value -2.I° Oe -I. cobalt and nickel has also been measured and reference may be made to the crystalline anisotropy and linear magnetostriction.2. (1963) and found to be weak but smooth between 200 and 370 K. WOHLFARTH of the logarithmic derivative ~ In M/OP .7 x 10-4 in the same units. The value for cobalt leads to 0 In M/OP = -3. cobalt and nickel at 4.0 in the same units for iron. The temperature dependence of this logarithmic derivative was measured for nickel and iron by Tatsumoto et al. There are some differences in the results of different authors due to the obvious experimental difficulties.60 x 10-2. this is the region of the paraprocess (see section 2. Hence the values of this quantity for the three ferromagnetic metals are remarkably constant. changes sign at about 440 K to reach very large negative values as the Curie point is approached. Tange and Tokunaga 1969). giving the following values of Oto/OH at 4 K for Fe.75 and . yielding ~ in M/dP = -2. where ht is defined by (24).H . where h0 is the magnetostriction coefficient defined in (24) (Stoelinga 1967) and the prime denotes a derivative with respect to H..0 . The value of ~ In Tc/dP for nickel is 5. (31) .5. The value of Oto/dH at low temperatures was proposed by Gersdorf (1961) to follow from the Landau theory of phase transitions which gives (Wohlfarth 1968) (see also Shimizu 1978) atolaH = 2KCMrxr. For Ni and Fe Franse and Buis (1970) (see also Kawai and Sawaoka 1968) give ~ ln K~/OP at room temperature as -0.3.P.2 × 10. 3. (1971). For polycrystalline specimens Oto/OH = 3h~+ anisotropic terms. The pressure dependence of some other properties of iron.4 x 10-4 kbar -I for nickel and -3. The question of isotropy etc. Volume magnetostriction The volume magnetostriction ~to/cgH has been measured for binary alloys between Fe. In all cases high fields have had to be applied to reach saturation where to . Ni and Co under pressure.2 x 10-4 kbar -~. Such variations may follow from the strong influence of degeneracies on K discussed in section 3. respectively while for Co Sawaoka (1970) gives -0. respectively: 4.2 K. see also Kadomatsu et al. The agreement with other measurements is only fair.2 and 1.4 x l0 -4 kbar -1. (1977) to estimate bulk moduli.1. The values of this calculated pressure are 212. respectively. however.4. These measurements show very pronounced anomalies of the thermal expansion coefficient near the Curie point. Shimizu (1978) and others in terms of the Landau theory. Wohlfarth (1968). Janak and Williams's so-called giant internal magnetic pressure is. 1. namely an s-d transfer and a change of the width of the d-band which influences the electron interactions.2. It is defined by them. These values were proposed by Shimizu (1974) to be close to the ubiquitous ] discussed in sections 3. however. comparison being made with the observed data of Kohlhaas et al.4. COBALT AND NICKEL 45 Here K is the compressibility.IRON. Shimizu (1978) claims. (1967). These methods have been used by Janak and Williams (1976) and Andersen et al.3 lead to an effective interaction between the itinerant electrons which is only weakly dependent on volume. nothing more than the magnetostrictive volume strain. 3. Thermal expansion The three problems partially relevant to magnetism are the low temperature values.0 for Fe. It is.9 and 2. Co and Ni. in order to apply this theory to materials with low values of the magnetization like Invar (see Nakamura.1. and C the magnetoelastic coupling constant defined b y these authors. Co and Ni. For the latter. Mathon (1972). Shimizu (1978) also discussed the temperature variation of the magnetic contribution to the thermal expansion of the three metals. volume 3]4). for magnetic materials. This anomaly has been studied very carefully for nickel by Kollie (1977) from the point of view of critical phenomena. including iron. Mr the saturation magnetization and Xr the high field susceptibility both at temperature T. this also occurs in relation (29). Critical indices a and a ' were defined in the usual way (Stanley 1971) and were both found to be equal to .. respectively. Although this Gersdorf formula correctly relates the volume magnetostriction to the paraprocess via the high field susceptibility it is not obviously justified to use the Landau theory for the ferromagnetic metals at low temperatures. However. apart from the compressibility. the variation over a wide temperature range and the critical behaviour near To. Mathon (1972) analyzed the data of Tange and Tokunaga (1969) by considering two processes under pressure. volume magnetostrictions. cobalt and nickel. The correlation effects treated by the methods of the spin density functional formalism referred to in sections 1. etc.3. Shimizu (1978) and others used the Kanamori theory of correlation effects (Kanamori 1963) and a dependence of the band width on volume characterized by an effective Griineisen constant ~ (Heine 1967). that these values are too large. near the Curie temperature the Landau theory is expected to apply (outside critical regions!) and Shimizu (1978) gives a detailed analysis. At low temperatures the following values of the electronic Griineisen parameter ye are relevant and are taken from the review of Collins and White (1964): 2. This problem was also discussed by Friedel and Sayers (1978) and is fundamentally important. 182 and 10 kbar for Fe. due to the volume independence of the correlation effect which was assumed. as by Gersdorf (1961).2 and 1. 20 0.24 Fe 0.48 1. Temperature dependence of C' = ~(Cil . 18.010.16 1.28 o Leese and Lord 0. of relevant combinations and/or of elastic moduli have frequently been carried out and a good review of the older literature is given by Kneller (1962). For Young's modulus this is the well known A E effect.08 1.04 1. WOHLFARTH -0.12 0. C.P.52 1 I ' I .. 18 shows the results for C' = ~(C=1.i n I1% 0. .00 •E r¢N 0 0.4. and fig.~. i .40 1.4. The squares are data of Leese and Lord (1968). It is seen that C= changes very little at Tc while C' has a positive anomaly of about 12% (measured as usual by extrapolating the data above Tc to very low temperatures and comparing with 0.32 z1% o 0. Measurements of single crystal elastic constants C1.2 and C. I 0.44. Elastic constants The relevant magnetic problems concerning the elastic constants of the three ferromagnetic transition metals are essentially the changes introduced by the onset of magnetic order at the Curie temperature.46 E.36 C' 0.96 0.C=9 and C44.16 0.CI2) and C~ for iron (Dever 1972). For iron there are later measurements by Dever (1972).093-__ 0. in excellent agreement with the specific heat based values given in table 8. 3.121 0 I 200 I I i I 400 600 Temperature (°C) I I 800 I Fig. .IRON. (1960) give again only a very small (positive) anomaly for C44 and a rather larger one. and the K term hyperfine (leading to an effective field H~). Hence the three metals display positive elastic coefficient anomalies at the Curie point which are frequently very small but may reach values ~ + 10%. the /3 term phonon (leading to the Debye temperature 0D). The classical AE effect arises from domain processes ruled by the linear magnetostriction (Kneller 1962). 3. Further experimental work on magnetoelasticity in iron due to de Vallera (1978) Gale et al. 1960). Here the specific heat is expressed as C = yT + / 3 T 3 + 0~T3/2+ KT -2 (32) where the 3' term is electronic. This effect is generally assessed and removed by carrying out measurements in saturating magnetic fields (see for example Alers et al.e. . Specific heat The low temperature specific heat of iron. The theoretical interpretation of the data is extremely difficult since the elastic constant anomalies have a number of contributing terms.5. Using this same method Janak and Williams (1976) obtained the giant pressures (i. volume 3/4) for which negative anomalies which may be very large are commonly observed. As already stated Friedel and Sayers (1978) ascribe the differences to the different volume dependences of exchange and correlation inherent in different models (Kanamori.4. The remaining anomaly is related to the volume magnetostriction in several complicated ways (Wohlfarth 1976. Hausch 1977) but a theory based on the itinerant model is being developed (Pettifor and Roy 1978). cobalt and nickel was measured by Dixon et al. volume magnetostriction) referred to in section 3. spin density functionals . (1978). . COBALT AND NICKEL 47 the actual values at this temperature). the a term spin wave. For nickel the data of Alers et al.2 and Shimizu (1978) claims that the resulting bulk modulus anomaly AB which is closely related to this pressure disagrees with experiment whereas his own thermodynamic analysis (similar to that of Hausch and Wohlfarth) is claimed to be more consistent. ).1. (1965) and the results are reproduced in table 13. No comparison has since been made with later measurements and with other ways of estimating a (related to the spin wave stiffness D) and with K . about +5%. Thermal properties 3. This relates the magnitude and sign of the anomaly to the structure and filling of the density of states curve but treats exchange and correlation by the spin density functional method. is concerned with the neutron observed changes of the phonon spectrum on passing through the Curie point. The accuracy of the values tabulated is fully discussed by Dixon et al.5. This is in complete contrast with Invar (see Nakamura. Yamamoto and Taniguchi (1955) measured Young's modulus for Ni-Co alloys and observed a relatively large value of about + 10% for nickel but a very small value (<1%) for hcp cobalt (AE[E decreases dramatically during the fcc/hcp phase transition). for C'. and Braun et al. Measurements of the total specific heat over this broad temperature range have often been reported and fig. respectively. Great difficulties arise in analyzing such curves into constituent contributions analogous to the low temperature analysis given by (32). The calculated value of yfe~ocan not be immediately compared with experiment due to the electron-phonon enhancement effect (Grimvall 1976) which is uncertain for these three metals but for which estimates were given in section 1.~ (kOe) 4.48 E. W O H L F A R T H T A B L E 13 Low temperature specific heat data (Dixon et al.3.741 472. the large number of possible contributions and the possibility of short range ordering effects above the Curie temperature.38 460. Braun and Kohlhaas (1965). (measurable by NMR and M6ssbauer spectroscopy).2.2 Ni 7. to the ferromagnetic state of the metals and thus contain a magnetic contribution given in terms of density of states by (Stoner 1939. a realistic estimate for nickel was given by Jacobs and Zaman (1976) as 2.3 223. been bravely attempted by Stoner (1936). These values of y refer. of course. the critical behaviour near Tc is discussed below. 1965) Fe v(mJ deg -2 tool -I) 0n K a(mJ deg -s/2 mol -I) H.7* 0. Shimizu 1977) Ym = Yferro.011" - *Specimen L use of eq. analyzed the specific heat data of several authors over the range 0 to 1200 K and deduced a paramagnetic y versus T curve by having the . Nevertheless. The Debye temperature 0D was carefully estimated from elastic constants by Konti and Varshni (1969) and Wanner (1970).2 (see also below). Analyses have. (32) by least squares. Jones et al. 1976).021" Co 4.028 477.4* 0. are due to Jones et al.P. (1974) and Grimvall (1975. This unfortunate situation arises due to the complicated temperature dependences involved. however.~/para where yte~o = ~ 2 k 2 [ N ( E + ) + N(E-)] Ypara = ~Tr2k2N (EF) (33) where EF is the paramagnetic and E ± the ferromagnetic Fermi energies. The ratio yp~/yfe~o for a strong itinerant ferromagnet like nickel is expected to be ~2. Values of y were discussed in some of the band calculations referred to in section 1. Shimizu (1977) and others. 1968). the magnetic contribution to the low temperature y value given by (33) is simple compared to the value of this contribution over the whole range of temperatures up to and above Tc (Stoner 1939. 19 shows the data of Braun and Kohlhaas (1965) (see also Braun 1964. The Curie temperatures (and other phase transitions) are visible. Shimizu 1977) although Shimizu gave calculated curves for iron and nickel. Two other attempts concerning nickel and iron. Specific heat of iron. cobalt and nickel (Braun et al. . (1974) conclude that this is a good model at these high temperatures. The calculated entropy of this temperature is 9. namely 9. in excellent agreement with that obtained from the experimental data. . being in excellent agreement with this at 1200K.0 J 60 l Cp 50 Co \ 40 39. high temperature harmonic phonon contribution given by the Debye theory and estimating the anharmonic phonon contribution from thermal expansion data. This is in contrast to the discussions of .---'-~NCi ~ Co Fe 30 /el7 Co vv . Since this calculated entropy is based on a single particle itinerant model Jones et al. about 2To. .r--eq v Fe Ix/ v v v v E v 20 300 500 ~ o II 1000 1500 2000 TIK~.0 g-atom. 1968). 19.6 J/mol K. Fig.9 in these units.deg 7O J I i 57. COBALT AND NICKEL 80 49 1 76. I~ i / . The y(T) curve peaks at Tc and runs into a calculated curve (from the band calculations of Zornberg (1970)) at higher temperatures.4 / h.IRON. ~. while Rocker and Sch6pgens (1969) obtained a = .50 E. The exponent may also be estimated using "the Rushbrooke inequality as an equality" (Stanley 1971. Measurements of these exponents have frequently been carried out and those of Shacklette (1974) (Fe) and Connelly et al.07-+ 0. Kraftmakher and Romashina (1966) obtained a logarithmic dependence of the specific heat near T~. Taking account of the residual differences. concludes that the thermodynamic data require persistent disordered localized magnetic moments in the paramagnetic phases. namely the observation of spin waves above Tc discussed in section 2. This conclusion in turn was criticized by Sakoh and Shimizu (1977) who concluded that there was no need to invoke entropy contributions from localized moments in the high temperature regimes. (34) and table 8 give for cobalt a = a ' = -0. The experimental data for the three ferromagnetic metals above the Curie points have even been taken into the liquid state by Vollmer et al. 1 from the measurement of Braun (1964). not listed in table 8.H -~. (1966) and the measured heat of melting should also be considered in future analyses of the vexed problem: can thermodynamic data give reliable information on the degree of localization of magnetic moments above the Curie point? Near Tc the most important question is the magnitude of the critical exponents ot and a' (Stanley 1971) and values of a (taken to equal a') for iron and nickel are given in table 8.5. Rocker and Sch6pgens 1969) a = a' = 2 . (1971) (Ni) are to be regarded as reliable as they agree with this compilation which covers a wider range of observations. WOHLFARTH Korenman et al.C o .0 .e. although qualitative agreement with their critical exponent analysis was established the data were insufficient to establish the value of ~ which had to be obtained from the formula (Stanley 1971) =2-2fl-Y= a (36) .P. A further critical exponent. (35) Mathon and Wohlfarth (1969) (see also Ho 1971) considered earlier measurements on nickel of Korn and Kohlhaas (1969) and. 3). both are seen to be rather small and negative. i.02 which is close to that of Rocker and SchOpgens (1969). Cn . relates the change of the specific heat at field H compared to that in zero field. For cobalt the situation is slightly less satisfactory. but it agrees with the magnetic measurements of Ponomarev and Thyssen (1977) discussed in section 2. For iron Grimvall (1975.2/3 y. Grimvall's conclusion was claimed to arise due to insufficient account having been taken of the peaks in the density of states curve for this metal (see fig. a = a ' = 0 .7. (1977) and the motivation for this work. however. (34) This relation gives values for iron and nickel in quite reasonable agreement with those tabulated in table 8. 1976). In addition. A general relation for the resulting temperature change A T is given in terms of the magnetization MH and the results are compared with the classical data of Weiss and Forrer (1926) which had earlier been expressed in terms of the classical formula A T .0 . M a g n e t o c a l o r i c effect Mathon and Wohlfarth (1969) analyzed the magnetocaloric effect of nickel on the basis of the Kouvel-Comly (1968) equation of state which includes the critical exponents discussed and tabulated in section 2. (37) The agreement had long been known to be rather unsatisfactory. It suffices.82 for Fe.75 and the classical value ~-=2.0 . For cobalt also Rocker and Sch6pgens (1969) were unable to deduce values of ~ from the measurements of Braun (1964) and used (36) to obtain K = . 3. and the use of the non-classical critical exponents of Kouvel and Comly led to considerable improvement. Using Kouvel and Comly's critical exponents. T r a n s p o r t properties 3. within the accuracy of measurement the value of K is thus the same for all the ferromagnetic transition metals. The measurements of Korn and Kohlhaas (1969) on iron in a magnetic field have not been analyzed in this way but relation (36) gives (using table 8) K = . including curvature effects at low fields H.1. COBALTAND NICKEL 51 giving ~ = . therefore. 0 5 .M ~ . this work summarizes the experimental data in concentrated transition metal alloys of iron.using (38) and their own experimental values of [3 and y is rather wide but includes these direct values for which a fundamental determination on the basis of renormalization group methods is awaited.IRON. 2.78. The range of values of ~. extremely small. Co and Ni. 0 7 . (1971) reanalyzed all the measurements of the magnetocaloric effect from the Kohlhaas school in terms of critical exponents and obtained the following values for ~-: 2.2. Noakes and Arrott (1973) remeasured the magnetocaloric effect for nickel near Tc and found ~r = 2.6.M02. When T = Tc Mo = 0 AT ~ M ~ (38) where ~r = 2 + ( y . The subject of the electrical properties of ferromagnetic metals is in principle very difficult since ehe scattering proces- . 7r = 2. to include here only a representative set of typical data for the pure metals and to summarize the relevant theoretical ideas.90.e.58 and 2. 0 6 .1)113. Rocker et al. cobalt and nickel. i. respectively.5.32. Electrical r e s i s t a n c e The article by Campbell and Fert (volume 3/4) includes an authoritative account of the microscopic mechanisms through which magnetism influences transport properties.0 .6. compared to the observed value (Weiss and Forrer 1926) Ir = 2. 3.6. 20. and found this prediction to be verified with ot as in table 8. (1967). The electrical resistivity p of the three metals has frequently been measured and fig. WOHLFARTH ses involved add their own inherent difficulties to those involved in the magnetism itself. The Curie temperature region itself was investigated for iron by Shacklette (1977) from the point of view of the Fisher-Langer (1968) prediction that dp/dT varies near T~ in the same way as the specific heat.e.cm 100 50 F -100 0 500 °i i °° 1000 . (1967) and others have derived curves giving dp/dT over a wide range of temperatures. These data have been excellently verified in independent measurements by Schr6der and Giannuzzi (1969). 1967). 20 gives the data of Kierspe et al. the situation is less clear: Thus Zumsteg and /~. specified by the critical index a.e. i. The crystal structure change (t~. . draw an analogy with some rare earth metals (see chapter 3 by Legvold). in fact. as Shaklette states. Kierspe et al.3') in iron was shown up in resistivity data of Arajs and Colvin (1964a).. For nickel. Kierspe et al.52 E. and found a fairly complicated behaviour. T(oC) 1500 Fig.P. the derivative curve became horizontal and finally decreased right through the T~ region. All three curves show an anomalous drop of p below the Curie point. Electrical resistivity of iron. For iron and nickel a sharp maximum in dp/dT occurs somewhat below To. cobalt and nickel (Kierspe et al. For cobalt the crystal structure change is clearly seen. p ~ T 2) at temperatures well below To. For cobalt no such sharp maximum in the temperature derivative was observed. For all three metals dp[dT-T (i. Very remarkable measurements of p in the solid and liquid phases and going up to the boiling point (!) were reported by Seydel and Fucke (1977). 22 +4. COBALT AND NICKEL 53 Parks (1970) also claim to have verified this prediction but the a (and a') values derived from dp/dT are not those regarded as reliable in table 8. 3. Measurements specifically directed towards this end have also been obtained.35 +0. (1973). . This verifies earlier data of White and Woods (1959) who had evidence from this term also for iron and nickel. estimations of the T 2 term coming from scattering by d-electrons. The T 2 dependence of the resistivity at low temperatures appears clear from the data of Kierspe et al.2. For the last point Radakrishna and Nielsen (1965) estimated the contribution to the T 2 term coming from magnon scattering to be about 15% of the total in the case of cobalt. the selection being made so as to fit TABLE 14 Room temperature Hall effect coefficients (Hurd 1972) Re* Fe Fe Co Ni Ni +0. see also Hurd (1974) and Cohen et al. (4) The T 2 dependence of the resistivity arises from the scattering in a very general way. (3) Below Tc the scattering d-electrons act in two groups with + and . Table 14 is extracted from Hurd's massive tabulation.5 -0. Up-to-date estimations of this effect for all three metals would be desirable using reliable evidence on the spin wave spectrum.spin thus leading to the observed dependence of the resistivity on magnetization (spin disorder scattering effect).56 R~* +7. due to Hasegawa et al. The same dependence also arises from a scattering process involving spin waves.6. Thus Radakrishna and Nielsen (1965) measured the electrical resistivity of cobalt up to 6 K and found an important T 2 contribution.05 -5. Hall effect Hall effect measurements on the three ferromagnetic metals have been summarized by Hurd (1972). On the other hand. exchange splitting and the phonon spectrum.24 -6.84 -0.18 -0.23 +0. (2) These conduction electrons are scattered by the itinerant d-electrons. Hence the scattering processes can not be distinguished in this way. (1967).0 Authors Volkenstein and Fedorov (1960) Dheer (1967) Volkenstein and Fedorov (1960) Volkenstein and Fedorov (1960) Huguenin and Rivier (1965) *In units 10-n2 II cm/G.IRON. As more fully discussed by Campbell and Fert (volume 3/4) the special features of the electrical resistivity of ferromagnetic metallic materials may be understood on the following basis: (1) The current is carried in the main by the s-electrons due to their lower effective mass (by ~ 10) compared to that of the d-electrons. (1965) also deserves updating having regard to later information about the band structure. 54 4O E. cobalt and nickel (Hurd 1972). I 40 (HR) Huguenin and Rivier !D! Dheer (A) Alderson et al.= ~ : ~ _ ~ ~.452 (D) < t~ 7 v -20 • ~. ~ ~ Pc .. .. The .::::: .. What is tabulated are the two coefficients R0 and R~ defined as ordinary and extraordinary coefficients of the Hall resistivity pH in the form prt = R o l l + R I M (39) where H is the (internal) field and M the magnetization. WOHLFARTH Fe PC RRR = ....... Hall effect coefficients R0 and Rmof iron..-. . also taken from Hurd (1972).'::" ~ 6 ~ F~SC RaR = 196-4S2 Im -Ni PC RRR = 57 (VF) --- -4 .j' "~x .:::" / ~ . ....... Fedo.Lk~ .IVFI. 21. ~ ____________ t Ni PC a a a = 480 (Ha) Cu PC RRR = 842 (A) -8 O / ..ov ~ ~ . 21. ~ ' ~ ~ ... with the temperature dependence of the tabulated quantities shown in fig.." RRR = 452 ~ i I i Temperature J R R I -12 0 1O0 R = 66 (VF) i IJ 200 (K) 300 Fig.P. an. .~. ~ .. . sometimes aH is written as pH = RoB + 47rRsM (39)* where B is the applied B-field. and Rs is the spontaneous Hall coefficient..RR = 480 I . ~ ~ ~ -60 Ni PC RRR = 57 (VF) I E" 0 Fo PC RRR = II (VF) RRR-.. j J 20 !..1 ". . ' .e~./ 1"1~'~'~'Fe SC RRR = 196 . Low temperature data for nickel were also reported by Radakrishna and Nielsen (1965) and here the thermal conductivity followed closely a linear law K = 0.IRON. The thermoelectric power of iron was analyzed by MacInnes and Huguenin (1973) in terms of the treatment of Fisher and Langer (1968) of the scattering of electrons from spin fluctuations which arise near the Curie point and which lead to the observed maximum in this case.6. (volume 3•4). Schr/Sder and Giannuzzi (1969) reported measurements of the Seebeck coefficient of iron. magnetoresistance in thin films being discussed by Hoffmann (volume 3/4). Low temperature values of the thermoelectric power of cobalt by Radakrishna and Nielsen (1965) showed that no contributions due to magnon drag (Roesler 1964) arise in this case. (1977) derived the thermal conductivity from measurements of the heat diffusivity and found that near Tc the temperature dependence differed markedly from that derived from the Wiedemann-Franz law. Fivaz (1968) and Cottam and Stinchcombe (1968). cobalt and nickel over a broad temperature range near the Curie temperature and observed. Other effects As in the article of Campbell and Fert (volume 3/4) reference will be made to measurements of the thermoelectric power and the thermal conductivity. Richter and Kohlhaas (1964) found that near the Curie point the thermal conductivity and the resulting Lorentz number show a very marked anomalous peak extending over only 10 degrees. Smit (1955) and Kondorsky (1969). Theoretical papers referring in particular to both R0 and RI of this metal are those of Irkhin et al. The thermal conductivity of all three metals was measured by White and Woods (1959) and found to increase anomalously with temperatures in ranges ~>½0Dwhere that of nonferromagnetic metals approximately reaches an asymptotic value. the interpretation of the observations involves a scattering mechanism for the itinerant charge carriers together with an appropriate spin-orbit interaction to produce the required asymmetry leading to a transverse electric field which has the macroscopic properties of the effect in ferromagnetic metals. they are too complicated to summarize here but the summary by Hurd may be referred to. A general result is that the coefficient Rs in (39*) is proportional to the square of the resistivity which for iron holds approximately above about 50 K (Volkenstein and Fedorov 1960. (1967). The theory of these effects is very difficult and has long been the subject of controversy. Dheer 1967) but not at lower temperatures. For nickel Papp et al. 3. that this coefficient has a pronounced maximum close to To. in agreement with other data.30T W/cm K.3. The Lorentz number was close to the "theoretical" value. thin film effects related to the Hall effect are discussed by Hoffman (volume 3[4). For nickel the Hall effect has helped in establishing the Fermi surface (see section 4. COBALT AND NICKEL 55 coefficient R0 is thus the one occurring in ordinary metals while Rs is characteristic of magnetism. To summarize the discussion of Hurd.7). A review is given by Hurd (1972) and by Campbell and Fert. . Theories of the anomalous effect have been given along these lines by Karplus and Luttinger (1954). The same caution may also have to be exercised regarding the following relevant papers. 3. This section is thus in a way to be regarded as part of section 4. in other branches of magnetism as discussed earlier). of course. The calculations give a pronounced peak in the real part of the xx component of the conductivity tensor at 0.7) data but much less than that from the band calculations of Callaway and Wang (1977a) discussed in sections 1. (1971) which led to an exchange splitting of about 0.4 and 1.2 and 1. It remains to unravel this situation in the future. .5. related to relevant electronic properties. 1. These data.5 eV (see table 3).P.8 eV.7.56 E. WOHLFARTH Due to the great difficulties involved in interpreting these data it seems best to leave them to speak for themselves.1) and neutron (section 2. and their temperature dependence. showing a marked change in the optical absorption with temperature.e. The evidence for this is not too firm and the wide scatter of the many experimental curves reproduced by Wang and Cailaway (1974) shows that optical measurements do not provide a wholly reliable guide to the magnetism of nickel.3. being a direct measure of the exchange splitting. namely band structures. exchange splittings. Shiga and Pells (1969) interpreted the temperature dependence of their measured optical absorption spectrum of nickel (specifically the width of a pronounced peak at 5 eV) by a temperature dependent exchange splitting which vanished at the Curie temperature.3. whose closeness to the above value may be a coincidence. Since the subject matter is only peripheral to magnetism.46 eV. Optical properties Magneto-optic effects and the magneto-optical conductivity are important for thin magnetic films and are discussed by Hoffmann (volume 3/4). only nickel will be briefly discussed. It is indeed unfortunate that no conclusions can be drawn regarding such theoretical problems as the relative importance of single particle and spin wave excitations below Tc and of spin wave phenomena above. were discussed in relation to other data by Fadley and Wohlfarth (1972) in a concise review of changes at Tc which will be referred to below. including in their band calculation spin-orbit coupling effects (these also arise. and these are in excellent agreement with the lower values obtained from photoemission (see section 4. No such peak was observed but an incipient manifestation of it was claimed to have been seen in the data of Lynch et al. i. 300 meV. The analysis of his optical spectrum to answer the question: "Where to where is A ?" is clearly in part debatable but a minimum value of 50 meV and an average value of 80 meV are claimed. For this metal Wang and CaUaway (1974) calculated the diagonal and the off-diagonal elements of the optical conductivity tensor. The final example of optical data which have relevance to magnetism is the work of Stoll (1972) who aimed at obtaining the value of the energy gap A referred to in sections 1. The discussion is here limited to a few measurements on one of the ferromagnetic metals which have a bearing on the theoretical problems referred to in the earlier parts of this article. The low temperature value of this AE was 0. e. It is considerably larger than the earlier UPS value of Eastman (1972). The aim of this extensive work. an attempt at details of density of states curves. (1977).1. 4. Future work will be directed towards the direct measurement not just of the bandwidth but also of the actual structure. admit that some features are missing while others are present which can not be explicitly accounted for. 3. (1978). i. The bandwidth of nickel was measured using this advanced technique by Smith et al. Explicit searches for the (low temperature) exchange splitting have been carried out for all three metals. 1).3 eV which is in good agreement with the calculated values of the band width (see fig.IRON. 3). and its temperature dependence Spin polarization of the electrons Fermi surface Wave functions and momentum distribution. The value obtained by a reasonable assignment of the observed peaks of the photoemission spectrum was 4.3 eV to their observed spectra. (1978) and on nickel by Williams et al. will obviate the need for invoking many body effects! These measurements differ from the earlier ones in revealing a new peak at low energies which is claimed to be significant. Relevant electronic properties This article will now be completed by a necessarily brief account of some relevant electronic properties of iron. see Eastman (1979). The difficulties in this field are related to specimen purity and the analysis of the observed data which are often complicated. The good agreement of Smith's value. who compare their data with a band calculation on iron (see fig. An independent measurement of A E was . and values obtained by other techniques (see for example Fadley and Shirley 1971). for example in the measurements of iron by Kevan et al. this being on the low side of the arguments of section 1.3 and certainly less than the value 0. Some results along these lines are already available.1. 4. COBALT AND NICKEL 57 Optical data of this type are thus not wholly conclusive but have led to a number of estimates of the exchange splitting which may be significant. Solid state spectroscopy 4. is to try to obtain information on the following matters: (I) (2) (3) (4) (5) Energy band structure and band width Exchange splitting.6 eV of table 3. has been used to investigate points (1) and (2) above. For a review. Ultraviolet photoemission spectroscopy This technique which when using angle resolution is popularly known as ARPSUPS. Even the former. For nickel Heimann and Neddermeyer (1976) gave arguments for assigning an exchange splitting of 0.1.3 eV. often based on very sophisticated experimental techniques. if substantiated. cobalt and nickel. occurring at +0. In a later paper Heimann and Neddermeyer (1978) return to the statement that an estimation of exchange splitting is not possible on the basis of UPS data alone. (1976) when combined with other data. studied in a similar way both iron and nickel using higher photon energies and again found no shifts of the order expected from an exchange splitting which varies as the (single particle) magnetization. The higher value is claimed to be more reliable and both are significantly less than the value of table 3. However. however. AE decreases to about half its low temperature value above To.7.35 and 0.2 eV over the same temperature range which is much greater than this uncertainty. Measurements on nickel are available from Pierce and Spicer (1970. Petersson et al. Apart from the low temperature value of AE its variation through the Curie point has been vigorously studied since on the basis of Stoner theory AE should vanish at To. Unfortunately. The exchange splitting was not explicitly deduced. respectively.8 eV. This was done.0 eV. 5 for the paramagnetic density of states curve). (1979) and Eastman et al. to be close to that suggested by Wohlfarth (1977b) to bring about agreement with the spin polarized photoemission and neutron data discussed in sections 4.P. the measurements of Kevan et al. The analysis is complicated due to this combination of techniques and the value 1. a theoretical curve was shown to give a shift of about 0. respectively. 1972) and Rowe and Tracy (1971). (1976) and Petersson and Erlandsson (1978). using two different photon energies 10.7 eV and thus giving AE = 1.31 eV and the gap A. X-ray data of Turtle and Liefeld (1973) were felt to give the same peak for the minority spin band. in the following way: A very well defined peak at -0. in good agreement with table 3.1 and 2. having values 0.9 eV has a debatable significance. (1978) (see also Eastman 1979) have reported what are probably at the time of writing the most accurate U P S data for Ni.58 E. (1977) obtained photoemission spectra which had again to be combined with other data. Thus fig. however.49 eV. the exchange splitting (at the top of the d-band) depends on this energy. Rowe and Tracy used photon energies close to those where Shiga and Pells (1969) observed .2 and 16. it agrees well. Pierce and Spicer measured the position of the leading peak of the photoelectron energy distribution curve below and above Tc and observe no change within the experimental uncertainty. Himpsel et al. with table 3. (1978). WOHLFARTH reported by Dietz et al. although here single crystal faces of iron were investigated. For cobalt Heimann et al. For iron. and are fully reported by Petersson (1977). 22 shows their data for the (100) face of Ni above and below To. All these values are thus claimed to give evidence for exchange split bands but the actual values of the corresponding energy are not yet sufficiently reliable to feel fully confident about their significance. and for both nickel and iron by Petersson et al.3 eV (relative to the Fermi energy) obtained in the measurements was identified with the sharp peak in the density of states curve of the majority spin band (see fig. in the measurements of Pessa et al. They find AE at low temperatures to have a value of 0. defined by (9). (1978) have already been referred to. see below. . there being no such effect at this temperature for palladium used as a control. occur. i.'~ . in that the solid state spectroscopy measurements have a time scale. 4-5 eV. This observation has not yet been explained and it is not clear how it bears on the problem of the exchange splitting and its temperature variation.~ / / I -4 i -3 I -2 Energy (eV) I -1 I 0 = EF Fig.2 eV T <T c T>Tc /.e._-. or do not.of the order 10-~4-10-m6s. Where they do not it was suggested that during the process the following may happen to cause the anomaly: (1) Final state effects related to localized holes in the valence bands or core states. 11 {- E em O = 0 o ..7). COBALT AND NICKEL I w 59 I I J Ni (100) I~o = 21. They observed very marked (essentially "critical") changes of the d-band peak and width exactly at To. (2) Life time effects. Angular resolved electron distribution curves of nickel (Petersson 1977). whereas for the more static measurements .. 22.IRON. As a result of these observations Fadley and Wohlfarth (1972) were motivated to ask the question: What changes in the ferromagnetic transition metals at the Curie point? They discuss a wide range of experimental observations for which such changes do. optical absorption anomalies (see section 3. 4. There was good overall agreement for iron and cobalt. (1977) gave a width of 4. and this is in good agreement with the calculated values plotted by McAlister et al. a further possibility of interpreting these data is related to the persistence of magnetism above the Curie temperature which is evidenced by the neutron data discussed in section 2. The earlier measurements (Alder et al. of hyperfine fields or of the static magnetization) showing changes at Tc the time scales are much longer. but for nickel the lower band width of 3. of course. most widely used to determine band structure. Despite the improved XPS resolution using the angular resolved technique (Fadley et al.'s paper measured and calculated d-band widths were compared.3 and L3 emission spectra remain unchanged. see Eastman (1979). some of which could be identified with band calculations. 4.3 eV reported in section 4.1.P. (1972) and by Kaihola and Pessa (1978). cobalt and nickel such measurements were reported by Cuthill et al. to be more relevant when discussing the influence of the Curie point. 4. Clearly.7. The latter results would tend to agree with the UPS data reported in section 4. This result was in contrast to the prediction of Wohlfarth (1971). 1973. Spin polarization of photoelectrons This technique was pioneered by a Swiss group at ETH Ziirich and nothing can detract from their achievement of constructing the sophisticated apparatus to this end. Unfortunately. Measurements of the spectra of Fe on crossing the Curie point have been reported by McAlister et al. In McAlister et al. WOHLFARTH (e. X-ray photoemission spectroscopy The XPS method has been used in particular by Fadley and Shirley (1968.1.3. in view of the higher resolution and the higher state of development. Clearly. 4. that for nickel (and cobalt) the polarization should be negative for energies close to the Fermi energy (where the .3 eV as already reported.1. 1976) the UPS data discussed in section 4. (1975).g.1.1. SXS should be repeated for nickel. A more satisfactory analysis of these solid state spectroscopy data will require consideration of the whole range of measurements discussed for the three ferromagnetic transition metals in this article.60 E. (1967) and McAlister et al.1 seem. The latter UPS data of Smith et al. 1970) to give information on the structure of d-bands of transition metals. later also made by Smith and Traum (1971). Soft X-ray studies The SXS method is. For iron.2.1.1. There was evidence for considerable structure. Siegmann 1975) had the polarization of the photoemitted electrons positive and decreasing with increasing energy. This would lead to an updating of the review of Fadley and Wohlfarth (1972).1 as coming from the earlier UPS measurements was also seen by SXS. these give opposing results in that the Americans find a shift of the bands which can be identified with a temperature dependent exchange splitting while the Finns find that characteristic features of the M2. with A = 0 (Wohlfarth 1971). 1972) (and also stressed by Wohlfarth (1971. As discussed in section 1. in good agreement with the neutron and optical data discussed in sections 2. Hence neither of these techniques bears directly on the problems related to the d-band and its exchange splitting. (1976). Chobrok et al.b) (about 300 meV for Ni) may or may not be due to the many body effect of electron-magnon interactions. the band calculations themselves may be at fault. Alternatively. Campagna et al. COBALT AND NICKEL 61 majority spin band is full) and should change sign to become positive at an energy about 2A above the Fermi energy. . Wohlfarth (1977b) (see also Moore and Pendry 1978) deduced from these data a value of A = 75 meV. Later measurements from the (100) face of a single crystal of nickel (Eib and Alvarado 1976) show precisely this behaviour thus showing that the earlier results arose from the inadequacy of the polycrystalline specimens. . If not. Oddly.7. Other related techniques Two other techniques have been applied to the problem of the emission of electrons from ferromagnets and the relationship of the results to the theory of their magnetism. (1977). cobalt and nickel (Tedrow et al. In view of this inadequacy of these two techniques it suffices merely to refer to some papers and point out one unusually interesting outcome of the tunnelling measurements: Field emission: Gleich et al. except through the effect of hybridization between these two groups of electrons (Hertz and Aoi 1973). Landolt and Campagna (1977). nickel is largely due to the free-electron-like s-p band". The authors regard this as proof of the applicability of the itinerant model to iron. respectively. This proposal in turn was severely criticized by Edwards (1978).IRON. (1977).1. Tunnelling: Tedrow and Meservey (1973). Paraskevopoulos et al. 1977b)) that "field emission f r o m . and the problem remains at the centre of interest at the time of writing. Dempsey and Kleinmann (1977) ascribe the single crystal nickel data to the emission of the photoelectrons almost exclusively from the surface layer. in fact. Eib and Reihl (1978) measured the spin polarization of photoelectrons from the (111) face of an iron single crystal. and Chazalviel and Yafet (1977). and "the free electron (field) transmission coefficient is roughly 1 or 2 orders of magnitude greater than the 3d transmission coefficient". It was first clearly pointed out by Politzer and Cutler (1970.4 the fact that this value is much less than that given by the band structure calculations of Callaway and Wang (1977a. Politzer and Cutler (1970. there has been no attempt to relate these measurements of the properties of the s-p electrons with the neutron-observed moments given in table 9. These are field emission and tunnelling through superconducting layers.5.4. The measurements using the tunnelling technique on pure iron.7 and 3. obtaining +60% at threshold.) shows a phenomenological correlation between the . 1972). 4. it also implies that iron is a weak itinerant ferromagnet.1. and Hertz and Aoi (1973). (1971). Neither of these methods is as useful as the photoemission technique described in section 4. The minority spin band contains about 3 electrons per atom and its Fermi surface is surprisingly similar Fig. See also fig. cobalt and nickel have been reviewed by Gold (1974) and Young (1977). 3. The corresponding Fermi surfaces for the majority and minority spin bands are shown in fig. showed this correlation to be remarkably well preserved. 6 and 1. this value is in reasonable agreement with the entry in table 3. There is at present no theoretical interpretation of this clear-cut result. 23.2. For iron Gold et al. Extension to nickel alloys by Paraskevopoulos et al. respectively and these are discussed in section 1. cobalt and nickel are given in figs. As far as the present article is concerned. The authors interpreted these early results on the basis of one-dimensional densities of states. . the matters of greatest interest are the exchange splitting and its temperature dependence. The two most widely used techniques are magnetoresistance and de Haas-Van Alphen effect. 23.0eV. Perhaps the tunnelled electrons feel a strong field outside the ferromagnet which is proportional to its bulk magnetization. 1978). especially de Haas-Van Alphen technique The Fermi surface studies on iron. A final technique was used to measure the electron spin polarization from nickel surfaces by using electron capture by scattered deuterons (Eichner et al. but the technique is only in its infancy.P. (1971) reported extensive de Haas-Van Alphen studies which they were able to analyze satisfactorily using an older band calculation (Wood 1962) rigidly exchange split by 2. Fermi surfaces of iron used to interpret de Haas-Van Alphen data (Gold 1974). WOHLFARTH observed polarization and the magnetization. 4. The Fermi surface. having a maximum value of +96% from the (110) plane. 4. The observed polarization was found to be experiment and sample dependent and also varied drastically with the crystal face.62 E. Some of the calculated Fermi surfaces of iron.2. 4-0. and the variation of the de Haas-Van Alphen frequency over this temperature range was found to be less than the resolution of the experiment. Cyclotron resonance experiments by Goy and Grimes (1973) were discussed by Wang and Callaway (1974). a value which should be confirmed by independent measurements. incidentally. For cobalt the Fermi surface was measured and the results analyzed by a band structure calculation of Batallan et al. Other de Haas-Van Alphen measurements for iron by Baraff (1973) and magnetoresistance measurements by Coleman et al. Stark (see Gold 1974. Tsui (1967) was able to make observations on the copper-like necks of the majority spin band. the minority spin lens sheets of the Fermi surface (see fig. was unable to account for the observations. implying that rigid splitting is a good approximation. (1973) who found that Ishida's band calculation (1972). COBALT AND NICKEL 63 to that of molybdenum and tungsten containing the same number. The temperature dependence of the exchange splitting of iron was measured in a remarkable study by Lonzarich and Gold (1974) over the temperature range 1-4. The calculated structures give a reasonable account of the de HaasVan Alphen frequencies. Other Fermi surface studies and the relationship to band calculations are discussed for iron and nickel by Callaway and Wang (1977a). For nickel de Haas-Van Alphen and other measurements have frequently been reported. particularly for the neck at the point F in the majority spin Fermi surface.39 eV.2. This problem was considered by Zornberg (1970) and Ruvalds and Falicov (1968). 23) were investigated. one part in 105. it also gives. These values are less than or equal to that given in table 3. Spin-orbit interactions were also taken into account in the calculations and in analyzing the measurements to explain the electron orbits around L in the minority spin band. The band calculation of Zornberg (1970) also gave good agreement with many observations of the Fermi surface of nickel. (1973) are also discussed in the above reviews where the discussion is too technical to reproduce here. (1975) who claimed that it gives a better account of their observations than those described in section 1. 23). (1967). A minority spin hole pocket associated with the level X5 was investigated by Tsui (1967) and Hedges et al. only slightly above the value of table 3. Specifically.6 eV. . Wang and Callaway 1974) observed de Haas-Van Alphen oscillations arising from large central orbits of the majority and minority bands which led him to postulate a rigid exchange splitting of the d-bands. The discussion involves consideration of spin-orbit coupling effect as is the case for the other two metals (see fig.2. the rigid exchange splitting being here 0. The calculation led to a rigid exchange splitting 1.IRON. described in section 1. The calculated minority spin Fermi surface resembles that of hcp rhenium. an energy gap value for this strong itinerant ferromagnet of 14meV. Other de Haas-Van Alphen measurements on cobalt were reported by Anderson et al. If the exchange splitting was proportional to the total magnetization then a change of one part in 104 would be expected. The low temperature dependence of A E is discussed below. and Fawcett and Reed (1962) obtained evidence on these necks from magnetoresistance measurements.2 K. WOHLFARTH Edwards (1974) showed that. Compton profile Measurements of the Compton profile of transition metals give information on the momentum distribution and the wave functions.1 and which may well be small enough to agree with the observations. while the change of the total magnetization 8M is given by 8M = 8Msp + 8Msw (40) coming from single particle and spin wave excitations.2.3. work function The review of Fadley and Wohlfarth (1972) was concerned with a number of physical properties of the ferromagnetic transition metals which do. For iron Mijnarends (1973) obtained detailed information on both properties. the temperature dependence of the work function of this metal (Christmann et aL 1974) shows no anomaly at all at the Curie point. His data were in good agreement with calculations based on the band structure of . On the other hand.3. The results were analyzed in relation to band calculations by Rath et al. These and other related findings discussed earlier by Fadley and Wohlfarth (1972) can not yet be regarded as having been explained satisfactorily. 4.P.1. Such measurements for iron were reported by Phillips and Weiss (1972) and for nickel by Eisenberger and Reed (1974). 4. Miscellaneous techniques 4.3. they should continue to be regarded as having a close relationship to the results of solid state spectroscopy discussed in section 4.1.3.64 E.3. at the Curie temperature.3. They are thus a valuable supplement to theoretical and experimental band structure determinations. Sakai and Ono (1977) were able to measure the momentum distribution of the magnetic electrons in iron and observed a negative conduction electron polarization as also given by the neutron scattering experiments summarized in table 9. Positron annihilation This technique enables Fermi surfaces and momentum distributions to be measured and is thus complementary to the studies of sections 4.2 and 4. Hence at low temperatures the exchange splitting depends almost entirely on the change of the single particle magnetization which was discussed in section 2.2. the change of the exchange splitting AE is given by 8(AE)__~o[~SMsp + _ k T 8M 1 AE ~-A~ swJ (41) where ot and /3 are ~1. 4. Among these the characteristic plasma losses are relevant and Heimann and H61zl (1971) have claimed that for the (111) face of nickel the volume loss energy shows an anomalous change at Tc of the order of AE. or do not vary. Plasma losses. (1973) and Wang and Callaway (1975). Phys. Neighbours and H. F6. Alder. For cobalt Szuszkiewicz et al. 197I. 1233. Liquid Metals. Barnier. 1964a. R. Rev. I. Birss. M. 12. Nickel-containing magnetic materials. 1947. Rev. Bll. R. 46. p. 257. Aiers. G. Kohlhaas... Colvin. P. Ferromagnetismus (Springer. One striking result is the claim that in the 5th zone an electron regrouping is visible at the Curie point. B12.. 25. 287. Edwards. 10. 311. Rev. Aisaka. Kohlhaas and O. 1973. Ahlers. Paris 276.T. J. Barmatz. 504. 1977. Solids. A. 1964. 1972.. Arajs. Phys.. M. Siegmann.I. BI2.V. For nickel Kontrym-Sznajd et al. Mag.K. M.H.R. Sol. Cologne. Anderson. 1961a. 1976.M. 40. J. 2424.. Spin distribution studies in ferromagnetic metals by polarized positron annihilation experiments were also reported by Berko and Mills (1971).M. 1951. L309. Bower. Keeler and C. G. D. J. 545. Braun. Z.K. Acad. Phys. J. Proc. 4.R. S. Andersen. J. O. 39. and D. M. 87. 695. D. et al.J..R. Phys. Sommers. U. Jepsen and J. Poulsen. 35. Phys. 6. 1964b. Phys. Bradbury. 1973. Intern. Paris.IRON. 2597. R. de Phys. 2839. 253. Physica B86--88.. M. 301. Stat.. and R. 1939. He also claims that there is no need to invoke a negative polarization of the conduction electrons. Y. and B. Conf. 5314. Chem.P. S.R. 1975. 96. Amighian. Ferromagnetism (Van Nostrand. and A. and T. 30A. 13. 797. Rimet. Berlin).. Rev. 1971. J. Bll.. Soc. Anon.. 1968. C. Phys. and A.J. International Nickel Publ. Sol. 429. Phys. BI4. Bozorth. 252. Angew. Froehle. Princeton). Briane. C. Arajs.. 1973. Pauthenet and G. Phys. COBALT AND NICKEL 65 Wood (1962). Phys. Campagna and H. Thesis. A. Phys. R.A. Phys. Roy. Stat. Hohenberg and A.M.. Aidred. Lett. 139. . Corner. Becker. R. Cooper. Rev. Paris. Chem. Barraff. A326. G. 32-C1. M.H. 1968. K. 1938. Voilmer.T. 313. Phys. J.. Kollar. AIdred. Appl.. B8. 2075. 249. Madsen. This finding would be sensational if confirmed.P. D. 1961. Solids 24. Rimet. Sci. J. Rev. 195. Acad. 1975. 1963. S... 2. Kornblit. 1965. J. contrary to the data of Sakai and Ono (1977) and those given in table 9. 1975. Y. B8. Sci. 1977. 3439. 1975. Arajs. Appl. Bennett. J. Tokyo.B. D6ring.M. Mills. J. H. Kornblit. Braun. Edwards and D.V. Anderson.H.C.. Aubert.D. and R. 1973. Sci.I. Proc. 1971. Colvin.C. and R. R.. A. 2144. 277. Bozorth.. Solid State Comm. Conf. Phys. Barnier.. (1976) have obtained only preliminary data which they are unable to relate to a Fermi surface. Phys. Rev. and W. no. 1960. 1954. D. Newns for their valuable advice. LR.V. 1969. Sheppard. B3. Aubert. 365. 1966. 1961b. and W. and R. A. Batallan. R. Phys. Physica B86-88.A. G. 1642. Procs. R. 1973. 189. Rosenman and C.. Braun. C. 1976. Acknowledgements I am grateful to D. Colvin. References Adachi..L Hudak and D. O. R. 400. Rev. Phys. and P. S. Stone. G. Acad. Pauthenet and G. F. Rev. R.M.R. Phys. Sato. Berko. (1975) again report only preliminary data.J. Yafet. 1674. Phys. P. P. to be published.E. D. Mag.S. 442. Roy. Rev. Reihl. A. H.V.. Wohlfarth.A. C. Procs.. Ann. Rev. 1978..E. 417. Colvin. Edwards. J.M. Corrias. Phys. du Plessis. 3293. Rev. 329. Sizmann.I. R. Progr. and H. Physica B91. A.. Loomis and D. BIS. 267. J. Phys. Mapother. A2.J. 1970. Gerhardt and C. Eastman. Technol. 39. D. Can.A. 1062.M. J. Paris 5. 1975.S.P. C. Nuovo Cimento 33B. Lett. Low Temp. Phys. M. D. Sci. 132. and L. Phys. Viljoen and L. 40. P. Dzyaloshinsky. Phys. 2294.. 1978. Rev.J. J.. Davies. 1514. 1966.E. D.J.M. Eastman. J. de V. 133. 1973. B7. 1978. T. 129. 1973. F6. Rev. C.. 1971. White. Davies. Edwards. Duff. 5. 1970. and J. 669.A. Phys. J. Proc. Proc. F1. K. 1966.. U. 1970. B3.C. de Vallera.. 40.F. P.. Phys. Phys.. F. Rev.E. Edwards.J. McAlister. Rev.R. L185. 1976. Cuthill. Electron spectroscopy (North-Holland. Lett.W. Electronic Callaway. 70. Rev. M.M.. Das. Phys.. Callen. Fadley.Proc. Herr and A. 1973.. and C.. P.F. Fadley. AIberts.M. Edwards.P. 29.M. Capellmann. Dietz. Cottam. J. M. 1964. 317. Escudier. Knapp. C3. 429. 39. Phys. Passell and G. Engelsberg. 1976.E.P. 487. 1972.N. BI5. Connelly. Phys. 980. Doniach. Rev. and G. Mat. Hertz. 924. 637. Ertl and O. Lett. and E. B.L. 1978.J. W.M.S.. Proc. Phys. 1979. 2095.S.I. Rev. Procs. 1912. and B. Phys. 3237. 274. 1973. Rev. G. Proc. S. 1977a. Cambridge. Rev.. Cooke. Soc. Eisenberger. Chazalviel. 1974. N. D. Wohlfarth. P. J. M.L. 183. Shirley. Lett. Conf. Dixon. 156. Roy. 1109. 1979. Utsumi and D. Phys. 1973. and C. Cooke.B. Naturforsch.J. Roy. P. 4..E. Conf.. 1974. Z. 1971. Phys. L289. Rev. Cooke. 1968. State Phys. 52.. Chobrok. Sellmyer. I. 1006. Danan. Wohifarth. F3. 1971. 1976a. Coleman. D. J. 1516.. 26. ICM Munich.P. A. Kondratenko. Soc. BI6. J. Amsterdam) p. 193. Cohen. 1976. 17. Phys. Phys. 1965. 10.W.F. Rev. Reed. H.. P. Proc. 1977. D.F. Buchanan.F. Eib. 179. and E. BS. 991. Minkiewicz. Shirley. 1108. 1971. 450.. Appl.M. M. 1978. Phys.66 E. Phys. . Shirane. Collins. Solids 32. J.G. Phys. Hoare. and D. Appl. Phys. Watson. Hoffmann. 39.. 1976b.J. and S. E. Chem. A285.F. Handbuch der Physik 18/2. D. E. and R. L'effet Hall extraordinaire (Univ. Dever. 21. 1978.. Collins. D. Eib. 1976. 1974. Sizmann.J.A.. 2191. du Plessis. J. Callen.G..V. R. Chem. 33A. W. and P.. 1963. H. J. Rev. J. 1977. G. Conf. Sorg. Lett.P.L. 435. Alvarado. Dempsey. Z. J. Edwards.B.T.A. Rev. J. G. 1987. and Y. 127. and E.M. Rau and R. 1969. 1971. Physica B91. 750. Hoiden and D.P. A.E. Roy. M. Phys. Soc. Giovannini and D. D. 1967. F. 561.P.. 37.E. Phys. Dalton. 328. Toronto Conf. Edwards.N. J. Geneva).M. S. 1218. Lett. 1973. Rev. 3.L. K. 373. and S. and E. Callaway. Campagna.. Phys. Morris and D. P. 40. and D. Edwards. Christmann. 1970. D.444. Phys. B3. 34. Rev. and M. W. C.. 1967. Procs. and D. de Chatel. 337. 164. D. Comments Sol. 1972. D. 29a. D. Schober. Soc. Maetz. and S. L. conf.S. Phys. Phys.S. Shirley.. Mag.. 578. Rev. 1691. R. G. Rev.R. 24. C1. Kieinmann. Grenoble. Nathans. 1968. D.. Inst. 1977.J. A303. 1052. Lynn and H. WOHLFARTH Dheer..E. Phys. Regenfus and R. 1977. Carr. 1967. Celasco.J. Edwards. Solids. Eichner. Arajs. 1967. Eastman. 43. R. du Tr6molet de Lacheisserie. Phys.. Phys. Wang. Moody. Williams and R.. 1297. V. 892. J. and W. M. A296. 13.P. Toronto Conf. F6. Thesis. J. Phys. A300.P. Procs. Lett. Meyer.N.E.S. 1973. Stinchcombe. 807. A. S. 704. Phys. 1968. 39. Proc. J. Fadley. 1965. and T. Wang.G.M. Phys. de V.A. Phys. J.K.E. Himpsel and J. J. 1968. Lett. Edwards. B9. T.B. Thesis. Doniach. J. 1977b. Vac.G. Inst. Prec. Physique 32.. J. 112. Soc. 900. Phys. Franse. and E. Toronto Conf. and G. Noordwijk Photoemission Syrup. 1965. 103. Soc. Soc. 67 Gold. Lett. and G. Proc. Int. Chikaznmi.J.. 665. Phys. 4084. 3252. 237. 9. COBALT AND NICKEL density of states. D. S. Kranz. Phys. Schmolz and M. A.J. 1970. Phys. J.. Fivaz. H. 1573. 1951. Feldmann. Thesis.C. E. and C.L. Wolf.. J. J. D. Phys. and C. Moscow 3. 36. Rev. 1970. Appl.F. R. Phys. Kortekaas.. Phys. 36. 1968. Phys. 323.. J. P. C. 1979. 329. Phys. R. L. Hatta. 1977.K. G.E. 1976.F. Suhl. G. Neddermeyer. Harvard. 1066. 1966. Dormann and N. Phys.J. 1974. 1955. Kaplan.. Z. J. Phys. Wakoh and J. Tohoku Univ. Stolp. 1117. Phys.M. Hasegawa. Fadley. 371. Buis. Fawcett.N. Rado and H. Rivier. Special Publ. Prec. B19.. L257. Phys. 68. and H..J. Hedges. 809. Rev. Fletcher. P. Gersdorf. 673. Yamashita. Phys. Herring. Fletcher. Lett.S. A. 1976. Franse.C. 1962. Hubbard.E. 822.. Thesis. Gale. Phys. K.K. Huguenin. 1958. Hunt. Lett. 1979. K. Phys.A. Phys. M.C. 539. Hubert. Phys.IRON. Phys. 201. Magnetics 7. 40. Hussain.. and H. Mag. B. Rev. 655. J. F. Rev. 78. Wagner and Z. Hausch.. Soc. Thompson. A.M. W. 1971. Physica 95B. Intern. p. Minkiewicz and L. Fekete. Sol. Fawcett.S. .. J. Masumoto. Grayovsky. 6. G.T. Goy. Mag. 35. Hatta. Friedel. 1968. 12. Int. and J. 39. B16. P.P. Heine. G.A. 1968. Hedges. 1974. 1978. Soc.C. Phys. Passell. S. Japan 40. B8. 67.F. Rev. Hausmann. and M. Phys. J.. Lett. 1976.M. Phys. BT. 20. Thesis.J. 1977. J. 1978. Addis. 2919. I. G. eds. J. 1. 38.E.. C-l. Rev. 316. J. Soc. and R. 726.P. Rev. 1978. 238. J. F6. 135. 1962.R. C.. Gleich. 61. G. Stone. Rev. Phys. Langer. 1964b. C. 1971. B16. Rev. J. 5054. 1969. Baird. 1278. Goebei. 2. C. 1971. K. A. 505. Lett.S. J. 26. Heimann. G. Inst. Phys.. L. Franse.. 1970. 1971. Radium 23.. 173. Stat. Physica Scripta. and W. Procs. 19. 32A. P. Rev. 1970... Aubert. and A. and K. Gersdorf. Physique 39. C.T. le?. J. W.J. R.. F4. P. 1977. 1961.M. Pessa and H. 1978. Fadley. Physica B91.. Fletcher. H61scher.. Hubbard. and G. Gold.. J. 299. and E. 1976. 1967.S. D. Phys. 1974. 1971. 1954. Phys. 509. Graham. J.C. H.E. Soc.. 1976. A216. Proc. J. Grimvall. Roloff. et al. 322. and N. 1969. 1963. Phys. Roy. 1964a.A. Knaap and D. A277. J. Sayers.J.. 1972. Franse. Gersdorf. 188. White. Grimvall. Phys. Velicescu. Rev.J. 84. de Vries. Griffin. 148. 63. B13. Kirchmayr. Neddermeyer. 27. 1962. R. 1978. Lett. Phys. Acta 38. Honda. Heimann. 1865. W. Gunnarson. 1971. Prec. 1485. Stone and A. Proc. J. 59. de Vries and T. Amsterdam. J. N.. 357. 145. Prec. and S. Proc. 153. Prec. Conf. 1976.M. J. Rev. Gold. Magnetism 4 (G. and M. P.C. Panousis and D. Gunnarson. VJ. Phys. Reed. 1977. Phys.T. D. B-l. 1566. E. 163. Solid State Comm. Aoi.M. 336. 2575. Sizmann. Soc.V. Furey. Trans. J.M. Rev. and J. A.P. and D. Soc. Rev.) (Academic Press. O. R.. P. Unger and J. Wohlfarth. E. and J. Marschall.. O. Proc. Rev. G.. 16. M. 1976. K.D.C. and H. and E. Hausmann. F6. Physica Scripta 14. Heimann. Neddermeyer. Fisher. Phys. Soc. Heimann. 587. Roy. J.N. Soc. C. George. S. Lett. 1965.S. Roy. 1968. and S. Regenfus and R. L-59. 224. H.M. 344.. Rep. Phys. Franse. 43. 455. Japan 17. F.. Phys. 84. J. 39. 477. Rev.. Fletcher. 1967. J.R. Lett. Gersdorf. G. Amsterdam. A276. 48.B. R. U. Low Temp. Heiv.V. Phys. Phys. Franse.. to be published. 3537. 1931. 1066. 1967. L. L127. C. He.V. 3. Grimes. Eastman. 1953. 13.E. Physica. Rev. 39. R. 52. Sci. Lett. Japan 20. Hertz. A.J. Phys.R. Comments Sol. 1977. E. H61zl. Gumbs. 1961.D. Glinka. 1975. Shaltiel. I. Himpsei. Hubbard. Wohlfarth. B18. New York). 4. 1973.C.. 20. Colloq.. 26. State Phys..J. Japan. G.R. S. J. V. 1973. Fletcher.M. Chikazumi. 19. Solid State Comm. C2. Thrane and G. 1263. b.E.S. 409. 1967.S. M.I. Collins. 1976. Jepsen. Phys.N. 119. 1967.R.. J. 1975. 1237.A.R. 1971. Phys. .B. Phys. Mathon.C.L. Kohlhaas.R. Kadomatsu. 1970.L. Lonzarich.E.. Phys. 1960. Sol. Soviet Physics J. Kondorsky.. P.. Kanamori. Kohlhaas and H. Rev. 39. 336. 28. E. Campagna. Proc.B. 25.A.E. Can. and J. Fukuda and T. Angew. Y. 2022. Can. Marschall. Madsen. Phys.A. 315. 1977. Japan. Leger. R.. W. 1978. 136. Andersen. J. Phys. Physica Stat. Berlin). Phys. Ehrenreich.M. 1966. Lowde. Phys. Stachowiak. and A. 1976. Gold. Hurd. 28. Phys. Irkhin. Jones. J.A. E. Phys. Rev.P. Korn. Straube. Phys. and C. Landolt-B6rnstein. 51. 8. State 8. K. Phys.A. M. 29.. 1972. 694. 1974.P. Mathon. Soc. J. 575. Landolt. Phys. Proc. J. Phys.. 1647. 22. Loriers-Susse and B. Trans.M. Kraftmakher. Wohlfarth. R. Phys. 30.1978. Lett. Z. J. Conf. 1969. E. 1969. Mook. R. A326.P. 2195. Appl.. Phys. Z..M.G. and T. Abelsky. Rev. 9. Janak. Rev. Soc. Kouvel..P. Mook. Soviet Physics J. Procs. Phys. and E. H. J. Phys. J. 182. Cuthill.P. Hartelius. 359. Zaman. and R. L. and D. Lynn. Rev. R. 1974. 63. 1968. Rev. Wilkens and M.F. R. 23.P. Ukai. Diinner and N.S. Murray and R. Lee. 663. 1962. and C.. 1978. C. R.I. Ishida. Yafet.E. J.D. Appl.E. J. 1971. Phys. Windsor. and M. Roy. 495. Campagna. Watson. M. 1954. Angew.L.J.P.E. R. Physica 63. Mijnarends. Kollie. Wierzchowski. Adv. C. W. 73. 20. and E. 1977. Adv. Konti. Weaver.W. Poulsen and O.W. Trumpy. 1971. unpublished. 151.A. Kohlhaas. Nathans and G. Minkiewicz. N.P. 1969. Sol. 1972. 1975. Rev. 624. H. 1974.T. 24.M. J. 1963. Sol. H. J. Cuthill. 29. Soc. I.. E. Huguenin. Pessa. Mook. 90. 2. Chem. Rev. The Hall effect in metals and alloys (Plenum.. 556. J. B14. B6. 132. G. 1972. J.. J. 1978. Rev. 2973. and G. P. 330S. C.M. Romashina. and N. Phys. 168. 1967. 605. Soc. 47. and R. 23. 1154. and R. Kaihola. Magnetics 10.D. 159. 940. Dobbyn. BI6. 4615. BI2. Lang. 95.W. Leese.P. Sawaoka. 1969. 1966. A. B. A. Mori. Lett. Star. J. N. Phys. J. V. Japan 33. Japan 37.E. Kouvel. SchmitzPranghe. Lett. Maglic.I. 1975. J. J. Asch. 1562.. 1973. 39.J. 1977. Y. N. Wehner.D. Rev.E. 148.. Int. 28. Phys.. Kontrym-Sznajd. 4250. 517. Asgar. Inst. Phys. 1968. and H. Moore. Proc. 1969. Solid State Comm. D. Nicklow. R. Shirane. Kneller.W. Meyer. Vodar. 1971. Phys. 3986. Phys. Japan 31. 4048. 307. and H. Williams.C. J. Phys.68 E. Fujii and T. S. Hurd. and M.. A.. Phys. B16. Phys. B7. H. A195. Kondorsky. 1974a. Sol. 241. and M.. and E. J. H. Gonska. MacInnes.S. Nicklow. 327. Watson. 26. 38. Soc. Voloshinsky and S. 35.M.A. A. F2. 1961. Angew. G. E. N. 44A. 1973.M.. Varshni.T. N. McAlister. 1973. J. 245. Phys.G.D. J. Jacobs..Y. J. Okamoto. 188. V. 309. 235.. private communication. Roy.. Lett.E. 6. Phys. Phys. 813. E. Rev. Magnetism. 1962. 1968.Y.M.J. G. E.. 2624. Rev. A302. 1968. Wohlfarth. 369. Kevan. Kondorsky. Progr. S. Soc. 52.W. 4199. 1403. Lett. Lord. Rosei and J. Dobbyn. Comly. Phys. 1972. P. McAlister.J. Pendry. and A. Bross.K. and A. Kawai. Petersson. P. M. Mathon. 179. W. Prange. Rev. J. Y. Luttinger. Phys. and A. J. J. 1975.. Z. WOHLFARTH Landolt. Japan 31. Knapp and R. Phys.I. Shirley. 4872. Solids 29. O. 291. New York). 32. H. Cll.V. Y. J.. T. and J. 9/1. Phys. Rev. 1973. 1968. A. 1974. Rev. BII. Procs. N. State Comm. Korenman. J. 27.. Lynch. 1141. 275. 1978. Soviet Phys. 1964. Appi. Phys.. Theor. A. Mook. H. 30.. Kierspe. Mori. Karplus. Phys. Mori. 36.S. 1973. R. U.. Rev. Williams and R.E.L. Soc.H. Ferromagnetismus (Springer.C.. Williams and R. Toronto Conf. Phys.J. 1972. Appl. Conf.F. Phys.. Tatsumoto.K. 1978. Lynn and R. R. I.. J. M. 1969. and . Moon. and J. J. W. 4177. Shimizu. 5. Minkiewicz.P. Sakai. Int. Rev. J. Ponomarev. 1965. 22. A. 475. Naturforsch. N. Solid State Comm. unpublished.C. 770. 5243. Angew. 1970. Sol. 1973a. Rev..E. Japan 20. Pettifor. J. Lett. and A.G.K. Japan..G. 525. 611. 1969. Moriya. 639. T. D.H.Phys. B8.W. 1973. 188. Tracy. 1977. 508. 27. and A. Phys. 3789. A207. Z. 1632.P. R. 1971. 184. C2. and M. Moriya. 1951. 34. Phys. Phys. Rocker.. BIT. T. 1964. 1970. Phys. L. Sato. Place. Phys. Lett. Myers. 581. 899. 356. M. T. Spears and S. W. 396. Nielsen. Erlandsson. and J. 1272. Surface Sci. and P. Kawabata. and P. Scott.G. (b) 70. Soc. Soc.E. 379. Moriya.P. Neddermeyer.M. Physica B91. Roy.. Kohlhaas. B. 5197. Rev. Sch6pgens. and D. 1972. Rep. Rev. Soc. Petersson. 184. Meservey and P. Stat. Rev. and G. 1969. 511. Mod. N. Phys. and R. R. 148.V. Stat. P. U. 1978. Phys. A273. Schr6der. Phys. R. Z. 1977b.P. M.W.I. Colloq. Hagstr6m.H.IRON.. Soc. Phys. Roesler. Proc.. Japan 11. Sol. J. T. and A. and W.T.J. Sievert. 50A. 1970. Moscow 4. J. Conf. H. B8. 1977. Szab6 and G. 1973. 34. J. C. Soc. 799. Thesis. Paraskevapoulos. Phys. 46. 111. Angew. BI5. 1973b. Phys. 164. Stat. 4907. P.J. Stat. L. 4014.. 1978. Noakes.. 4213. Tawil and J. Scott. Riedi. (a) 44. 247. M. 21. J. Physica Bgl. K. Phys. 1969. Phys. Phys. Phys.. Siegmann. Sol. 1977. 1. Scott. Pessa. Pierce. Phys. and E. 1968. Rath..A. Shirane. 1975. Soc.. 1975. Phys. Shimizu.P. Sawaoka. . 677. Rev. Shimizu. and H. D. I1. Soviet Phys. Reck. Solid State Comm. Chem. 1972. Japan 45. Edwards. Callaway.. Kawabata. Rev. Rev. 172. Shimizu.A.M. Phys. Ono. H. 1973. Pierce. Heimann and H. Phys. Grenoble. Ukai and H. and V. Phys. Angew. B.B. 7.. 1957. 173. Thesis. Phys. 1971. 492. G. 3006.S. Phys.A. 1956. Rhodes. Phys. and K. Sucksmith. Kawabata. Y. Shacklette. D. Cutler. Petersson. Politzer. Phys. and Y. Miiller. Naturforsch. 25.. 1975. 1965. Rebouillat.. Sol. Ruvalds. Fry. and R. 427. 28.. Tedrow. Rev. Shacklette. Petersson. Phys.R. B9. Z. Soc. 1847. Richter. P. Phys. 251.. 39. K133. Japan 35. 1973c. 490. B-III 1.228. Papp. P.G. Physique 32.. Sol.C. Stat. 1970. Weiss. Roy. J. Phys. 1787. 1963. Katsuki and H. M. 855. and V.T.A. Nathans. Phys.C. 19a. Cutler. Shiga. 1969.M. Z. and W.. H. Sol. Soc. and M. and L. (b) 47.. M. Pells. BI4. W.S. 669. M. Physica B86-88. L. K75. J. T. Rev. Spicer. M. F. 102. Appl. Yamada.C.D. 1977. Z. and A. Rev. COBALT AND NICKEL Mori. J. Melander. 1972. Moriya. Yoshida. 383. J. Ramakrishnan. 1977. G. BI0. 1974. J. Giannuzzi.. 1974. Fucke. 279. 1966. J. Thyssen. Phys.. and W.M. 1964. CI. A. Politzer. Zehler. 1976.E. Seydel. B6. 1520. G. 1974b. Rev.C. 69 Rhodes.W. G. Wohlfarth. 1965. Wang.P. M. Proc. 732. 1978. Proc. 1971. L. and W. J. 1978. Chem. 235.. Nakagawa.. and H. 10. 994. Arrott. Phys.L. C. 1969. J. 32a. Rev. Japan 37. Phys.T. R.G. L. Solids 1. B14.G. Phys. 1977.. Phys.N. 1977. Sakoh. Spicer. 1972. 17. B16. Sturner. 5139. Radakrishna. 1330. Riedi.P. Phys. Chandrasekhar. and M. R. Solids 42. 1976. and P. Phys. and A. Roy. T. FS. Sch6pgens. Tichy.487.W. and D. C. Rowe J. Riedinger. T. Basel. Lett. 1962.. and B. 28. Physica I. J. W. Rev. M. J.. 1968. 37. Phys. Shimizu. J.C. Shuil. Procs. R. 277. NaucieI-BIoch. 27. 1977a. Rev. Rocker. 1977. 93. 1977. Phys. Yamada. 1977. J. Stat.. and R. 3488. 32. C. Rev. Kohlhaas and H. Thesis. Phys. Rodbeli. P. 30. 14. M. Japan 34. 1962. D. Link6ping.E.E.M. I. Phys.M. 17C. 652. V. B6.S. J. 1974. and D. Moriya.G. Falicov. Lett.M. Rev. G. B. D.G. Rev. Rev. A.S. R.G. Phys. Sakoh. Phys. E. Phillips. Soc. D. Phys.P.. Soc. 1972. 1968. Liefeld. J. 128. 1965. E.P.. Sucksmith. Wohlfarth. Wang. 1926.P. 7. Phys. and T. F. Appl. and J. 1955. I. Phil. 11. 1976. Soc. Phys.70 E. 38. Phys.. 372. Rev. Fuld¢. Lett. Mook.. and M.S.P. Phys. 305.S. Phase transitions and critical phenomena (Oxford University Press. S.. Japan 28. Phys. 1977. 41.G. Rev. Stoll. Callaway. 164. Nottingham 51.. LC. Fujiwara..C. 520. Tatsumoto. Physica Bgl. Wakoh.. 41. P. B6. R. 24. New York) p. Braun. Proc. Jacobi. Bohnen and P. H.. 1964.. Japan 21. 48. Butcher.. 1095.C. J.M. Phys. Phys.W. 2287. Phys.Z. Phys. E. E. 244. Callaway. BT. J. Phil. N. Appl.. 1972. Wohlfarth. Cailaway and C. H. Wohlfarth. Lett. Paris 5. S.T. 524.. M. 83.. and J.. Bryan.J. BI4. Trans. J. J. E..C.S. AS0. 571.C. Lett. . Phys. Quantum theory of atoms.. Roy. Soc. Takayama.A. 17.P. Soc. Polon. R..P.877. 4897. Smit. 1971. Stoelinga. L59. and S. 1388. J. 1962. and S. Phys. Yamashita. Japan 17. and R.. 40. 1960. 1976. Japan. D. Rep. Oxford)... B. Taniguchi. Phys. Phys. Soc.I. Can.P. 341 I. Phys. Wakoh. Phys. 933.. Physica 31. J. Wohifarth. Wood and K. 181. Wohlfarth and D. J. 40. Myers. 3.P. Rev. 574.P. White. 1348. Thompson.S. Phys. 48. Lett. 362. Thesis. Singh. Callaway. Rev. Phys. E.P. Mag.S. 1975.D.H. Tange. 1955. 25..P. Rosenfeld and G.P. Magnetics 14. 68. 1970. Wohlfarth.. Yamada.P. 1977. Wohlfarth and A. 1978b. and R. A225. J. Callaway. 39. C. R. 318.. Pavlovic. Phys. E. E.J. 59.V. E. Vollmer.. Stoner. and R. 153. 1968. Yamamoto. P. Smith. Tokunaga.M. and J.Phys. 339. Lett. Thompson. Slonczewski. Wohlfarth. Turtle... Physica 21. 260. Stringfellow. E. Wohlfarth. and J. H. Zornberg. 1962. 1978a. Mod. Rev. Roy. 1936. Soviet Phys. 30. Roy. Soc. J..D. Rev.D. 719. 1965. Hermanson and G. unpublished.C.H. Rev. R. Solid State Comm. 554. J. Stoner. 1971. Trans... 1970. Soc. Soc.E. 1968. S. Wohlfarth. Kontrym-Sznajd. Rev. J.E. E. J. Smith. Williamson. H. Phys. Phil. Tange and Y. B1. 1971. Phys. 459. Phys.. 1970. 115. Wang. G. E. J. 1712. and J. Mag. 362. Traum. Phys. Appl. 119. N. 20. Japan 18. E. Lett. 126. Physica B91. A235. A169. 1967. H. Fujiwara. 113. 7. Proc. Wohlfarth. 1973. Wood. Tedrow. 4194. Phys. Soc. M. Fedorov.H. J. 36A. 1123. E.E. O. Yamashita. 1970. D. 452.. R.P. E. Phys. Proc.. Woods. 1962. J.C. B9.M. Proc. Ingalls. 1953. 298.M. S. Prog. K.. Trans. 1977b. Phys. F4.P. 211. 1974. E. Sci. 38A. 374. F6. Wohlfarth. M.V.P. Mag. Williams. Rep. Williams. Lett. Phys. Wang. Solid State Comm. Thompson. 153. Mats. Szuszkiewicz. A251. 1968. Wohlfarth. 1978. 1977. 42.M. R. C. Young.P. 34. Rev. and H. 21. J.E.. Rev. 6.. 2179. Smit. 1966. Wong. BI5. and J. 1977.P. C. Amsterdam. Phys. J. Tsui. 1962. J. Rev. Rev. Zumsteg.L. 1951. Buckshpan and R. 27. 1939. 1959. and J. 1976. Weiss. Phys. 1973. W. Windsor. 1967. 29A. 1227. Phys. Lepeyre. A165. E. C2. 1205. E. Wang. H. and J. G.E. 517. Phys..P. 165. Naturforsch. J. H. Kato. Thompson. I.C. Wohlfarth. Phil. E. and G. CI. 1969. Meservey. J. Rev. de Vries. Roy. Stoner.. 485.M. Wanner.J. 1977a.M. M. Anderson. K. 1819. 35. E. Bll. J.C. and R. Tohoku Univ.D.R. E. Soc. Acta. Soc. 1938. S.J. Roy. Wohlfarth. 1974.C. P. 1954. C.. Wohlfarth. 1966. P. Japan. 1963. Hirooka. Kohihaas and M. Wohifarth. Rev. Phys. Rev. 1214. 1974. Comments on Solid State Phys. Gersdorf and G. Stoelinga. 950.M. 1959. E. 1970. 1966.. Mag.. 1970. 1967.. B7.S. 2417. Parks. Rev. 669. 1976. J. 27. 1969. E.B. C.E. Rev.. J. 131. J. Phys. Ann. Phys. Phys. 273. Tang¢ and T. molecules and the solid state (Academic Press. Wang.349. E. 123. Volkenstein. Phys. Phys. H. 1949. Stanley.K. 255. and A. E. E. Hum. Phys. J. 1971. Proc. Radium 20. Tatsumoto. 1270. 1976.. Phys. Soc. B14. B-I. Forrer.V. WOHLFARTH Wakoh. 21a. E.P. P. Vol. SPIN GLASSES* J. Ferromagnetic Materials. Wohlfarth © North-Holland Publishing Company.A. 1 Edited by E. MYDOSH AND G. 1980 "/! . NIEUWENHUYS Kamerlingh Onnes Laboratorium Rijksuniversiteit Leiden Netherlands *This work was supported in part bythe Nederlandse Stichting voor Fundamenteel Onderzoek der Materie (FOM-TNO).chapter 2 DILUTE TRANSITION METAL ALLOYS.J. . . . . . . . . . . . . . . . . . Appendix: Table AI on the main properties o f giant m o m e n t alloys . . . . . . . . 2. Spin glasses . . . . . . . . . . . . . . . . . . . . . 1.3. .3. . 4. . . . . T h e o r y of r a n d o m alloys . . . . . . . . . . . . 3. T h e freezing p r o c e s s . .1. . . . . . . . . . . .2. . . . . . . . . . . . . . . . . . . . Transition metal-transition metal combinations . . . . . . . . . . . . . . . . Mictomagnets and cluster glasses . . . . . . . . . . . . . . . . .I. . . . . . . . . . .2. . . Spin glass alloys .1. . . . . . . . . . . . . .3. 3. . . . . . . . 2. . . . . . . . . . Microscopic properties . . Conclusions and future directions . . . . .4. . . K o n d o effect and weak m o m e n t s . Macroscopic properties . . . . . . . T e r n a r y and special transition metal alloys . . . . .2. . . . . .2. . . . .2. Concentration regimes . . . . . . . . .CONTENTS 1. . 1.2. 3. . . Spin glass freezing . . . . . Macroscopic properties .3.4. . . . . 3. Noble metals with transition metal impurities . . . Listing of alloy s y s t e m s . . . 1. . . . . . 2. .2. . . 3. . . . . . . . . . . . Percolation and long range magnetic order . . . . . . . . . . . . . . 4. References . . . Giant m o m e n t s . Microscopic properties . . . . . . . . . . Survey of additional theories . . . . . . . . . . . . . . . 3. . . . . . . . . 4. . . . . . . 2. Introduction and description of terms . .3. . . . . 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2. . . . . . . . . . . . . . . . .1. . . . . . . . . . .1. . . . . . . . . . . . . . . .1. i. . . . . .2. . . . . . . . . . . . . . . Experimental properties . 4. .2. . . . Curie temperature determination and properties of other giant m o m e n t s y s t e m s 3.1. . . . Giant m o m e n t s . . R a n d o m molecular field model . . . 4. . . . . . . 73 73 75 76 79 80 81 81 82 84 85 88 88 91 101 108 113 114 126 133 137 137 143 143 149 150 152 175 72 . . . . . . . . . . i. . . . . . i. . . . . . . . . . . . . 2. . . . . . . . . . . . . . . . . . . .2. . . . . . . 3. . . . . . . Giant m o m e n t f e r r o m a g n e t i s m . . . .5. . . . .2. . . . . . . . . . . . . . . . . . . . .1. . . . . . . . . . . . . . . . . . 4. . .1. for each system a percolation limit can be defined (a critical concentration above which long range order occurs. For some alloys (the giant moment systems).1. Secondly and of prime importance in this article. ferromagnetic ordering may be expected at rather low concentrations. non-interacting or very dilute 3d-magnetic impurities dissolved in a non-magnetic host can be classified under the general heading of the Kondo effect. the interaction has an oscillatory nature and spin glass ordering will prevail. but for smaller concentrations the spin glass state is found) which will strongly depend upon the properties of the host material. Kondo effect and weak moments For very dilute concentrations of 3d-impurities in a non-magnetic matrix. Introduction and description of terms The subject of dilute transition metal alloys may be divided into two classes of interest.e. we consider the impurity spin-spin interactions which lead to giant moment ferromagnetism and spin glass "freezing".1. the second a random arrangement of frozen spin-orientations. yet. large magnetic clusters are formed and randomly freeze out at low temperatures. the 73 . this limit will be very low. Both of these effects depend strongly on the conduction electrons to propagate the magnetic interactions over large distances. ferromagnetic alignment. for other alloys this limit can be as large as the nearest neighbour percolation concentration. The boundary between these two dissimilar states of magnetism is controlled by the magnetic behaviour of these itinerant electrons. longer distances between impurities). Firstly. Here the nomenclature mictomagnetism or cluster glass is used. the long range. 1. the magnetic properties of the host material and the concentration of the magnetic component decisively determine the type of magnetism which may exist in the alloy.a localized antiferromagnetic interaction of the isolated impurity spins with the surrounding conduction electrons. These latter two cases represent different examples of magnetic ordering-the first a long range. If this behaviour is such that the indirect interaction is ferromagnetic over long distances. However. for smaller concentrations (i. Thus. As the percolation limit is approached from below. Therefore.or antiferromagnetic order. but non-uniform. since only the direct interactions can support a long range ferro. albeit non-uniform. However. and an analogous temperature may be defined as Ts~ = h/(kB'rsf). An alternative approach to the interaction between a local moment and the conduction electrons is the localized spin fluctuation model.74 J. editors.the Fermi energy. This leaves only an interaction with the itinerant conduction electrons which may be described by an s-d exchange Hamiltonian. NIEUWENHUYS magnetic spins may be treated as isolated from each other. For T < T~ the appearance of logarithmic divergences in the calculations denotes a broad temperature transition to a quasi-bound state which is unable to strongly respond to external magnetic fields (non-magnetic) and possesses an enhanced electron scattering cross-section (resistivity minimum at low temperatures).e.J. When this rate is greater than the orientation changes produced by thermal fluctuations k~T.~ TK. In table 1 a collection of Kondo temperatures is given for many of the alloy systems which exhibit interaction and ordering effects at sufficiently high concentration. At high temperatures the impurities behave like free (paramagnetic) moments. /~ = glxaV'S(S + 1). Heeger (1969). the moments becomes "weak" and lose their magnetic character. respectively.A. GrOner (1974) and Griiner and Zawadowski (1974). Here the local spin fluctuates in amplitude at a rate ~-~ where ~'sf is the spin fluctuation lifetime. the impurity becomes non-magnetic due to its interaction with the conduction electrons. 1971). good magnetic moments exist. . Van Dam and Van den Berg (1970). specific for each alloy system. Of course. while for T . below a characteristic temperature. i. These two models give quite similar experimental predictions.> T~. etc. we can greatly eliminate the role of the Kondo effect and weak moments by increasing the concentration and creating good moments via a strongly magnetic local environment: for. ~ = . or temperature TF). This temperature is known as the Kondo temperature TK and it signifies the breakdown of higher order perturbation theory which is used to calculate the physical properties from the s-d Hamiltonian. Here J(<0) is an antiferromagnetic exchange coupling. The enormous amount of literature on the Kondo effect has been summarized in several review articles beginning with Van den Berg (1964) and later Daybell and Steyert (1968). and N(0) is the conduction electron density of states at the Fermi surface. T~: = (D[kB) exp(-1/N(O)lJI) where D is the band width ( . 1973). Rizzuto (1974). for T . EF. The occurrence of the Kondo effect is thereby a hindrance to spin-spin interactions and magnetic ordering. As before a broad temperature interval separates the magnetic from the non-magnetic regime. and Fischer (1970. Thus.J $ . Below this temperature the moments are "weak" and cannot simply interact with each other. More recent reviews include the collection of papers in Magnetism V (Rado and Suhl. and for the present article we can assume the two characteristic temperatures to be equal. MYDOSH AND G. T~: (single impurity)>> TK (pair)>> TK (triple). and S and s represent the 3d local moment spin and the conduction electron spin. Kondo (1969). In the calculations. the impurity spin appears non-magnetic and there is additional conduction electron scattering. s. This behaviour represents the simplest type of ferromagnetic ordering to appear in a dilute.05/xR) m o m e n t on the 200 or so surrounding Pd atoms.% Fe) concentration due to the long range. For the description of a large number of experimental properties.1K IK 50 K 20 mK 0.2.DILUTE TRANSITION METAL ALLOYS. ferromagnetic interactions. yet experiments on P d F e reveal moments ---12/~a. these magnetic entities (impurity m o m e n t plus polarization cloud) can be considered as one magnetic m o m e n t which is then called "giant".2K <10-6K Transition metal-transition metal Mo Rh Pd Pt --100 K 200K 10 K 10 K 10 mK 0.3K 25 K simple 1000K 0. SPIN GLASSES TABLE 1 Isolated impurity Kondo (spin fluctuation) temperatures for important dilute alloy systems Host Cu Ag Au Impurity: V Noble metal-transition metal Cr Mn Fe 2K 10mK 1 mK 10mK <10-6 K 75 Co 500K -500K Ni >1000K ->1000K 1000K -300K 30K 5K 0. Thus. . Sometimes the term giant m o m e n t is also used for the large magnetic entities which are caused by chemical clustering of magnetic atoms or groups of nearest neighbours needed to produce a m o m e n t (local environment). parallel. random alloy. Figure 1 sketches a static giant moment. and ferromagnetism occurs at very low (0.1 at. localized. In this article we will use "'giant m o m e n t " only for those m o m e n t s associated with one "good m o m e n t " impurity.~. Giant m o m e n t s The term giant m o m e n t describes the unique behaviour of dissolving a single.1 K IK exchange enhanced 1. via a strong. itinerant electron polarization extending for about 10 . the Fe m o m e n t induces a small (---0. indirect. This overall m o m e n t is the sum of the localized m o m e n t plus an induced m o m e n t in the surrounding host metal. A typical example of such a system is P d F e in which the Fe m o m e n t is approximately 4/~B. magnetic m o m e n t in a non-magnetic host and thereby producing a net m o m e n t m u c h greater than that due to the bare magnetic impurity alone. Since this interaction is ferromagnetic the K o n d o effect is unimportant. Simultaneously. magnetic system characterized b y a random freezing of the moments without long range order at a rather welldefined freezing temperature Te.where ( ) refers to a thermodynamic average. while the second shows that. Here we shall only treat metallic systems which are composed of at least one transition metal component. although short range magnetic order may be present. there is less agreement on its exact meaning.->oo. The first equation demonstrates the random.R. MYDOSH AND G.1 Pd 2 nn !/i Ft" Pd 3nn I I J I t t PY°°i 8 © r. and the macroscopic moment for a spin glass in zero external field is always zero. ] I is the amplitude modulus and a configuration average over all sites. The spin glass state is a new phase which is not possible in a translationally invariant system. For the purposes of this article. *This term was first suggested by B.3. 6 Fig. freezing of the spins. but static.¢. S~. the above may be expressed (Sherrington 1976) as I(Si)J # 0 for T < Tf.76 J. this expression appeared.2 ~2E Pdlnn 0. 2 a. is with similar low lying metastable states believed to be important in the low temperature properties of " r e a l " glasses (Anderson et al. in a paper from Anderson (1970) linking localization in disordered systems with the magnetic alloy problem. . 1. NIEUWENHUYS 3 ~B(bQPe m o m e n t ) 0. there is no long range order.A. Much of the experimental behaviour is probably related to the existence of a large number of low-lying energy states which are metastable for the reorientation of small groups of spins. Pd. and (Si)(Si)~0 as IRi. 1972).J. The analogy. below-Tf. metallic.j~/J-. Mathematically. we offer the following working definition: a spin glass is a random. 1. A schematic representation of a spin glass alloy is shown in fig. Coles to be applied to the strange magnetic behaviour of the weak moment A_~uCosystem (Bancroft 1970). fop t¢. Spin glasses Due to the newness of the concept spin glass*. Giant moment polarization cloud (schematic). 2. apparent from the word "glass". again at Coles' instigation. • oooooooooJoo Ioooooo~. Such a wave packet has a local character. The freezing tern- . o. o .-~.d i m e n s i o n a l s q u a r e lattice).~o o o o o o o e o~o o o o Fig." QW~:ooooooo oooooooooooo~ooo-.t.h-o. e. P(H). ~ o ~ o ~ .p • o%0 o • e o • ~. o.. Yosida 1957) interaction. Cu or Au with about 0.'rv • o • of.~o oo:~oooooooo • • o ~ o • • • • • • • • • 0 • oq.~ o o o • • • ¶ e. 0 ~ .~o~o • • • • • • o~J~ o o o o o o o 9. order.. and a random distribution of directions because of the oscillatory nature of the RKKY. • ~%-~. SPIN GLASSES 77 oeooooeoooooooeeooooooooooooooo o~ • o. 3.o•o~oe••••• oo•~"o• • ooooooooo~q~Ooooooo~oooooooooo ooooo~ooo~o~ ~oooooooooooooooooo ooooooooo:~.o o ' ~ ' ~ o o o o o o o ~ o • • • • • • • • • • • o/o • o. H.. .~9. J is the s-d exchange. Consider a moderately concentrated magnetic alloy. . a wave packet built from superposing all the RKKY contributions with random phase. the effective molecular field. due to the infinite range interaction. which has the form ~..~Jooooooooo • ••••••••o~o• •o~O•~'VoJC•oJoofo• • o. the system has at most short range.% Mn or Fe.'oo • • oo•oJo• o q. ... is a superposition of contributions from all the impurities in the alloy. o.o~ooooooooooooe~eoo oooo~oooo ~'ooooooo~ooooooo oooo ~ooooooooooooooo~ooooo~oooooooo oooooo~oooooooooooooooooooooooo oooooooooooooo~ooooooooeooooooo Oo OOOO0000OO • Oo ooo oo 00o oo~oo~oo • o ~ o o o o o o eo o o i • o . The RKKY interaction between two impurities is shown in fig.~.DILUTE TRANSITION METAL ALLOYS. 0 . S p i n g l a s s w i t h m i c t o m a g n e t i c c l u s t e r s ( 2 . Furthermore.oo. N(0) the density of states per atom per spin of the host metal.....*0 oo oo oo o o • o o e o o o O o ~ o oooo~'. kF the Fermi momentum and r the distance away from an impurity.. ~(r) is oscillatory and of infinite range (neglecting mean free path effects).oooo~oooooo ooooo oooo o ooo oooo • ~ ' ~ 0 o oo ooooo~o oooo oooo oo ooo ooo • ~. The range of the magnetic order corresponds to the size of. H has a distribution of magnitudes.l o o o o oooooooo~ • • • a. 2.. Since the magnetic impurities h a v e random positions in the lattice at low concentrations. Note that the alignment may be parallel or antiparallel depending upon the separation between the impurities. o • o~o • • • • • oo • oo o o • o'o o o o o o o b. Kasuya 1956.o/~'~ • oio • • • • elototo • • • o~o oto • oo:o~f~oooooo~oooooooooo oooooooo • q'o~o~o • oo oo~oo oooo o oo ~ o o oo oo oo • ~o~.-~. The magnetic impurities are interacting with each other by polarizing the conduction electrons-the RKKY (Ruderman and Kittel 1954. but no long range. A more specific description of a canonical or archetypal spin glass has been suggested by Rivier (1974).~ • o ~ o • • • ~J__D • • • • • ~ .. This gives the random freezing or orientations of the spin glass moments. thus.o~ • • • • • • elf_.g.e • • • • • • e:e%'~ • • • • • • ~.~'~ o o o o o o o • .r.~o~'o ooooo o o o o o o o o o o o o ooooooooo~./o • • • o o • • • • • o o o o o e.1 to 10 at.'~ ~ ' .-_ 6~rZJ 2N(0) [-sin(2kFr) ks(r) (2kFr) 4 cos(2kFr)] _ (2kFr)3 J" Here Z is the number of conduction electrons per atom. ~ .~.. Again we use the thermal disorder energy. ~'(r) = A/r 3. ~'(~) = kBTf or Tf = c(A/kB).. Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two impurities in terms of the Pauli susceptibility XP. So there can only exist a ferromagnetic order when these all-parallel polarization clouds contain more than one impurity. the functional form of ~ ( r ) for a giant m o m e n t is more complicated (see section 4)... .. The same type of primitive reasoning may be applied to the giant m o m e n t alloys. 1 and 3. the molecular field from a spin S acting at a distance ~ on another spin S must be greater than thermal values for freezing to occur. the same procedure of setting kBT¢ = ~(F) (where Tc is the Curie temperature) may be used to calculate Tc(c) (Nieuwenhuys 1975). on average.r' -2 .J. Nevertheless.~. . In other words. . By considering only the amplitude of the R K K Y ... This means that no matter what the concentration is there will always exist a temperature for which the R K K Y interaction will be dominant and cause this random freezing. 1975).78 J. 1). E x c e p t at very large distance (very small concentrations).61 Y. An important difference between the giant moments and spin glasses becomes clear by examining the itinerant electron polarizations sketched in figs.e. which now destroys the correlations between the spins. . TK = 0. . MYDOSH AND G. i. For a low concentration alloy the average distance of impurity separation is ~ ~ ( l / c ) 1/3.. ~ apart. H o w e v e r ..A. NIEUWENHUYS 1o I I I I I I I . perature arises from a very simple model of D. the conduction electron polarization is always positive (see fig.. 00-2 X p) .A. 3.~ Od 2 xp) 2k~.. Here only good moments are assumed. At the freezing temperature.. Smith (1974. -4 -6 I I I I I I I I I I Fig.. we have the strength of the interaction as a function of distance. kBT. Mictomagnets and cluster glasses As the concentration of magnetic impurity is increased.000/zB form. among the randomly positioned impurities. Sometimes in the . with various times. 3) the oscillations introduce an element of "conflict".4. When the magnetic behaviour is dominated by the presence of such large magnetic clusters. along with plastic deformation can greatly affect the cluster formation and magnetic behaviour. In the spin glass case with its R K K Y polarization (fig. 1. SPIN GLASSES 79 For any arbitrary distance (except again the very largest). However. ferromagnetic order will result. 1972a. the terms mictomagnet or cluster glass have been used in the literature.or antiferromagnetically. Of special interest here are the hard magnetic properties such as the peculiar displaced hysteresis loops and the remanerlce and irreversibilities in the magnetization.b. and a long range. depending upon the particular 3d element (and the neighbour position). 1976a) use the name "cluster glass" to describe similar very large moment effects in more concentrated alloys. More recently. Coles and co-workers (Murani et al. The origin of mictomagnetism goes back to a series of early investigations by Kouvel (1963) and his "ensemble of domains" model. there is a greater statistical chance of the impurity being first or second nearest neighbour to another impurity. magnetic clusters can form as a result of concentration fluctuations in a random alloy. In addition. Tustison and Beck 1976.. Since the wave functions for the 3d electrons have a finite extent. Figure 2 shows some of these clusters within the dotted lines embedded in the spin glass matrix. there is an interatomic overlap and a direct magnetic exchange results. Thus. at these larger concentrations short range chemical or atomic order and even chemical clustering (non-solubility of the alloy) may occur.e. not fully localized as for example with 4f electrons. We need not solely restrict ourselves to the R K K Y interaction for any mixture of opposite interactions when combined with the spatial randomness can produce the conflict leading to the spin glass phase. This encounter of competing positive and negative alignments is essential to the formation of the spin glass state. has extended the experiments with careful consideration of the metallurgical state and invoked the concept of a random freezing. It has been experimentally found for a number of typical spin glass alloys that both of the above mechanisms produce a predominance of the ferromagnetic coupling and very large effective moments -----20-20. temperatures and cooling rates. Such deviations from randomness can greatly influence the local magnetism. the conduction electrons surrounding a giant moment are always positively polarized. 1977) who coined the word "mictomagnetism". Beck (1971. these clusters will freeze with random orientations in a manner analogous to the spin glass freezing. the mictomagnetic phase is especially sensitive to its metallurgical state. This adds a short range interaction which can couple neighbouring impurities ferro. Tustison 1976. i. Heat treatments. At sufficiently low temperature.DILUTE TRANSITION METAL ALLOYS. also called "frustration" (Toulouse 1977). However.g. the fcc (triangular) symmetry is unfavourable for antiferromagnetic order and many spins are needed to build this. loose magnetic clusters and weakly coupled "spines" to the central chain are present which can behave in a mictomagnetic way and perturb the long range properties. coherent. two sub-lattice structure in fcc space. e. that is. Since mictomagnetism and cluster glass refer to alloys of higher concentration. and . Then the closed bonds must continue in a macroscopic path through the crystal. introduced in section 1. Here. 1. For. Present interest concerns the behaviour of the loose spins and the "spines". of course. Here the percolation limit is =45 at. Sato and Kikuchi 1974). see fig. Now.g. For.2. When the concentration of magnetic impurities is such that the clouds of one impurity include other impurities and a ferromagnetic path reaches from one end of the sample to the other. requires 58% of the total sites to be occupied (Essam 1972). For a simple nearest neighbour ferromagnetic interaction in a face centered cubic lattice. this concept will not receive great attention in the following sections. above which we have a ferromagnet. long range. The schematic lattice in fig. Another type of percolation in bond percolation where an interaction or bond which couples two particular sites is present or absent.80 J. e. the percolation limit (that concentration for which there is a non-zero probability that a given occupied site belongs to an unbounded cluster) has been reached. as our title states. 2 is far below the site percolation concentration which.5. percolation is obtained.b. AuFe. We in this article reserve giant moment solely for induced moment systems.% magnetic component. we limit ourselves to dilute alloys. With antiferromagnetic bonding ffcc crystal). As mentioned before a modified concept of percolation is sometimes applied to the giant moment alloys. Percolation and long range magnetic order For the sake of completeness. Bond percolation is useful in describing the conductivity process (metal-insulator transition in disordered systems). each magnetic site will have at least one magnetic nearest neighbour. Duff and Cannella 1973a. NIEUWENHUYS literature the term giant moment is applied to these mictomagnetic clusters. 1. for a square lattice. the extent of the giant moment polarization will represent the magnetic entity. let us proceed and further increase the number of magnetic atoms. When such a macroscopic connection or uninterrupted chain extends from one end of the crystal to the other. concentrations less than 10 at. CuMn.A. At some given concentration for the particular crystal structure. Thus.J.% (Essam 1972. Percolation theory has been reviewed by Essam (1972) and Kirkpatrick (1973). The magnetic consequences of percolation are that a long range but highly inhomogeneous magnetic order occurs. a much larger concentration is necessary. the percolation concentration is between 16 and 19at. there can be no spin glass or mictomagnetic state above the percolation limit. MYDOSH AND G.% (Sato and Kikuchi 1974). above which we have an antiferromagnet. the critical concentration will be very small due to the large size (many lattice sites) of the induced polarization. the K o n d o t e m p e r a t u r e should be less than . s h o w n b y a " g o o d " in table 2: A___u_uCr.b) and the electrical resistivity (Ford and M y d o s h .A__uMn and A___ggMn. a n u m b e r of special cases exist. e. spin glass behaviour*: ( a ) " g o o d m o m e n t " s y s t e m s . r e p r e s e n t e d b y X T and XS. Since percolation and the resulting long range o r d e r require a non-dilute concentration. there is little tendency here to induce magnetic polarization on the host sites. in conjunction with a p r o p e r homogenization process. i. Noble metals with transition metal impurities We begin with the well-studied noble m e t a l . 1974a.there are only three other uncomplicated spin glass s y s t e m s . In table 2 the various c o m b i n a t i o n s of noble metal solvent-3d solute are given. Thus.g. This latter criterion. Besides the a r c h e t y p a l e x a m p l e s of C__uuMnand A__uuFe. Listing of alloy systems 2.DILUTE TRANSITION METAL ALLOYS. as f o r e x a m p l e with C___uuFewhich p o s s e s s e s a rather p o o r solubility and a TK = 30 K. p r o b l e m s are e n c o u n t e r e d for m a n y of the other c o m binations. . provides for a r a n d o m distribution of impurities and eliminates difficulties with chemical clustering. low field susceptibility (Cannella and M y d o s h 1974a. SPIN GLASSES 81 their effect on the overall properties of the system.3 d transition metal alloys. 1976a.b. giant moment behaviour will not occur. *Since the noble metals are all diamagnetic. respectively. 1974) are v e r y similar f o r these five alloy systems. M y d o s h et al.T h e e x p e r i m e n t a l properties.% of the 3d metal m a y b e dissolved in the noble metal host. with either the K o n d o t e m p e r a t u r e (see table 1) or especially the solubility limit.%. c > 10 at.e.1 K. we shall not discuss these c o n c e p t s in any detail. 2. XS or XT means that the spin glass behaviour is limited by lack of solubility or too high a Kondo (fluctuation) temperature. and (b) a f a v o u r a b l e solubility such that at least 10 at. and invoke two criteria to find the simplest. respectively. but nonetheless shows the TABLE 2 Spin glass combinations Impurity: Host Cu Ag Au XS XS XT XS XS GOOD GOOD GOOD GOOD XS + T XS GOOD XS XS XS + T XT XS XT V Noble metal-transition metal Cr Mn Fe Co Ni "'GOOD" represents the most favourable combinations.1. B y referring to table 2. so that n o complications are e n c o u n t e r e d with the w e a k e n i n g of the local m o m e n t s at low t e m p e r a t u r e s . H o w e v e r . / N ( 0 ) } -1. such that there is a large Pauli paramagnetic susceptibility Xv = 2/~N(0). 1971). 1974a) and magnetic susceptibility (F. That is. Tf. Frossati et al. The deviations from randomness (precipitation of Fe for c ~> 1 at. while for Pt. changing into broad maxima (Cannella and Mydosh 1974a). I.~dFe(/-~e~---12ttB). A non-noble metal system which may be grouped with the above collection is Z__nMn.f e w hundred K e l v i n . MYDOSHAND G. N(0). an intra-atomic exchange. As before TK is strongly dependent upon the local environment. binary combinations of transition metals may be examined for favourable examples of spin glass and giant moment systems. For this system an effective magnetic concentration of Co triplets should be used instead of the actual one.r N ( 0 ) } . upon further increasing the Mn concentration (c > 4 at. Boucai et al. modified spin glass behaviour is observed (Cannella and Mydosh 1974a..~ is the Stoner enhancement factor. we would include A__uuCofor which the Co solubility is poor. 1971a. 1975. but not as bad as C__uuFe. Also. a further requirement is an exchange enhanced host.. Smith 1973.The difficulty here is with the very l a r g e . 2.b. then. the hexagonal crystal structure is important to elucidate the anisotropy mechanisms present. Tholence and Tournier 1976).%). Table 3 gives a collection of the various possibilities. This results in an exchange enhanced susceptibility X =Xv { 1 . However.W. Although the solubility of Mn in Zn is rather limited (in the thousand ppm region).2.e.~ . Transition metal-transition metal combinations By using the previous criteria of good moments and high solubility. -= = 3. a triplet is required. the number of Co nearest neighbours. .6 ~ B ) (Crangle and Scott 1965).82 J. In order to reduce T~ ~ 1 K for AuCo (Tournier 1974). Beginning with the giant moment alloys. Such interaction effects are very difficult to observe due to the small probability of finding "pairs" at low concentration and the utmost in experimental sensitivity (SQUID devices) and ultra low temperatures (= 10 mK) are required (Hirschkoff et al. in this more complete category. yet Fe pairs or triplets may (Tournier 1974). F. should be present on the host sites. 1975). a large density of itinerant d-states should be near the Fermi energy. Secondly. For Pd. PdCo(/~en= 10/~) (Nieuwenhuys 1975) and P t F e ( ~ . i. 1977). -~ = 10. NIEUWENHUYS magnetization characteristics of a mictomagnet (Mishra and Beck 1973). This means that only Pd or Pt hosts will produce the giant moment polarization. Smith 1974b) show all the characteristics of a spin glass.8/~ff) ferromagnetism prevails (Nieuwenhuys 1975. Another special system Z__£Mn which has recently been investigated via magnetization and magnetoresistance also exhibits many spin glass properties (Jones et al. where the factor { 1 .K o n d o (or spin fluctuation) temperature. An especially interesting situation is with PdMn where for c < 3 at.J. at first. The simplest giant moment systems are P_. Star et al.A. The high TK means that isolated or single Fe atoms cannot participate in the magnetic interactions.%) are reflected in the low field susceptibility by the sharp peaks at the freezing temperature. Specific heat (du Chatenier 1964.% Mn the giant moment (/xe~= 7.W. 1976. Hence. increases (Hagasawa 1970. For. the probability of having two Mn atoms at first or second (or even third) nearest neighbours increases. This then supplies the essential element of "conflict" or " f r u s t r a t i o n " for the appearance of the spin glass phase. both have very weak moments in the dilute limit: TKP(_P_~Cr)~ 200 K and TKP(_P~Cr)~ 4 0 0 K (Star 1971). 1976). On the contrary. 1975a.R K K Y spin glass with two completely different exchange mechanisms (Nieuwenhuys and Verbeek 1977). Williams et al. For example. locally "blot o u t " the uniform exchange enhancement. and then. XS or XT means solubility or too high a Kondo (fluctuation) temperature limits the appearance of both the spin glass or giant moment states. Tholence and Wassermann 1977). Zweers and van den Berg 1975. in a non-enhanced Pd or Pt . 1979).DILUTE TRANSITION METAL ALLOYS. becomes a (semi) giant m o m e n t ferromagnet (p. P t M n has a good m o m e n t and conflicting exchanges. when introduced into the Pd or Pt host. Zweers et al. with sufficient Cr present. 1975. when stabilized by increasing the Co-concentration. An anomalous mixed phase with peculiar experimental properties occurs between 3 and 4 at.M n antiferromagnetic exchange to the longer ranged ferromagnetic giant m o m e n t polarization (Coles et al. Cr impurities. A similar pair of systems are P d C r and PtCr. and thus shows typical spin glass effects (Wassermann and Tholence 1976.b). but in this process the Cr loses its magnetic m o m e n t (weak m o m e n t with a high TK). Mn nearest neighbours couple antiparallel and thereby produce the competing M n . Van Dam 1973).% (Guy and H o w a r d 1977. The platinum host alloys and their smaller exchange enhancements tend more readily towards spin glass and weak m o m e n t behaviour. PdMn m a y be regarded as an example of a n o n . mixed behaviour of PdMn. P t C o is a weaker m o m e n t system which. the total room temperature susceptibility at first decreases. Swallow et al. Moreover. now however.a) (Crangle and Scott 1965. as the Cr concentration is increased. A simple interpretation can be made in terms of the following model (Mydosh 1976). SPIN GLASSES TABLE 3 Transition metal-transition metal spin glass/giant moment combinations Impurity Host Cr Mn Fe Co 83 Mo Rh Pd Pt XT XT XT SG SG GM + SG SG XT GM XS + T simple XT GM XT SG GM SG exchange enhanced SG and GM represent favourable combinations for spin glass or giant moment behaviour. 1975. Only when the Cr concentration is large enough to provide a suitable Cr local environment does a stable or good Cr m o m e n t appear. Nieuwenhuys et al. 1977).~ ~ 4p. Note the strong. Here there is some recent evidence that a spin glass state may exist between the weak and giant m o m e n t phases (Rao et al. For example. Ford and Schilling 1976. For the majority of systems there is a general concentration dependence from non-magnetic.. By utilizing certain binary combinations for the host. The special cases of R___h_hFe (Murani et al. and thus. table 3 lists three favourable candidates for spin glass behaviour: MoMn. Since the host metals are not exchange enhanced. Neutron and M6ssbauer measurements give values of/~ar up to 80#B (Cable and Child 1973. Co. The same procedure may be employed to generate really giant moments by doping Fe into CuNi. 1976.A. Little is known about Cr in Mo or Rh and we would speculate that they fit into the general scheme of weak moments (Coles et al. but nonetheless giant moment P_. MYDOSHAND G. Here there is no giant moment phase. 1970. VFe and VMn. to finally. a giant moment regime is not possible here. Ni3Ga(~ = 35) and Ni7~126(--. RhNi. Liddell and Street 1973). Ternary and special transition metal alloys A few additional systems should be briefly cited to complete this survey of giant moments and spin glass alloys. a long range ferromagnetic (Ni. For c < 2 at. NIEUWENHUYS matrix.3. by polarization effects.= 25) (the stoichiometric compound is an itinerant ferromagne0.2. Fe) or antiferromagnetic (Mn. giant moments (Chouteau 1976). At this point we should also mention the weak. 1971) which become spin glasses above a definite concentration. Mn or Cr nearest neighbours are present to produce the local magnetic moment which is per se a magnetic cluster. RhMn and MoFe. Ling and Hicks 1973. Caudron et al. The latter system has already been found to exhibit typical spin glass properties (Amamou et al. and such alloys represent a canonical example of a localized spin fluctuation system (Lederer and Mills 1968).% Cr in Pd (Roshko and Williams 1975). 1974) are weak moments and require a sufficiently large concentration of magnetic impurity (---1 at. giant moment ferromagnetism (/~c~.%Ni.% Cr in Pt (Roshko and Williams 1977).% Fe and 20 at.% Ni there is no local moment associated with the Ni. when diluted with Fe impurities all yield super-giant moments. weak moments. the exchange enhancement can be greatly increased. Rusby 1974) and RhCo (Coles et al. RhNi or PdNi hosts where the Ni concentration is kept . the word "dwarf" or "destroyed" moment is more applicable.5/~a) appears with a rapidly increasing Curie temperature Tc(c) (Crangle and Scott 1965). Co. Above 2. Returning to the dilute alloys and considering the simple hosts Mo and Rh.J.84 J.2at. Fe. Cr) order. The Cr concentration necessary to produce the spin glass type of order is at least 7 at.ddNialloys. and =17 at. The model used here is that the Ni atoms belonging to nearest neighbour groups of three or more are magnetic and produce. if anything.% Co) before spin glass behaviour manifests itself. 2. The word weak as used in this article refers to the "environment" model stipulation that a particular number of Ni. the R K K Y oscillating interaction can occur leading to a spin glass state at low temperature. 1977). This descriptive model may further be applied to the higher concentration alloys such as CuNi. to an intervening spin glass or mictomagnetic regime. This leads us to the general conclusion that the spin glass phase is the most common in random dilute alloys. Mn or Cr. leads to the formation of the spin glass state (Budnick et al. the problem of amorphous magnetism presents itself. for 60at. however. A large assortment of disordered alloys may be fabricated in thin film form by quenchcondensation or sputtering. and there are very few of these available. However. Concentration regimes It has become clear from the preceding sections that the concentration is most important in determining the magnetic state of the alloy.% Ag substitutional in Pd (Hoare et al. Mydosh 1974. a large exchange enhancement may be attained. Thus. thus preventing the study of giant moments in an amorphous host. Kim and Schwartz 1968) can lead to a conflicting interaction and the spin glass state.% Fe) giant moment and the low (0. amorphous systems with a large exchange enhancement have not been produced. Up until now we have considered crystalline (even single crystal) metallic systems with a random distribution of 3d-impurities. and below the Kondo tern- . 2. the host is diamagnetic (pseudo-noble metal-like). and the further addition of 3d-impurities.28 at. 1965b. 1953. There is yet another method to increase the exchange enhancement of Pd and that is alloying with a few percent Rh (_~ = 12 for Pd95Rhs). Figure 4 gives such a schematic representation. positive polarization of the giant moment system (fig. the exchange enhancement of Pd or Pt may be reduced and even totally destroyed (diamagnetic susceptibility) by alloying with silver or charging with hydrogen. magnetic alloy. A recent investigation of the high (0.DILUTE TRANSITION METAL ALLOYS. which makes the creation of the giant moment and the resulting ferromagnetism possible.% Fe) spin glass concentration differences has been carried out via positive muon depolarization experiments (Nagamine et al. SPIN GLASSES 85 below that for ferromagnetism. Burger et al. and in bulk form by splat cooling. Mehlmann et al. Fe. Consider now a concentration regime division for a conducting non-enhanced. 1973) and an interstitial H/Pd ratio of 0. 1975. Conversely. Co. the strong.c). with the selection of a particular host. Levy and Rayne 1975. which result in the Kondo effect. 3). By relaxing the condition of lattice order.015 at. 1974.4. At the very dilute magnetic concentrations (ppm) there are the isolated impurity-conduction electron couplings. the large distance.65 (Jamieson and Manchester 1972). There exists adequate experimental evidence that a simple spin glass state does occur (Mydosh 1978). Thus. However. Nevertheless even for the simple PdFe system. 1976). 1977a.b. This localized interaction causes a weakening or fluctuation of the d-electron spin. We might expect here certain difficulties especially regarding the reduced mean free path and its effect on the conduction electron polarization. at very dilute Fe concentrations. So far. 1976. rather small negative conduction electron polarization (Moriya. the extra electron scattering caused by the Rh prevents any significant increase in the/~en produced with the inclusion of Fe. 1) is altered into the weaker oscillations of the R K K Y interaction (fig. .~. ~ .~ .86 J. MYDOSH A N D G."'.. 0 "~ 0 0 .A.. 0 o o: m . i N u o 0 o I. m o 'J T ¢o 0 "2 ~N o: .:"'~ "= '~.w :. c~ ~ 0 c~ .~" • .J'.:':":'..:::..- > "4 . N I E U W E N H U Y S o 0 % .--.'::.J.~ i5 .::::::'i":'.:::':'"::??T.':1. v. When the magnetic behaviour is dominated by such clusters. remanence. but inhomogeneous ferro. 5 such a general scheme is shown. and scaling the three temperatures of interest TK.c phase diagram. we take TK = Tf(c0) as the concentration. Then as the local environment builds good moments (c > co). namely the freezing process at Tf. Yet. the spin glass regime for a giant moment ferromagnet may compose only a very narrow concentration region.~ Tf and with the incorporation of dipolar interactions ( ~ !/r3). the local environment model tells us that there will be "pairs" (or "triplets") which possess a much lower Tr than the singles. there is no lower concentration limit to spin glass consequences. Usually. etc. Tf and To. the spin glass regime appears. we would employ the term spin glass almost up until the percolation limit above which a long range. Here. So by properly adjusting the values of co and cp. however. The qualifying "almost" has to do with the existence of magnetic clusters 20-20.5at. we have the weak moment concentration regime. 5. specific heat. which exhibits the most dramatic experimental effects (see section 3.) are universal functions of the concentration scaled parameters Tic and He. co.2). it is the random freezing. the Kondo effect prevents strong impurity interactions which are the basic ingredients of the spin glass problem. long range magnetic order is present. in principle. which also scale with c. In addition..t/c. Nevertheless. These good moment pairs may then interact with other pairs and give rise to spin glass behaviour.SPIN GLASSES 87 perature the impurity appears non-magnetic. Thus. 1977). . any of the previously mentioned alloy systems may be described within the very general phase diagram depicted in fig. the magnetic behaviour may be nicely described within the model of N6el super-paramagnetism (Tholence and Tournier 1974. in addition Tf ~ c. the nomenclature mictomagnet or cluster glass is used to emphasize the anomalies generated by these very large magnetic clusters. Figure 4 indicates these various concentrations for a typical noble metal-3d alloy.000/~B just below the percolation concentration. 1977). 4 in order to give it the character of a T . persisting over an extended concentration range. Therefore. TK represents an average Kondo temperature which decreases as a function of the concentration. and finally above the percolation limit cp. a more general class of behaviour is present to much higher concentrations. Up to a concentration of a few thousand ppm (-~0. Although the scaling regime and its associated model represent an adequate first order approximation at low c. The giant moment alloys may also be included in this scheme with co and cp much less than in the previous example. This means that the measurable properties (magnetization. below which the Kondo effect plays a large role in modifying the spin glass behaviour (Larsen et ai. In fig.DILUTE TRANSITION METALALLOYS. until we run out of measurement response or temperature. At low temperature T . For TK > Tf.%). based upon the RKKY exchange is particularly appropriate to the problem of interacting impurities. A temperature dimension should be added to fig.or antiferromagnetic order occurs. a "scaling" approach (Souletie and Tournier 1969). c phase diagram for a dilute magnetic alloy.1. while Kim (1970) attacked the many impurity problem. 5.88 J. If the host material were a normal metal in which the conduction electrons can be treated as free electrons. The occurrence of the giant moment is then depicted by assuming that the bare magnetic moment of the dissolved 3d-atom polarizes its surroundings. the generalized susceptibility will alter from the RKKY form to roughly (within the random phase approximation) . itinerant.4_.3). Experimental properties 3.. in order to understand the magnetic properties of alloys exhibiting the giant moment phenomena. with special attention to PdNi. and the polarization. if the intra-atomic exchange interactions between tlie band electrons are important.A. one should first understand the origin of these moments by treating the atomic physics of the 3d-atoms in a surrounding of highly polarizable.J. Therefore. this susceptibility x(r) is given by the RKKY formula (see section 1. General (schematic) T . In this case no significant polarization would be present. Fe and Mn impurities in Pd and Pt by Moriya (1965b) and by Campbell (1968). II/ """"x / co Cp C Fig. NIEUWENHUYS T LRO Tf TK / ~. For the purpose of this introduction we adopt a description of the giant moment based mainly upon the linear response approximation. is governed by the generalized magnetic susceptibility of the host material. This problem has been discussed for Co. MYDOSH AND G. as a function of distance. since the spatial integral over the susceptibility would approximate zero (neglecting the nonphysical small distance divergence). host-electrons. However. 3. Giant moment ferromagnetism The giant moments associated with the 3d-transition metal atoms are directly related to the large magnetic susceptibility of the host metals in which they are dissolved. 2) where kF is the Fermi wave vector.IXRKKV(0)} -~ defines the Stoner enhancement factor _-". to a giant moment. (3. The ferromagnetic ordering occuring in alloys which exhibit the giant moment phenomena might now be explained by a model similar to that used to explain the spin freezing in the spin glasses (see section 1.4) where cr equals ~3.IXRKrv(q) (3. The magnitude /~en of the giant moment is given by (Takahashi and Shimizu 1965. Schrieffer 1968).DILUTE TRANSITION METAL ALLOYS. Substituting eq. The simple relation given by eq. Doniach and Wohlfarth 1967) /~eff ----"/~bare(1 q. 6).fXp + ~(q/2kF) z" Xp (3. oJ = 0) = XRKKY(q) 1 -. the result being x ( r ) = Xp-~r exp(-r/~r) 3k 2 . (3. They concluded that the polarizability decreases with increasing polarization. Whether this giant moment will be sensed in an experiment as a magnetic unity. the spatial integral of X = x ( q = 0) may considerably differ from zero. This effect has experimentally been observed in Pd and Pt based alloys by a decrease of the total magnetic moment per impurity at increasing concentrations (see fig. and lead to an extra net polarization in the host metal.3) x ( r ) may be calculated by taking the Fourier transform of eq. Kim (1966) argues that the presence of the magnetic moments implies an extra exchange interaction between the band electrons and thus drives the alloy to itinerant ferromagnetism. will be a point of future discussion. and thus.-1 /z. SPIN GLASSES 89 x ( q .1). O) = 1 + ~(q[2kF) 2 (3.otX(q ----0)) (3.5) breaks down when the itinerant electrons are very strongly polarized.3). Thus. which for small values of q can be approximated by 1 u(q. 0) = 1 .3).a.5) where /Zbar~is the bare moment (as measured on an isolated atom in vacuum) of the dissolved magnetic atom and a is a coupling constant. (3. in the case of an enhanced magnetic susceptibility of the host metal. The generalized susceptibility of the RKKY form is proportional to Xe (the Pauli susceptibility) times the Lindhard function (Lindhard 1954). In this formalism the extra exchange enhancement is obtained by eliminating the local moment-itinerant electron interaction via a . (3. the exchange enhanced generalized susceptibility becomes x ( q .2) into eq.F. On the other hand.1) where {1. (3. Kim and Schwartz (1968) examined the spin polarization around a localized moment in a magnetized band. and f is a measure for the strength of the intra-atomic exchange interaction (see Kittel 1968. (1965b). P d F e dilute alloys would be an itinerant ferromagnet even if the Fe localized moments were in the paramagnetic state.90 PB ~M 12 ". I . at fairly small concentrations of magnetic atoms. Maley et al. All data have been obtained from magnetization and susceptibility measurements.[XP). Craig et al. I . Phillips (1965).. 6. (1962). they reach the following conclusions. versus concentration. Without magnetic ions. Kitchens et al. Either the indirect interaction will be of long range and positive.A. except those indicated by M. canonical transformation. (1962).2. Unfortunately. T h e y assumed the properties of the host to be independent of the magnetic concentration and the polarization to be uniform (no distance dependence).% Fig. a ferromagnetic order of the giant moments. which have been deduced from M~ssbauer experiments. Moment per solute atom nB. expressed in Bohr magnetons. F r o m a comparison with the experimental results these authors deduced that S should have . (1970). No matter which of the models is adopted to explain the ferromagnetism. which later measurements showed to be inapplicable to deduce the magnetic m o m e n t (Nieuwenhuys et al. Craig et ai.. and with magnetic impurities. Clogston et al. NIEUWENHUYS I ' I ' J I ' ] 1~ 8 ~M -Co 6 . -1 n~2. According to this point of view. (1967). the ferromagnetic phase transition taken place at Tc = cg2S(S+ 1)~Z2Xo]3kB.1. (1962). the susceptibility is given by X0 = Xp/(1.~. Crangle and Scott (1965). by analysing experimental results on the basis of their intermediate model. Bozorth et al. (1965). Takahashi and Shimizu (1965) developed a transparent molecular field model. J. the host will be near the Stoner criterion for itinerant ferromagnetism. MYDOSH AND G. which treats the giant m o m e n t problem in a simple way. Burger (1964). I . I . Foner et al. We will come back to this point in section 4. °o 2 4 6 8 or. Denoting the interaction between the itinerant electrons by T and the interaction between the itinerant electrons and the localized impurities by o~. where S is the magnetic quantum number and c the concentration of magnetic atoms. Data sources: Crangle (1960). these authors used the high temperature susceptibility results. This figure has been taken from Boerstoel (1970). or approached from another point of view. 1978). A similar conclusion had already been reached by Rhodes and Wohlfarth (1963).J. it is clear that the exchange enhancement of the host will create. McDougald and Manuel (1970). the main results of the experiments are tabulated in table A. Star et al. the Fermi level will lie near the upper boundary of the narrow d-band. consequently the 5s and the 5p states will be filled up to the Fermi energy. 1972).3 x |0-19J (1.1. Magnetization and susceptibility Let us focus attention on the simplest alloys: PdCo. Due to the fact that the main part of the itinerant electrons at the Fermi level are strongly interacting 4d-electrons. and thus to a larger Pauli susceptibility than expected for normal metals.8eV) higher (McLennan and Grayson-Smith 1926).1 at. it is obviously impossible to discuss them all. The question whether the giant moment can be considered as a (dynamical) magnetic unit.DILUTE TRANSITION METAL ALLOYS. Macroscopic properties Experimental evidence for the existence of giant moments associated with 3d-impurities dissolved in exchange enhanced host materials can be obtained from magnetization and susceptibility.1. the magnetic susceptibility is further increased by a factor of about ten. however. Pd as host material is one of the best with which form giant moments alloys.8/~B per Mn atom (Bozorth et al. Fe and Mn on Pd there are two striking features in the experimental data from the magnetization measurements.%) (same references). 3. by taking examples from the Pd-based alloys. the so-called Stoner enhancement.3 × 10-12erg) (or 0. causing the 4d-band to contain only 9. Due to the large amount of previously reported experimental results (over 300). In section 4. causing ferromagnetism. Regarding Co. and 7. In metallic Pd the 5s and 5p states are lowered in energy due to the changed boundary conditions (Hodges et al. The strength of the magnetic interaction in the alloy. Then a general discussion of the other alloy systems will follow. The electronic structure of the Pd-atom consists of the krypton inert gas core surrounded by 10 (full shell) of 4d-electrons. as will be discussed later on. 1970. In the following sections the experimental results will be discussed within the framework sketched above.2 we shall return to the theory. This means that the intra-atomic interactions are only 10% too small to drive Pd into an itinerant ferromagnet. 1961. To. PdFe and PdMn. specific heat and transport measurements. 1 in the appendix. might be answered by the value of the magnetic quantum numbers and the effective g-value. 1975). These To-values as a function of the concentration also contain information about the strength of the interaction as a function of the distance between impurities. and ferromagnetism persists down to fairly low concentrations (~0. Therefore. giving rise to a large density of states at the Fermi energy. the energy of the (4d)9(Ss) I configuration is only 1.SPIN GLASSES 91 a small value (between 1-2) for Fe and Co dissolved in Pd. is characterized by the value of the transition temperature. McDougald and Manuel 1968.64 electrons per atom instead of 10. The giant moment is fairly large (10-12/~B per Co or Fe. In the following paragraphs we will restrict ourselves to the general features exhibited by the various properties. Therefore. ~. Therefore. The . The effective moment deduced in this manner from the Curie constant is in fair agreement with the value obtained from the saturation of the magnetization (see table A. MYDOSH AND G. NIEUWENHUYS critical concentration for ferromagnetism is thus very low compared to other alloys (AuFe). 1964). T0 was obtained from an Arrott plot of H/o. . 1962). i. the number of Bohr magnetons for aX0(80K) = 5 and c~X0(80 K) is 9.A. Thus. The gradual transition obviously finds its origin in the statistical concentration variations present in the alloy (which are relatively larger at lower concentrations) combined with the strong distance dependence of the magnetic interaction (being r -~ exp(-r/tr)). 8) the magnetization as a function of temperature at different external magnetic 24o "-5 ×lOS i i i i i i D . respectively. obtained from plots of X-~ versus T and the ferromagnetic transition temperature deduced from Arrott plots (Arrott 1957). 1964).J. This "difficulty" in determining Tc is presumably caused by the width of the transition to the ferromagnetic state.5.% Co in Pd for different enhancement factors. H o w e v e r .92 J.% Co dissolved in Pd.XPd = + °tXed(T))2 3kB(T . to be simply proportional to the host susceptibility (Clogston et al. i/(x . the excess susceptibility due to the magnetic impurities is represented by 02 2 c p e f f Ot 2 Xpd(T) X . Another remarkable aspect of the behaviour of the magnetization is its difficulty in achieving saturation at the higher concentrations. Pelt. 7.0) or cP°ff2(l X -.1 in the appendix). These non-linear deviations become relatively larger as the concentration of magnetic atoms is reduced. as is further revealed by other experiments. 7 we reproduce the susceptibility of 1 at. the transition from the paramagnetic state to the ferromagnetic one occurs gradually at lower concentrations.e.O) (3. or by assuming Pefe to be equal to p~(1 + otX0) (Shaltiel et al.d/I o_ "-% x 8o @ ~ f. The incorporation of this temperature dependence can be done in two ways: either by assuming the Curie-effective moment. !°/o Co in PO ~.6.7) In fig. The magnetic susceptibility follows a modified Curie-Weiss law when allowance is made for the temperature d e p e n d e n c e of the host susceptibility (Van Dam 1973).versus tr2 (after Shaltiel et al. the Arrott plots are not always the desired straight lines. As an example we show (fig.Xpd(T) = 3kB(T . there exists a large discrepancy between the paramagnetic Curie temperature.t- i I O T --T t' c 80 I 160 I I 240 K Fig.85 and 10. Also.X0) curves for 1 at. .1 T).4 T (54 kOe) and T = 1. 9 (also m e a s u r e d by Star..5K T = 4. Magnetization of PdCo 0.24 at.5 K the m e a s u r e d magnetization per Co a t o m is only 8t~s.. T = 1. 8 12 16 K 20 Fig.001 T [B < 10 G]) in m o s t cases via the a.4 M T' 4. An explanation for this effect cannot be given straightforwardly without k n o w l e d g e of the band structure of the alloy• A p a r t f r o m using the C u r i e . or Maxwell 1965).W e i s s fit to determine the Curie t e m p e r a t u r e f r o m the susceptibility. .3. see N i e u w e n h u y s 1975). This type of 8 / . since d M t o t / d S e x is 8. Wiebes et al. fields o f P d C o 0. E v e n at 5.DILUTE TRANSITION METAL ALLOYS. 2 5 K as a function of temperature.% as a function of temperature. Excess magnetization of PdCo 0. No saturation of Mimp has been achieved.'. as can b e seen f r o m fig. 8..g.c.% at T = 1. SPIN GLASSES 12 I I t I ' -- 93 ~'8 o I kOe a 1 8 kO~" COat ~ 9 kOe v 27 kOe • 54k0¢ 8 . induction m e t h o d (see e. 9. while the saturation magnetization per Co impurity ( m e a s u r e d in alloys with lower concentration) is m u c h higher. 1964.42 x 10 -4 emu/mol. one can also use results for t h e susceptibility obtained at t e m p e r a t u r e s in the vicinity of Tc in v e r y small external magnetic field (B < 0.24 at.% as m e a s u r e d b y Star (see N i e u w e n h u y s 1975). (1 kOe = 0. T h e transition t e m p e r a t u r e is then f o u n d f r o m the knee in the X versus T c u r v e in the case of a ferromagnet.35 K and T = 4 . The susceptibility of Pd has been assumed to be 7.1 at.2 X 10-4 emu/mol at 50 kOe and 1.25 K CO H i i 10 ~ I 20 i ) 30 f kOe 4-0 Fig.35 K. 10.% for parallel fields up to 250 Oe.1 in the appendix. x(T) of PdCo 3 at.025 T [250 G]) the main X versus T curve became rounded and an additional sharp peak appeared at a temperature which was then identified as To. (1975). all taken during warming. N I E U W E N H U Y S 100 \.A.J. and to PdGd alloys by Cannella et al. The results found in this way are marked by an * in table A. to PdAgFe alloys by Budnick et al. Their X versus T curves did not show a knee sharp enough for an accurate determination of To. The vertical scale has been multiplied by factors shown on the curves (1 Oe = 10-4Tesla) (after Maartense and Williams 1976).% as an example of this low field methods. MYDOSH AND G. (1974). Specific heat Investigations of the specific heat of Pd-based giant moment alloys have been . to P__~dMnalloys by Nieuwenhuys (1975) and by Zweers et al. measurement has been applied to P__ddMn. Maartense and Williams (1976) used this susceptibility method for P_ddCoalloys in a somewhat different way. after applying a small dc magnetic field (up to 0. (1977).94 J. In fig. \ L__ x. x3 t0 T{K) Fig. However. 10 we reproduce the results obtained by Maartense and Williams (1976) on PdCo 3 at.PdCo and P__ddFealloys by Burger and McLachlan (1973). DILUTE TRANSITION METAL ALLOYS.35 at. N i e u w e n h u y s et al• (1972) and N i e u w e n h u y s (1975).o. AC versus T for PdFe 0. Wheeler (1969). 1E I Oi / AC / / 7 • T 4 8 ll2 K 16 Fig.1T). C h o u t e a u ct al. Experiments on the specific heat of dilute alloys cannot be performed over a wide concentration range.~. Boerstoel et al. (1972). so that in practical cases accurate specific mJ i I J a o ~a o Q 12 °° 4 AC' • H = !O kOe o 4 ~ K 12 Fig. (1965). . 2E • oo° • mJ mol K 2¢ . the specific heat of the host materials has to be subtracted• This latter contribution increases roughly proportional to T 3. since in order to deduce the extra specific heat due to the magnetic atoms. SPIN GLASSES 95 carried out by Veal and R a y n e (1964). i lb.% (I kOe = 0.% at zero external field. lla. AC versus T for PdFe 0. Coles et al. Boerstocl (1970).23 at. (1970). the multiplicity) of the giant moments are mainly governed by the dynamics of the bare magnetic moment of the impurity. As can be seen from the figs.A. % . 1972) as well as of the magnetization (Star et al. 200 I Pd .g. The magnetic entropy.%. I I ' (g at) K 150 mJ _ ~ d l © © O~) T 2 4- 6 8 K 10 Pig. These small values for the entropy have been found by extrapolating the magnetic specific heat to higher temperatures as T -~.45 at. 11. b.J. .96 J. (c)1.35 at. and for PdMn in fig.% and (d) 2. an analysis of the specific heat (Boerstoel et al. i 9 a t . Cmwes c' and d' represent measurements after 220 hours homogenization at 1000~C subsequent to the usual homogenization (24 hours at 950°C) (after Boerstoel et al. AC versus T o f P d M n alloys containing ( a ) 0 . quantum numbers obtained from magnetization experiments by fitting the experimental data to a Brillouin function (incorporating an appropriate molecular field) are generally much higher (of order of 6) for Co and Fe in Pd.%. 2 for Fe and ~ for Mn). 12. Typical curves for the specific heat of PdFe are shown in fig. the conclusion must be drawn that the dynamics (e.%. However.% at H. In the case of Mn the curves have much sharper "bending" as a function of temperature. 12.x = 0. but it should be noticed that the concentration of Mn is much higher than that of Fe.35 at. Sin= cR ln(2S+ 1)=f(Cm/r)dr. (b) 0. the magnetic ordering in these dilute alloys gives rise to a wedge shaped maximum in the magnetic contribution to the specific heat. and for Mn up to 9 at. This limitation implies that the measurements on Co and Fe which span Tc must be carried out for c < 0. deduced from the specific heat results agrees with a small value of the magnetic quantum number of the giant moment (~ for Co. this contradiction does not exist in the case of Mn.54 at. Therefore.Mn I . 1la. M Y D O S H A N D G. 1975) gives the same small quantum number (-~). The broad maximum (in contrast to the A-shaped peaks found in the pure ferromagnetic metal and many insulators with a translational invariant magnetic lattice) is obviously due to the gradual character of the magnetic transition in these random systems. Remarkably. N I E U W E N H U Y S measurements are limited to T < 3 0 K . The large magnitude of the magnetic moment of Fe is revealed by the relatively large field dependence of the specific heat. 19?2). 8T [18kOe] and (c) B = 2.and they obtained quantum numbers of order 5. b I 0 T :.. 14 on P__d_dCo0. SPIN GLASSES 97 There have been several attempts to solve the observed discrepancy between the results for the magnetic quantum number as obtained from the specific heat and those from the magnetic measurements.075 at." . (1970) have pointed out that the high temperature extrapolation as a T -2 is not correct for random alloys.~ 1. which is still much smaller than those obtained from magnetic measurements._ . Chouteau et al.%. if the measurements are extended up to 30 times Tc (as was done by Boerstoel (1970) in the case of PdCo 0. 13.% I|. and since the specific heat should (apart from details) behave like Be. PtCo.2 + b T -I to analyse their results on P__ddFe. the coefficient b appeared to be much smaller than a. resulting in an error in the magnetic quantum number of only 15%. for measurements in large external fields (Boerstoel 1970). (1973) and Nieuwenhuys (1975) on P__ddMn. I ~ I ~ I ~ I .'. the specific heat will only contain part of the total entropy and this results in too small a magnetic quantum number. (1972).7 T[27kOe].. . From the results of these experiments the magnetic quantum number can be calculated via the entropy content. Such experiments have been carried out by Boerstoel et al. and in fig. In fig. 9 T [ 9 k O e ] . Specific heat experiments on dilute alloys in large external magnetic fields may reveal an answer to this discrepancy.190t.(dMldT).075 at. 13 the results are shown of an experiment on PdMn 0. Nieuwenhuys et al. (1970) is correct.%.. In the case of zero-field measurements the extrapolation as used by Chouteau et al. there are a number of magnetic moments still coupled at temperatures far above To Therefore. I ' I ' I ' I ' I ' I ' mJ /__'~_--_ _ Pd-Mn 0.19at. I J . These authors used an extrapolation according to a T . AC versus T of PdMn 0.dashed curves: Schottky specificheat (after Boerstoel 1970). Koon's argument is certainly correct for measurements not extending to about 10 times To.% at ( a ) B = 0 . However..19at. a Brillouin function fit as used in the analysis of the magnetic measurements can be made. P___tFe and PdCo very dilute alloys. 2 4 6 8 10 12 K 14 Fig. Full curves: experiment. Koon (1974) has called attention to the point that due the randomness of the alloy.%) we estimate the error in the entropy obtained to be 4%. 8 .. ( b ) . however.DILUTE TRANSITION METAL ALLOYS.. The dashed line in both figures 16! . 01Z. 1972). Results of calculations based upon this model can explain the observed specific heat (see fig. the other alloys investigated (PdFe. In this respect the PdMn alloys are an exception. MYDOSH AND G. full curve: results of a model calculation (Nieuwenhuys1975). \ o~ o ~ r / I /// t d o° o o I 0 T 4 8 K 12 Fig. AC versus T of PdCo 0. However. i. Unfortunately. dashed curve: Schottkyspecific heat. As mentioned earlier. and also not when a larger S (as obtained from magnetization) was used. NIEUWENHUYS m ~oTK1 4~ j .' / I ~ . in agreement with statistical mechanics applied to stable well-quantized magnetic moments.075at. It then follows that the excellent fits of the magnetization (and the related splitting in the M6ssbauer effect) to Brillouin functions with large values for the magnetic quantum number are to be considered with great care.A. From this work it is clear that in the case of PdMn the results based on the specific heat are in complete agreement with the Brillouin function based on the magnetic quantum number deduced from the entropy (Boerstoel et al. PdCo. PtMn and PtCo) did not behave according to Brillouin functions with S obtained from the entropy. Fe or Mn have been carried out by Sarachik and Shaltiel . 14) and the magnetic measurements. there is no discrepancy present between the magnetization analysis and the entropy analysis for PdMn (Star et al.% at B = 1. In this approach the induced moment is assumed to be time dependent. An attempt to describe the behaviour of the single giant moments has been put forth by Nieuwenhuys (1975). a time dependence which may or may not be followed by the bare moment. no additional experimental nor theoretical support for this model has been provided up until now.J. represents the calculated Schottky specific heat (after correction for internal fields).8T [18kOe]. From this investigation it has to be concluded that the magnetic entities associated with giant moments do not (generally) behave in agreement with the appropriate Brillouin [unctions. 14. 1975).98 J. Circles: experimental results obtained by Boerstoel (1970).e. Electrical resistivity and thermopower Measurements of the resistivity in the vicinity of the transition temperature on alloys of Pd with Co. DILUTE TRANSITION METAL ALLOYS; SPIN GLASSES 99 (1967), Wilding (1967), Mydosh et al. (1968), Williams and Loram (1969a,b), Williams (1970), Kawatra and Budnick (1970), Grassie et al. (1971), Nieuwenhuys et al. (1972), Koon et al. (1972, 1973), Mydosh (1974), Coles et al. (1975) and Nieuwenhuys (1975). In general the scattering of conduction electrons by ordered magnetic impurities is smaller than in the non-ordered case. Therefore, a decrease in the electrical resistance is expected, and also observed, when the temperature is lowered below the ordering temperature. It should be noted that in the case of the giant moments alloys, the d-like itinerant electrons hardly contribute to the electrical conduction, because of their larger effective mass. Therefore, the whole giant moment acts as a scattering source for the conduction electrons (being s-like). In fig. 15 a typical curve for the resistance as a function of temperature for Pd-based alloys is shown. There are mainly two ways of deducing the transition temperature from the resistivity versus tem- BQcrn t74 1.73 1.72 1.71 Pd-Mn 1a t . °/o tTO / 3.3 ~ , • 3 . 4 3 . 5 I • I K " - |.74- • 1.69 - ~ ~cm t738 / / --exper,rnentat curve 16p 1.67 |.734 I / I , I , I I Fig. 15. The T 2 Boerstoel 1970). 3 4 K incremental resistivityAp of PdMn 1.0at.% versus T (after Nicuwenhuys and 100 J.A. MYDOSH AND G.J. NIEUWENHUYS perature curve. One is identifying Tc with that temperature where the curve bends (in table A.1 denoted by "knee"), the other is defining the transition temperature as that temperature where the temperature derivative of the excess resistivity attains its maximum value (denoted by dAp[dT). The first method originated from the molecular field theory (see e.g. Smart 1966) and the calculations by Yosida (1957a,b); the latter one from a theory by Fisher and Langer (1968), according to which the specific heat and dp[dT should behave in the same way at temperatures in the vicinity of To. For sharp transitions the two methods will result in the same temperature; for broader transitions discrepancies will occur. In addition, the electrical resistivity gives a measure of the relative broadness of the transition. As mentioned earlier, this relative broadness is expected to be larger at lower concentrations. Measurements on P d F e (Mydosh et al. 1968, Kawatra et al. 1968, 1970) and on P_P_d_dMn (Nieuwenhuys 1975), shown in figs. 16a,b, confirm this picture. The resistivity can also be used to determine the type of magnetic ordering. The so-called resistivity step, ( A p ( T = T c ) - A p ( T =0)), depends on the character (ferromagnetic, antiferromagnetic or mixed) of the ordering. We will come back to this point. Measurements of the thermopower, Q, of Pd-based alloys as a function of temperature have been performed by Gainon and Sierro (1970). These measurements do not add more new information about the magnetic ordering than electrical resistance does. There are indications that d Q / d T behaves similar to dp/dT and gives significance to the speculation that a " d i v e r g e n c e " in the temperature derivative of a particular transport property determined the critical temperature (Tang et al. 1971, Parks 1972). a -o.8'-o4' Os' o'a 08 Fig. 16a. dAp/dT as a function of E= ( T - Tc)/Tc. Curve (a) refers to PdFe 0.25 at.%, (b)to PdFe 0.5 at.% and (c) to PdFe 3 at.%. Data sources: Mydosh et al. (1968), Kawatra et al. (1969 and 1970). DILUTE TRANSITION METAL ALLOYS; SPIN GLASSES i i 101 T: ~> c~ /t 15 Ot */* ~P/c I -1 0 (T-To')/Tc I1 (T- T~)/T~. Fig. 16b. The incremental resistivity of P__O_dMn0.15at.% and 0.31at.% as functions of E= 3.1.2. Microscopic properties MSssbauer effect (ME), nuclear orientation (NO) and NMR (on impurity atoms) With both the M6ssbauer effect and the nuclear orientation method it is possible to measure the effective magnetic field at the nucleus. Suitable M6ssbauer nuclei are 57Co, and 57Fe. 54Mn is useful for the nuclear orientation studies. M6ssbauer effect studies of giant moment systems have been performed by" Nagle et al. (1962) on PclCo, Craig et al. (1962) on P d F e , Kitchens et al. (1965) on P__tFe, Craig et al. (1965a) on P__ddFe,Craig et al. (1965b) on PdFe, Woodhams et al. (1966) on PdFe, Maley et al. (1967) on P__ddFeand PtFe, Dunlap and Dash (1967) on PdCo, Segnan (1967) on P t F e , Trousdale et al. (1967) on P___ddFe,Alekseevski et al. (1968) on P d S n C o (also NO), Reivari (1969) on PdCo, Carlow and Meads (1969) on P___ddFe, Clark and Meads (1970) on P___.d_dRhFe,Ericsson et al. (1970a) on PtFe, PtCo, P__d_dCoand PdFe, Ericsson et al. (1970b) on PtCo and PtFe, Erich et al. (1970) on P___O_dNi,Maletta (1972) on (Ni3Ga)Fe, Tansil et al. (1972) on P__d_dNi, Liddell and Street (1973) on (Ni3Ga)Fe and (Ni3AI)Fe, L e v y et al. (1974) on PdAgFe, Scherg et al. (1974) on P t F e and by Gierisch et al. (1977) on P__ddFe. Nuclear orientation studies have been carried out by" Cracknell et al. (1967) on P___C_dCo, Gallop and Campbell (1968) on PtCo, Balabanov et al. (1969) on P___d_dSnCo, Ali et al. (1974) on P t C o , T h o m s o n and T h o m p s o n (1976, 1977) on P d M n and P d H M n , Flouquet et al. (1977, 1978) on P d C o and P__ddMnand by Benoit et al. (1977) on P d C o and PdMn. Finally nuclear magnetic resonance experiments on the nuclei at the impurity sites have been done by: Ehara (1964) on PdCo, Budnick et al. (1966) oqn P d F e , Skalski et al. (1968) on P d F e and K a t a y a m a et al. (1976) on PdNiCo. 102 J.A. MYDOSH AND G.J. N I E U W E N H U Y S It has been experimentally demonstrated that the observed splitting of the M6ssbauer resonance is proportional to the macroscopic magnetization of the impurities. The great advantage of the M6ssbauer effect over the macroscopic magnetization measurements is that it can be carried out on very dilute samples and if necessary in zero external field. Using the M6ssbauer effect it could be proven that the giant moments also exist in the paramagnetic state (very dilute alloys), and a spontaneous magnetization occurs (in zero field) below the ferromagnetic transition temPerature (e.g. P___CdCo,Dunlap and Dash (1967) and PdFe, Craig et al. (1965) and Trousdale et al. (1967)). It should be noted that the ratio between the effective magnetic field at the nucleus, He~, sat and the magnetic moment, Msat, is not known with great accuracy. Fits of the M6ssbauer effect results to Brillouin functions therefore contain an extra parameter ( H sat e~/Ms~,). Bearing in mind the discussion about the difficulty to describe the magnetization of most of the giant moment alloys by a Brillouin function, the conclusions from fits of M6ssbauer effect data to Brillouin functions should be considered with some care. Particularly, a wrong choice of the magnetic quantum number may greatly influence the results for the saturation moment (Nieuwenhuys 1975). The M6ssbauer effect and especially the nuclear orientation method enable (or sometimes force) the experimentalists to go to very low temperatures, where, if Kondo or spin fluctuation effects play a role, discrepancies from normal behaviour should be found (e.g. an unexpected decrease of the magnetic moment with decreasing temperature). Apart from the macroscopic behaviour the first indications for such anomalous behaviour have been found by Maley et al. (1967) in PtFe. Additional evidence has also been found by Gallop and Campbell (1968), Ali et al. (1974), Scherg et al. (1974), Flouquet et al. (1977a) for PdFe, PtCo and PdCo. Further, the measurements of the nuclear magnetic resonance of the host metal nuclei in PtCo by Graham and Schreiber (1966, 1968) did show a decreasing moment with decreasing temperature. On the other hand, nuclear orientation experiments by Benoit et al. (1977) and by Flouquet et al. (1977b) proved that PdMn behaves within the experimental error as it should according to a Brillouin function with J = ~ and g = 3, thus in complete agreement with magnetization and specific heat observations. In the row of the 3d-metal giant moments Mn forms an exception, due to its normal behaviour. /HS~t As long as it was assumed that r_r n,fu e~ is proportional to IM/Msatl interpretations of the results obtained from ME, NO or NMR measurements could be made fairly easily in terms of the magnetization, provided appropriate allowance was made for relaxation effects compared to the time window of the experiment. Difficulties in the interpretation arise when the magnitude and the sign of the effective field at the nuclei of the impurities are considered. We reproduce here table 4, published by Katayama et al. (1976), of the experimental hyperfine fields. According to these authors the positive sign of the hyperfine fields on Co and Ni in Pd is a puzzle. The rules, which these systems are expected to follow, are well established from measurements on a large number of ferromagnetic alloys (Kobayashi et al. 1966). Also the other systems mentioned in the table do follow these rules. Two possible origins for the positive contribution to the hyperfine DILUTE TRANSITION METALALLOYS;SPII~IGLASSES TABLE 4 Experimental values of the hyperfine fields (lkOe= O.IT) Experimental System H~ (kOe) PdMn PdFe PdCo PdNi Pt_Mn PtFe PtCo -360* -304 +230 + 190 -375* -316 -180 103 *Gallop (1969). field can be suggested. One cause may be a strong s-d interaction, so that via this interaction the 4s-electrons give rise to a positive polarization. It is, however, unreasonable to assume such an interaction to be present in P__ddNiand PdCo and not in e.g. PdFe or P__d_dMn.Another possible explanation may be an orbital momentum at the impurity site. Such orbital moments would be associated with the quadrupole effect due to the non-spherical distribution of electrons at the magnetic site. Indications for quadrupole effects have been found in the M6ssbauer effect on P dNi (Tansil et al. 1972) and in the NMR investigations on PdCo by Katayama et al. (1976). Also the observed magnetocrystailine anisotropy, observed in the ferromagnetic resonance (Baggauley and Robertson 1974) and in the electrical resistivity (Senoussi et al. 1977) point towards orbital moments for PdCo and PdNi. Why P__ddCo and PtCo behave differently in this respect is still a puzzling question. Electron paramagnetic resonance (EPR) For the giant moment alloy systems, only the electron paramagnetic resonance of Mn in Pd has been intensively investigated, and one observation on PdFe has been reported. (The intensive EPR investigation on Pd-rare earth systems, reported in the literature (see Taylor 1975) falls beyond the scope of this chapter.) The interpretation of the electron paramagnetic resonance in dilute magnetic alloys may be hindered by the so-called "bottleneck effect" (Hasegawa 1959). This effect is caused by the different strengths of the coupling of the conduction electrons to the impurity and the coupling of the conduction electrons to the lattice, which joins the resonances of the impurity and conduction electrons and leaves them disconnected from the lattice. However, Coles et al. (1975) concluded from their experiments that P__ddMnis not bottlenecked. The first detailed investigation of the EPR in PdMn has been carried out by Shaltiel and Wernick (1964), later such investigations were extended by Cottet (1971). Large positive g-shifts have been found by these authors and also more recently by Alquie et al. (1974) (see table 5). The influence of the magnetic ordering on the EPR 104 J.A. MYDOSH AND G.J. NIEUWENHUYS TABLE 5 Summary of EPR data for Mn in Pd Reference Shaltiel et al. (1964) Cottet (1971) Conc. (at.%) 2 0.23 0.5 ! .0 1.5 Frequency GHz 9 35 g-value 2.08 2.18 2.15 2.12 2.12 dAH ~-~ (GK-) --95 80 80 70 -55 -- Shaltiel, Wernick (1964) Alqui6 et al. (1974) Coles et al. (1975) 2.0 2 0.1 1 50 10.9 9 2.12 2.105 2.12 2.12 2 0.6 0.9 2.3 2.5 3.75 4.6 5.5 6.0 7.0 2.12 2.15 -+0.02 2.14 -+0.01 2.13-+0.01 2.15-+0.01 2.14 -+0.02 2.16 --+0.02 2.16 -+0.02 2.16 -+0.02 2.17+-0.03 40 50 62 55 57 40 47 58 52 -- (1 GK-I= 10-4T K-I). properties of P__dMn has been studied in detail by Coles et al. (1975). The rather peculiar magnetic ordering as a function of concentration is clearly revealed by the E P R results. T a y l o r (1975) has reviewed the area of E P R on magnetic ions in metals and in particular the P._ddMn system. The collection of these various data are given in table 5 which is taken f r o m the review of T a y l o r (1975). The origin of the large positive g-shifts might be the same as that of the giant m o m e n t itself. H o w e v e r , assuming no bottleneck effect, the g-values in E P R are still smaller than those deduced f r o m the specific heat ( N i e u w e n h u y s 1975) and magnetization (Star et al. 1975), using getr=g(1 +aXPd). Very recently this discrepancy has been eliminated by the experiments of Alquie et al. (1978). T h e y o b s e r v e d E P R in very dilute P__d_dMn alloys and f r o m their results it can be concluded that P__.ddMnis at least partly bottlenecked, since (i) the o b s e r v e d field for resonance is t e m p e r a t u r e dependent, (ii) the variation of the linewidth with T is non-linear, and (iii)the coupling to the lattice can be increased by cold working or addition of Pb. F r o m the analysis of these results, the authors find that the g-value of bare Mn is 2.1 and that of the Pd d-band electrons is 2.25, which implies that the true (unbottlenecked) Korringa g-value and linewidth slope for Mn in P__d_d are gK = 3.1 and d A H / d T = 0.3 T / K [= 300 Gauss/K]. N o t e that this gK is in excellent a g r e e m e n t with the effective g-values obtained f r o m magnetization and specific heat. An observation of the electron paramagnetic r e s o n a n c e of Fe in Pd has been DILUTE TRANSITION METAL ALLOYS; SPIN GLASSES 105 reported by Devine (1976, 1977), who obtained from his experiments a g-value of 2.15 and a slope of the linewidth, dzlH/dT, of 0.0031T/K [31G/K] when extrapolated to zero concentration. From these values he calculated an exchange parameter, which is in agreement with that obtained from resistivity measurements. Note also that the g-value observed in EPR is much smaller than the value needed to describe the giant moments. Although we assume on the basis of other experimental results that the observation of EPR in PdFe might be possible, there is some doubt about Devine's result, since the temperature at which his observations were possible did not exceed 5 times To. At these temperatures small ferromagnetic clusters (due to short range order) have been observed in PdFe (Malozemoff and Jamet 1977, Nieuwenhuys 1975). In spite of many efforts, the paramagnetic resonance of none of the other giant moment systems has yet been observed. Nuclear magnetic resonance (host metal nuclei) Investigations of the nuclear magnetic resonance of the host metal nuclei have been carried out by Itoh and Kobayashi (1966) on PtFe, PtCo, PdFe and PdCo, by Graham and Schreiber (1966, 1968) on PtCo and by Sablik et al. (1973) on PdFe. Two kinds of information may be extracted from these investigations. The resonance frequency contains information about the effective magnetic field at the host nuclei (thus at some distance from the magnetic atoms) and from the relaxation rate, information about the influence of the impurity atoms on the electron-nuclei interaction can be deduced. Itoh and Kabayashi (1966) found a broad resonance spectra for PtFe 1 at.% in the ferromagnetic phase, in which several maxima could be observed. By assuming these maxima to be due to the different neighbours shells (the maximum at the highest frequency due to the first nearest neighbour Pt with respect to Fe, etc.), a plot of the relative polarization at the Pt atoms as a function of the distance from a Fe atom can be made. We have reproduced this plot in fig. 17. This graph confirms the generally accepted picture of giant I I I I f 3 Fig. 17. Relative 4 5 6 7 ~, polarizationof Pt atoms as a function of the distance from the Fe impurity (after Itoh and Kobayashi 1966). 106 J.A. MYDOSHAND G.J. NIEUWENHUYS moments. According to Itoh and Kabayashi (1966) similar results have been obtained for PtCo, PdFe and for PdCo. They observed a relaxation rate, T~T, of 0.13 s K in PdFe which is slightly larger than that of pure Pd(0.11 s K, Narath et al. 1966). They did not investigate the concentration dependence of the relaxation rate in PdFe, contrary to Sablik et al. (1973) who found large concentration dependencies of the relaxation rate, resulting in a sharp maximum at 0.5 at.%. These latter authors ascribe this maximum in T~T to a concentration dependent intra-atomic Coulomb interaction in PdFe. The Fe atoms are supposed to increase this interaction at the lowest concentration, whereas at higher concentrations the saturation of the polarization of the Pd atoms plays a role. The combination of the two effects causes the maximum in T~T. Positive muon spin rotation (Ix +SR) One of the most recent techniques to investigate internal magnetic fields in magnetic substances is the/x÷SR. This method consists of implanting a beam of /x + into the alloy and then measuring the Larmor precession frequency (proportional to the magnetic field at the/z + site) by observing oscillations in the emitted positron intensity (/z+-~e÷+ ~+ v in 2.2/~s) at some fixed angle. For an extended description of this technique the reader is referred to Kossler (1975) and Yamazaki (1977). For the purpose of this chapter it is important to note that this new technique enables the experimentalists to measure the (mean) magnitude and the width of the distribution of internal fields, almost without disturbing the magnetic system. Two P._MdFe samples (0.015at.% and 0.28at.%) have been investigated by Nagamine et al. (1977a,b,c). They find that the relative widths of the internal field distribution are 18.5 and 3 for 0.015 and 0.28at.% sample, respectively. The authors consider this result as an evidence for the spin glass ordering in the more dilute sample. (Theoretically, spin glass-like ordering is expected at the lowest concentration (Nieuwenhuys 1978).) However, it should be noted, as mentioned earlier in this chapter, that the distribution of internal fields becomes much broader with decreasing concentration, albeit the interaction may remain ferromagnetic for the main part. In section 4.1 this distribution has been calculated. Diffuse magnetic neutron scattering In this article we have been attempting to describe the phenomena observed in giant moment systems by assuming these giant moments to consist of a bare magnetic moment due to the solvent atom itself surrounded by a cloud of partly polarized host material atoms. Evidence for the existence of such magnetic entities may be obtained from diffuse neutron scattering measurements. An extensive description of this and other neutron scattering techniques can be found in Marshall and Lovesey's book (1971). Diffuse neutron scattering experiments have been performed by Cable et al. (1965) and by Phillips (1965) on P_.~dFealloys, by Low (1965, 1969), Low and Holden (1966) and Hicks et al. (1968) on P__ddFeand PdCo alloys, by Aldred et al. (1970) on P___d.dNi alloys, by Cable and Child (1972) on (Ni3Ga)Fe, by Ling and Hicks (1973) on (Ni3A1)Fe compounds, DILUTE TRANSITION METALALLOYS;SPIN GLASSES 107 by Dorofeyev et al. (1976) on PdFe alloys, by de Pater et al. (1975) and by Cable and David (1977) on PdMn alloys. From these measurements it became clear that the bare moment of Fe and Co is of order of 3/-~B. According to de Pater et al. (1975) the bare moment of Mn in Pd is about 5/~a, in agreement with specific heat and with EPR investigations. Cable and David (1977) performed scattering experiments with polarized neutrons, thereby avoiding possible errors due to critical scattering. They conclude a bare moment of 4/~a for Mn in Pd, however, they did assume a rather small number of antiferromagnetically coupled Mn atoms (in view of the magnetization results of Star et al. (1975)), which may have caused an underestimate of the bare moment. The rest of the giant moment is spatially distributed over the matrix. A plot of this spatial distribution for PdFe and PdCo as obtained by Low and Holden (1966) is reproduced in fig. 18. In view of this plot it seems evident that our picture of the giant moments is basically correct as confirmed by neutron scattering data. Similar results have been obtained for Fe in NiaGa by Cable and Child (1972), who also reported a large critical scattering amplitude at temperatures in the vicinity of To. Although no adequate theory for the critical scattering phenomena exists (certainly not for critical scattering in random dilute alloys) this scattering is obviously related due to the divergence of the magnetic susceptibility at Tc (and the large increase in the fluctuations and correlations of the magnetization). The dependence of the critical scattering amplitude on the scattering vector, q, contains information on the correlation length of the magnetic ions. In very recent experiments Verbeek et al. (1978b) and Verbeek (1979) investigated the critical scattering in PdMn and in PdFe. Their preliminary conclusions are that the scattering amplitude is sharply peaked as a function of temperature, and that the correlation lengths for these random ferromagnetic alloys are extremely large (more than 20 A). Remarkably, the critical magnetic neutron scattering is xl~ 3 6 PB A3 I I I I O~ 0 I I I r 2 4 6 8 ~, 10 Fig. 18. Magneticmomentdensity as a functionof the distance from the solute site in dilute PdFe and PdCo alloys(after Low and Holden 1966) 108 J.A. MYDOSHAND G.J. NIEUWENHUYS the only sharply peaked property of dilute PdFe alloys observed up to now. These experiments also showed that critical scattering effects should be taken into account when analyzing small angle scattering on "single" moments, such as those performed by Low and Holden (1966). Nevertheless, the general picture of the giant moment is not destroyed by these latest experiments [see Verbeek (1979)]. 3.1.3. Curie temperature determination and properties of other giant moment systems As previously mentioned, the determination of Tc of dilute Pd-based alloys with Co, Fe and Mn (and also of the other dilute giant moment alloys) is not always straightforward. The broadness of the transitions to ferromagnetism makes it possible to obtain different results from different experiments. Nevertheless, the concentration dependence of Tc can be explained rather well in the case of Pd-based alloys. As discussed in section 3.1, the interaction strength as a function of distance is given by r -~ exp(-r/(r). From microscopic experiments (see section 3.1.2) o- is known to be of order of 3 ,~ for Pd. Assuming J(ro) to be proportional to ro~exp(-ro/tr), where r0 is the mean distance between the magnetic impurities, a comparison with the experimental values can be made (Nieuwenhuys 1975) and this is shown in fig. 19. It should be noted that at still larger concentrations T~ will increase less rapidly than proportional to c since then the d-band becomes magnetically saturated and the magnitude of the moment per atom decreases. So far the discussion has been mainly restricted to Pd-based alloys with Fe, i i i i • • • Pd Co Pd F e Pd M n A : 0.64 K A = 0.63 K A= 0.063 K IOC / • :¢" y: IC .•/4 1 ! :P "7" I c I I 0.5 llO 20 at.% Fig. 19. The ferromagnetic transition temperature of PdCo (A), of PdFe ( 0 ) and of PdMn (ll) as a functionof the concentration.The solid line results from a calculationby Nieuwenhuys(1975). -0.05 0.1 0.2 I DILUTE TRANSITION METAL ALLOYS; SPIN GLASSES 109 Co or Mn, we now briefly consider the properties of the other giant moment systems. The related alloy PdNi has special features. This system is characterized by a critical concentration for the occurrence of magnetic moments, which might be explained by a high spin fluctuation temperature. Detailed descriptions of the work on P__ddNialloys may be found in papers by Chouteau et al. (1968a,b), Schindler and Mackliet (1968), Aldred et al. (1970), Van Dam (1973), Chouteau et al. (1974), Beille and Chouteau (1975), Murani et al. (1974) and Chouteau (1976). The general view of this system is a model in which single Ni atoms and pairs are not magnetic, but groups of three or more neighbouring atoms are magnetic (due to the stabilization of the fluctuations by a more magnetic local environment (Chouteau, 1976)). This means that the transition non-magnetic~,-~--magnetic occurs gradually, the largest change as a function of concentration is found at 2.3 at.% Ni (Murani et al. 1974). On the other hand, Ododo (1978) used the Landau expansion of the Gibbs free energy to analyze the experimental data on PdNi. He concludes a critical concentration of 2.8 at.% Ni, which coincides with the maximum in the linear term of the specific heat as a function of concentration (Van Dam 1973). Theoretical calculations on the P__ddNi system considering a possible critical concentration have been carried out by Harris and Zuckermann (1972), Kato and Shimizu (1972), Levin et al. (1972), Edwards et al. (1973), and Kato and Mathon (1976). In the first three papers the zero-temperature susceptibility has been calculated within the CPA approximation. Kato and Shimizu used a numerical procedure to include a more realistic generalized susceptibility for Pd, while the others used an approximation for x(q). All these three works find or assume a critical concentration for P_.AdNiof about 2.3 at.%. Edwards et al. (1973) used the Landau expansion for the free energy to calculate the susceptibility of PdNi. Their results indicate a critical concentration of 1.8 at.%. Finally, Kato and Mathon (1976) have argued that no critical concentration is present in P__ddNi alloys, since the results obtained thus far are due to spurious solutions of the Landau equations. This then brings us back to the gradual change in the magnetic properties of PdNi mentioned above. These results on P_ddNi,force us to consider the stability of the magnetic moments as a function of concentration. The instability (or non-existence) of magnetism, i.e. weak moments, is generally characterized by a spin fluctuation temperature, Tsf which is concentration dependent, (see section 1.1). In the electrical resistivity terms proportional to log(TlTsf) (Kondo or spin fluctuation type) and in the magnetization (and M6ssbauer effect) temperature dependent magnetic moments have been found. In most cases a decrease of the magnetic moments has been observed below T~f. Investigations of this effect on a variety of Pd and Pt based alloys have been performed by Gallop and Campbell (1968); (PtCo); Shen et al. (1969) P(_~Co); Loram et al. (1971) (PdCo); Loram et al. (1972) (PtFe); Tissier and Tournier (1972) (PtCo); Costa-Ribiero et al. (1974) (PtCo); Scherg et al. (1974) (PtFe); Ali et al. (1974) (PtCo); Swallow et al. (1975) (PtCo), and Williams et al. (1975a,b) (PtCo). Williams (1976) has proposed an explanation for this non-stable behaviour based on the configura- 110 J.A. MYDOSH AND G.J. NIEUWENHUYS tion-fluctuation approach (Hirst 1970, 1971). According to Williams the spin ttuctuations/Kondo behaviour of the giant moments might be caused by configuration fluctuations of the bare moments. In fig. 20 we reproduce his graph of the characteristic temperature versus alloy composition. We also ascribe the peculiar paramagnetic behaviour of PdCo, PtCo, PdFe and PtMn alloys to such weak moment effect. It can be seen that PdMn has the lowest characteristic temperature, which would agree with the experimental results of a stable moment. Since the magnitude of the giant moment is given by /z =/Lbare(1 + otXo) it is very interesting to compare the results obtained on Pd-based alloys to results on alloys with host materials of which the exchange enhancement, ~, can be varied. Base materials with the highest exchange enhancement factors (of order of 35) are Ni3A1 and Ni3Ga (de Boer et al. 1967, 1969, de Chatel and de Boer 1970). The magnetic moment per dissolved Fe atom in these base materials is expected to be very large, as has also been found from magnetization measurements (Schinkel et al. 1968, Maletta and M6ssbauer 1970, Schalkwijk et al. 1971, Maletta 1972, Cable and Child 1972, Liddell and Street 1973, Ling and Hicks 1973). In table 6 we collect the results as obtained by several authors. It is of course important to determine whether the assumption of /z being proportional to (1 + aXo) holds for these giant moment systems. Since Ni3Ga compounds can be made with slightly different compositions, thereby changing X0 over a wide range, this assumption can be tested on (Ni3Ga)Fe and other similar alloys, as has been carried out by Schalkwijk et al. (1971). In fig. 21 their plot of /z versus X0 is reproduced, from which it is clear that the linear response picture of the giant moment holds fairly well. On the basis of this experimental result one would expect similar behaviour for Pd-type alloys. 103 ÷ 10z 0-1 ,I? / , , , , , , . Ti V Cr Mn Fe Co Ni Fig. 20. The estimated characteristic temperature (in K) for various 1st transition series impurities in Pd (.) and Pt (+) (after Williams 1976). Magn.0Ga26. (1968) Liddell and Street (1973) Liddell and Street (1973) Liddell and Street (1973) Ling Ling Ling Ling and and and and Hicks Hicks Hicks Hicks (1973) (1973) (1973) (1973) (Ni74.0)Fe 10 ppm (Ni~4. NS Magn.3 Fig.~ XO (e'~U#mole Ni ) I I I I I 0 2 4 6 8.% 1 at. 21.% 0.% 0.4 27 28 41 80 85 58 40 36 29 33 24 9.Ga2~ are included for comparison (after Schalkwijk et al. (1968) Schinkel et al.~AI25. M6ssb. (1968) Cable and Child (1972) Schinkel et al.05 at. SPIN GLASSES TABLE 6 Magnetic moments per dissolved Fe atom in Ni3AI and Ni3Ga base materials Tc [K] /~ [/~a] 21 69 84 lI 13.sGa25. M6ssb.sA125.% 0.sAI25.5) (Ni74.5)Fe 10 ppm (Ni75. (1968) Cable and Child (1972) Schinkel et al.5)Fe (Ni74AI26)Fe (Ni74.10 .DILUTE TRANSITION M E T A L ALLOYS. Magn. 1971).2 (Ni~4.sAI26.s)Fe 0. Magn. M6ssb.5 12 25 32 34 16 46 70 79 18 14 8 111 Alloy (Ni74. Mbssb. M6ssb.sAI25.2 at. M6ssb. NS Magn.% l0 ppm 10 ppm 10 ppm Method M6ssb. Magn..5)Fe 20 ppm 250 ppm 0. M6ssb. Values for iron in palladium and in Ni7~2~ and for Co in Ni.1 at. (~B) 30 ' / + Ni74AI26 o / 20 I0 / / / Co in NiaGa . Reference Liddell and Street (1973) Liddell and Street (1973) Liddell and Street (1973) Maletta(1972) Maletta (1972) Schinkel et al.5)Fe 0.5 (Ni74.% 0. 0 .sAl2s. Magn.1 at. Effective moments per iron atom as a function of the host matrix Susceptibility per tool nickel.5)Fe 1 Fe in Ni3G__~a 40 ~e'~e at. Magn.Ga24.9)Fe 10 ppm (NiTsGa2s)Fe (NiTsGa25)Fe (Ni75Ga25)Fe (NiTsGa25)Fe (Ni75Ga25)Fe (NiT~Ga~)Fe (Ni75Ga2~)Fe (Ni75Ga25)Fe (Ni73.9 at. It was already known from magnetization measurements by Rault and Burger (1969) that PdMn alloys with concentrations larger than 8 at. (see table A.05 at. Doclo et al. 1971. which prevail at larger distances between the magnetic ions.%. NIEUWENHUYS Susceptibility measurements on PdAg and on PdRh alloys (Budworth et al. Spin glass behaviour is therefore found over the whole concentration range (Sarkissian and Taylor 1974. this concentration is much larger because of the smaller exchange enhancement. in contrast to the ferromagnetic indirect interactions. Huq and Moody 1977. As mentioned in section 1.1 order like spin glasses.1 in the appendix. This could be interpreted by assuming that the direct Mn-Mn coupling (being of great importance at these concentrations) is antiferromagnetic.A o ( T = 0)] was . so that a direct comparison to pure Pd becomes impossible. a number of studies have focussed on these alloys. A great number of the Pt-based alloys mentioned in table A. This fact leads to a peculiar type of spin glass in PdMn at higher concentrations (also in PtMn). Therefore.3 the oscillatory character of the interaction (RKKY) may become important in giant moment alloys at the lowest concentration (large distance between magnetic moments. The resistivity measurements by Williams and Loram (1969a. Indirect (RKKY type) interactions are not the only possible antiferromagnetic interaction. Verbeek private communication) do show qualitatively the same behaviour for the contribution of the y ~ N(0)-term. This was deduced from the fact that the resistivity step [ A o ( T = To) .A. Direct (nearest neighbour) interaction between Mn-ions are also antiferromagnetic. The PtMn system forms an exception again since at small concentration this is a spin glass because of the RKKY oscillations and at larger concentrations it is a spin glass due to direct antiferromagnetic interactions (to be discussed below). "other alloys"). For PdFe this concentration may be 0.%) and a decrease upon alloying with Ag. MYDOSHAND G. 1975).112 J. Tholence and Wassermann 1977). Specific heat investigations (Hoare and Yates 1957. Budworth et al. (ii) The transition temperatures are not proportional to the matrix susceptibility (Nieuwenhuys 1975).5-1 at.2. similar influences on Tc are to be expected upon alloying with Ag or Rh.b) made clear that also at smaller concentrations a partly antiferromagnetic ordering was present. 1960.% did order antiferromagnetically. like Cu. For Pt-based alloys.J. Nieuwenhuys 1978). see also section 4. 1960.% or smaller (Chouteau et al. Sn and Pt act in the same way as Ag. 1969) have shown an increase in the susceptibility compared to that of pure Pd upon alloying with Rh (c < 5 at. Since the transition temperature is proportional to the magnitude of the susceptibility. For Co and Fe in Pt the boundary may be 0. The main features of these investigations are: (i) The magnitude of the giant moment is not proportional to the matrix susceptibility (Guertin and Foner 1970). but also introduces extra scattering centres in the alloy. PdAgFe alloys become a spin glass (Budnick et al. The first two results can be explained by the fact that one does not only change the matrix susceptibility upon alloying. Other metals. (iii) At higher Ag concentrations. In this model the susceptibility maximum corresponds to the disappearance of a strong magnetic anisotropy. Craig and Steyert 1964. The sharpness of the experimental effects indicated a . This led Kouvel (1963) to suggest a model which describes the magnetic properties in terms of mutually interacting ferromagnetic and antiferromagnetic domains. Cannella et al.5 mT[~-5G]) ac susceptibility technique. A sensitive external magnetic field dependence of X was also observed in the T-region of the peak (Cannella and Mydosh 1972). 1970) which also found magnetic transitions characterized by the sudden onset of hyperfine splitting at well-defined temperatures. Initially. These results were then correlated with a series of earlier M6ssbauer investigations (Borg et al. (1971) discovered sharp peaks in the temperature dependence of the susceptibility. SPIN GLASSES ! 13 smaller than expected on the basis of measurements in strong external fields. Star et al. Therefore. of Zweers and Van den Berg (1975) and of Star et al. it was only recently that sharp effects were found at well-defined temperatures. 1968. Later on the work of Coles et al. In order to explain an additional (linear at low temperatures) contribution to the specific heat of A_A__~Mn(de Nobel and du Chatenier 1959) and CuMn (Zimmermann and Hoare 1960). Window 1969. resistivity and field cooling showed peculiar properties. 1963. 1969 and Klein and Shen 1972). These results were interpreted within the random molecular field model (Klein 1964. Gonser et al. Even for applied fields as small as 0.01 T [100 G]. in this concentration range. remanence. there was certain confusion as to the nature of the magnetic ordering. Further experiments of Kouvel (1960. a noticeable smearing of the x-peak occurred. 1965. a displaced hysteresis loop. 1970.1 T [1000G] revealed a broad maximum at a temperature where the magnetic remanence disappeared (Lutes and Schmit 1964). (1975) and Nieuwenhuys and Verbeek (1977) concluded from various experimental results that up to the third nearest neighbour distances the interaction between Mn atoms is dominated by the direct antiferromagnetic interaction. (1975). Window et al. This causes PdMn alloys in the concentration range from 3 to 10 at.2. for a discussion of which one is referred to section 3. Marshall (1960). Spin glass freezing Although interacting dilute alloys have been investigated over many years.% to be peculiar alloys in which the direct antiferromagnetic and the indirect ferromagnetic interactions are of comparable importance. Study of the susceptibility in fields around 0. and Klein and Brout (1963) developed molecular field theories for these systems using a probability distribution P(H) of internal fields. The susceptibility peak temperature agreed well with the M6ssbauer splitting temperature (Borg and Kitchens 1973). 1961) on magnetization.%.5 at. and the susceptibility behaviour approached that of the previous measurements by Lutes and Schmit (1964). Violet and Borg 1966. 3. P__d_dMn may be called a spin glass.DILUTE TRANSITION METAL ALLOYS.2. as for example. (1975) showed that antiferromagnetic interactions are important in P___d_dMn alloys as soon as the concentration is larger than 0. By employing a very low field (~0. 5 mT [5 G].2.01 T[100 G]) susceptibility x and include the Faraday and other high field methods in the section on magnetization. disorder and amorphism became articulated in the concept "spin glass". 10-3emu/cm 3 8at°/o | 2. the ideas of randomness.-. 22. and a most intriguing question presented itself: order out of randomness? We now proceed to discuss the various experiments performed on spin glass systems. 1966) by analyzing his neutron scattering data had already pointed out the absence of long range magnetic order in these types of alloys. 22. (1971. MYDOSHAND G. Thus.114 J. This figure further represents the typical behaviour for all the spin glass alloys (Cannella and Mydosh 1973.8 / 5at. However. A division is made here between the macroscopic and microscopic properties. NIEUWENHUYS long range antiferromagnetic order._u_uFealloys are shown in fig.°/o ~e'o.1. 0 T>20 40 60 K 80 Fig. mutual inductance bridge which required a driving field of ~0. 3. After Cannclla and Mydosh (1972). Low field susceptibility x(T) for four AuF¢ alloys. and the connotation antiferromagnetism was often applied. 1972) using a very sensitive.2 \\\\ "o 0.C 2ato/oA - / / / \ y . low audio frequency. Finally a simple phenomenological model is used to describe the freezing process and a collection of freezing temperatures for some characteristic alloys is given. three regions of temperature are noted: above. Random alignments of frozen spins were extracted from the analysis of the M/Sssbauer lines and their intensity ratios (Borg 1970).A. The first measurements in small fields were carried out by Cannella et al. In addition. . Macroscopic properties Susceptibility We limit ourselves to the low field (<0. below and at the freezing temperature. Arrott (1965. otO~o 1. The temperature dependences for a series of A_.J. 1 9.0 -7.5 ~.0 11.8 ~.12 0.3 0.5 Tf[K] -2.1 2.2 0.0±1.5 0.0±1._yuFe . Above the peak temperature which we denote as the freezing temperature Tf.4±0.6 is obtained for magnetic concentrations between ~ 0.3 ~3. and we are unable to follow the high temperature TABLE 7 Salient parameters obtained from low field susceptibility measurements on noble metal-based spin glasses c[at.58 0.5±0.2±0.~ 0.3 0.7 10.3 27.4±0.28 -0..2 8.6±1.2 0. Thus X extrapolates to a finite value for T ~ 0 and a ratio X(0)/x(Td~0.0±1.3 5.5±0.4 12.5 5.1 0.~ 0. SPIN GLASSES 115 1974a. and a collection of the important parameters are listed in table 7.5 5.b).3 43.5 7.~ 0.8 10. Such distinct temperature effects were totally unexpected on the basis of the random molecular field model and the previous high field Faraday susceptibility.60 O[K] -0 ~1 ~0 -2 ~2 ~6 ~-2 -~0 40 ~2 ~9 ~6 -40 ~1 --1 ~7 -~0 tO tO A.0 7. x ( T ) = x(O) + bT" with n ~ 2.8 1.0 2.5 1. At low temperatures.0 >20 ~3. cusp-like peak which occurs.5 -5. and 0 the paramagnetic Curie temperature.3 1) x(O)lx(Tf) --0.6 3.0 10.5±0.0 6.0 10. n is the density of magnetic atoms.0 17.53 0.4 P~ = g/~aX/S~ 4.DILUTE TRANSITION METAL ALLOYS.5 6.58 ~0.5 1.60 ~0.25 0.50 0.5 10.5±0.5±1. a modified Curie-Weiss form.3 17.48 0.0 1.0 5.6 30.2 0.58 0.__ggMn CuMn Au Mn A.0 5.0±0.0±1.1 and a few atomic percent.3 2.0 0.5 8.5 6.5 4.65 0. X = ng2t~gS(S + 1)/3kB(T .5 29.57 0.7 5.1 3.5 1. The magnitude of the peak is rather small. S their spin angular momentum (for simplicity we neglect possible orbital contributions).%] 0.25 0.29 0.1 0.60 0.8±0.7 8.3±0. The remarkable feature of these measurements is the sharp.0 5.0). The disadvantage of the mutual induction method is that for T >> Tf its accuracy is severely limited.5 5.0 11. These measurements have been extended to a variety of spin glass alloys which show the same general characteristics. may be obtained with both S and 0 functions of the concentration.5 6.8 3. 6 4.~ -0. G u y (1975.8 3.b).5 ~.0±0.0 ~. A___qCo CuuFe C u r i e . MYDOSH AND G. At f r e q u e n c i e s u p to a few t h o u s a n d H z there was n o a p p a r e n t f r e q u e n c y d e p e n d e n c e in X ( C a n n e l l a a n d M y d o s h 1974a. at t h e s e v e r y low T a n d c.3 14.0-10 m T [ 1 0 .50 -0.0 4.0 13.68 0. this m e t h o d does n o t p o s s e s s sufficient s e n s i t i v i t y .1 11.75 --.6 0. r a t h e r t h a n a c u s p .3 5. So.9 !.5 9. 0 m T [20 G] are n e e d e d to p e r f o r m m e a s u r e m e n t s s e n s i t i v e e n o u g h to d e t e c t the spin glass freezing.2 0.27 0.68 0.4 -3. This signifies a c o m p l e t e s m e a r i n g of the f r e e z i n g p r o c e s s with e x t e r n a l field. U s i n g this static p r o c e d u r e . at v e r y low c o n c e n t r a t i o n s (~<0. 1978) has o b s e r v e d a s h a r p p e a k in x ( T ) .2 .0 7.75 ~0.8 2.9 7.5 3.0 92. N e v e r t h e l e s s .2 4.39 0.b.58 0.5 4. .5±0.34 0.0 3. u n d e r short time c o n d i t i o n s . F r o s s a t i et al.7 0. T h e S Q U I D t e c h n i q u e ( w o r k i n g s e n s i t i v i t y 1 0 6 e m u / g ) is in fact a m a g n e t o m e t e r w h i c h r e q u i r e s a n e x t e r n a l field bias 1. A n o t h e r a p p r o a c h to the low field s u s c e p t i b i l i t y has b e e n to refine the F a r a d a y m e t h o d w h e r e b y fields of o n l y ~ 2 . NIEUWENHUYS TABLE 7 (contd.30 0[K] ~-2 -~-I ~1. -0.0 5. 1977a.W e i s s tail.1 10.J.3±0.11 0.50 0. c o n f i r m i n g the a.5 4.0 13.5 3.5 4. a step. A series of such e x p e r i m e n t s h a v e b e e n able to f o l l o w the f r e e z i n g t e m p e r a t u r e d o w n to 10 m K with r e d u c e d c o n c e n t r a t i o n s ~>10ppm ( H i r s c h k o f f et al.50 -0.5 x(O)Ix(Tt) 0.0 0.7 2.5 ----1.%).8 1. so s u p e r c o n d u c t i n g q u a n t u m i n t e r f e r o m e t r y d e v i c e s ( S Q U I D ) m u s t be used. w h e n the .6 12.0 Tr[KI 8.7 6.5±0.4±0.A. b . 1976).9 22.67 0.1 at.4 15.1 11.0 7.0 5.c.5 7.2 27.3 25.0 2.1±0.1 6.1 0 0 G ] .9 36.0 -1.9 1.0 5.2 6.11 0.0 38.5±1.5 4. D o r a n a n d S y m k o 1974a.5 -6. 1971a.0±0. c .7 3._~uCr . b.28 0.!16 J.5±0.3 0.0 7. m e t h o d .0 4.) c lat. a p p e a r s in the M ( T ) / H d e p e n d e n c e .0 0.0 41.0±0.0 Pe~ = g / L B X / ~ 3. -3.5 ~4 -12 ~17 n0 ~0 --5 ~-11 ------~-I -2 -~-2 --I ~0 AuFe A. %1 0. F u r t h e r m o r e . T ) = XoH + 12c'B [12. Despite the four adjustable parameters.t a molecular field constant). 1966. This occurs for T <. Instead a modified form was proposed by Beck (1972a. Another way of handling the high field. (1970. irreversibilities and relaxation appear at T ~< Te.DILUTE TRANSITION METALALLOYS. irreversibilities and thermomagnetic history.c. de Mayo 1974). Once field cooling and field cycling methods are used remanence. A sampling of the general behaviour is given below. A simple Brillouin function does not easily fit the data. Magnetization There exists a large number of magnetization experiments which have been carried out long before the term spin glass came into use. (1975) and Mukhopadhyay and Beck (1975) M(H. and over a long time scale the spin glass slowly relaxes into a new metastable state. At high temperatures.b. M is initially linear in H and bends off at large fields. The M-H curves show the usual curvature as the temperature is reduced (Careaga et al. 1976) has . Here dMldH remains finite. This prompted Beck to treat the magnetization. They developed the free energy in a power series of the concentration in order to investigate the RKKY interaction on the thermodynamic functions of a dilute magnetic alloy. and only for T >> Te is the free ion paramagnetic moment found. Borg and Kitchens 1973. 1975). These magnetization studies yield no dramatic changes as the temperature is lowered through Tt.b). This marks a distinct contrast to the high temperature (T > Tf) behaviour where none of these effects occur.SPIN GLASSES 117 magnetization M(H) is allowed to come into long time (a few hours) equilibrium at each temperature. These experiments demonstrate that the true equilibrium ground state of a spin glass is obtainable only in zero field x(T)=Iimn_. it is extremely difficult to saturate the magnetization even at very low temperatures and fields above 10T[100kG]. in terms of dynamical clusters which begin forming at very high temperatures due to local correlations between the spins. a quite different behaviour of x(T) is found for T < Tf. However. Franz and Sellmyer 1973./. For gizaH ~>ksT ~>cJ'. the approach to saturation of the magnetization is predicted to be M = glzBSc{1-[2(2S+ 1)cJ'/gl~BH]}. F.W. the application of a very small static fields perturbs this state. 1971). Mukhopadhyay et al. By tabulating /2 and c' as the temperature is reduced. high temperature magnetization is via the virial expansion theory of Larkin et al. provided the measurements are begun in zero external field.o[M(T)/H].Z the average moment with a concentration c' and . Smith (1974a.Tf and marks the onset of remanence.H + A ( M x H ) ] T (the parameters in this equation are X0 a field independent susceptibility. one obtains a growth of the average moments and a decrease in their concentration (Mukhopadhyay et al. The cluster formation (/~ and c' values) is strongly dependent upon the heat treatment used. For. it is very difficult to obtain good agreement with the experimental data over a significant temperature interval. By adding Xir to X = limH~o(MlH) (called the reversible susceptibility). theory) measurements on a variety of alloys systems where the above (weak interaction) limits are valid. then a small hysteresis and IRM develops (outer loop of part (a)). Figure 23 illustrates this behaviour for a typical spin glass. The positive M value for H = 0 is the TRM.F~ 0 . Guy 1977b). The thermoremanent magnetization (TRM) is a field cooling effect for which the sample temperature is reduced from T > Tf to T < Tf in field H. an irreversible susceptibility may be defined as Xir = TRM(H)/H. After Tholence and Tournier (1974). 24 further show these remanences and irreversibilities. I I I 0 H 5 10 15 20 kOe Fig. Here saturation is reached in a lower external field. MYDOSH AND G. Field dependences of the thermoremanent magnetization (TRM) (field cooling) and isothermal remanent magnetization (IRM) (field cycling) for AuFe at T ~ Tf.. This displacement is a dramatic illustration of the unidirectional lQ-2emu Ig I I i I 03 TRM A_y_u . A saturation in the IRM is observed for sufficient large H which depends upon the alloy concentration. .I O J" I >.A. From the TRM. Remanence and irreversibilities Below the freezing temperature for a spin glass. The isothermal remanent magnetization (IRM) is obtained by cycling an external field 0---> H ---> 0. From this analysis the scaling behaviour is verified and the magnitude of the RKKY exchange J' can be determined for each system.118 J. At this lower temperature H is set equal to zero and the magnetization measured. Part (a) is the zero field cooled M . the inner portion being reversible up until a certain threshold value of the external field is exceeded. The hysteresis loops in fig. Xtot. may be indirectly obtained. 5 °/o 0. Xtot is simply constant for T < Tf and thus the characteristic step or "kink" appears in Xtot(T) at Tf. and there is a rather sharp switching to negative M values for a relatively small (much less than the field cooling field) oppositely applied field.H character. and then measuring the magnetization. the total susceptibility. NIEUWENHUYS carried out magnetization and susceptibility (X = ng2tz2S(S+ 1)/3(ksT+cJ') from the Larkin et al.J. Part (b) represents a field cooled spin glass with a displaced hysteresis loop. a remanent magnetization and an irreversible susceptibility are found (Tholence and Tournier 1974. 23. 8Tt. exchange anisotropy caused by the field cooling and freezing process. Thus.. exponential form (Borg and Kitchens 1973). is observed which varies in a manner which differs from the usual. The magnetic measurements in the low temperature region may be qualitatively described using an activation model with a distribution of energy barriers for non-interacting particle moments (Street and Woolley 1949). Zimmermann and Hoare 1960) of the magnetic contribution to the specific heat. and of both the IRM and TRM. The most sensitive present day experiments disclose that nothing happens at Tf.--(c) _~ I . .. A time dependence of the magnetization. Cm.tr(T) log t. This means that a spin glass has a long-time relaxation into its new equilibrium state when perturbed with an external field. For comparison. simple.DILUTE TRANSITION METALALLOYS. Plots of ~[Mo versus T suggest the existence of two temperature regimes above and below 0. Smith 1974a). A better fit (Guy 1977a) to the low field decay data is M ( T . It was initially thought that the maximum in Cm indicated the freezing temperature Tf. but also these magnetic viscosity effects occurring at low temperatures. ~. showed a linear low temperature dependence which was approximately independent of the concentration. A broad maximum in Cm developed at higher temperatures and the very high temperature fall off was proportional to 1/T (F. t) = Mo(T) . and (c) a ferromagnet. Schematic hysteresis loops for (a) zero-field cooled spin glass." iI I = H Fig...SPIN GLASSES M 119 T< TO + . (b) field cooled spin glass. 24. It should be noted that all of the above properties are functions both of the temperature and the concentration..W. any first principles theory full treating the spin glass alloys must not only consider the freezing behaviour at Tf.6Tf for both the IRM and TRM.'l" -. Guy (1978) has further studied the behaviour of or(T) and found a maximum in this decay coefficient at 0. Specific heat Early measurements (de Nobel and du Chatenier 1959. However. the recent measurements of Cm and X on the same samples showed that the maximum appeared at a temperature significantly larger than Tf.After Mydosh(1975). a typical ferromagnetic loop with its virgin curve is given in part (c). The implications from Guy's experiments are that the spin glass behaviour far below T~ is quite similar to a blocked super-paramagnet and that the relaxation effects are intrinsic to the nature of the frozen state. Sm is the magnetic entropy) occurred at the freezing temperature. was already developed above Tf.. . e. U 2O t CUo988 M n o Ol2 . -6 120 . .. After Wenger and K e e s o m (1976). .. I . Smax= cR ln(2S + 1). there is evidence of deviations from the strict linear temperature dependence. °•" "° • . in certain cases Cm extrapolates to negative values as T-->0 (Wenger and Keesom 1976).g.. a good correlation could be obtained for one system PdMn (Zweers et al. Thus.. I 10 I I I I 20 I . 1977).. N I E U W E N H U Y S Figure 25 illustrates this point along with the overall Cm behaviour.120 J. •••. a large percentage (~70%) of Sin.J. °°. in the amorphous GdAI2 spin glass a clear T 3/2 term has been seen (Coey et al. I I -5 6O E -~ 4 0 j. • . This indicates the presence of short range magnetic order or correlations for T >> Tf which take away some degrees of spin freedom giving S . The experiments of Wenger and Keesom (1975. 160 )1. For even the revised cluster or fluctuation theories show a small effect in Cm at Tf which would require a unique measurement sensitivity• The application of an external magnetic field shifts the maximum in Cm to higher temperatures and slightly smears the general shape (Trainor and McCollum 1975)." . . Measurements in the opposite temperature extreme T >> Tf show a l I T dependence which is slower than the l I T 2 Schottky tail. 1977) where a maximum in Cm/T (= dSm/dT. ° • °. These specific heat results create a special challenge for both experimentalists and theorists..024 I I I 0 T 10 20 K 30 Fig. At very low temperatures (T ~< 1 K). 25. E 4C """ °•° I /" I C u0..A..•" •..• I K 30 I • .° E E U 8C °.. Furthermore. the limiting temperature variation would be Cm ~ T" with n > 1. 1976) further revealed a significant magnetic specific heat contribution well above Tf. 'MYDOSH AND G. This correlation was less apparent for the other spin glass systems with a knee developing at = Tf. o I T I o y. Magnetic specific heat for two CuMn spin glass alloys• The arrows represent the freezing temperature as obtained from the susceptibility peak. .976 N1n 0." 8O I I • . When converted into entropy change. For low enough concenv. At best. •. a maximum develops in Ap. Larsen et al. Thus. For the spin glass alloys. i. In general. 1977. a much slower Ap(T) variation gradually leads to . the interaction between the spins gradually breaks up the resonant. 1977). A magnetic (spin-split) virtual bound state of the 3d impurities along with disorder scattering from the randomly frozen spins gives this large. Some evidence has been offered for the appearance of a limiting T 2 dependence at the lowest temperatures ~<0.DILUTE TRANSITION METAL ALLOYS.In T[TK must be considered. Tm ~ Ac ln(AclT~) > >Tf. Figure 26 illustrates the overall behaviour of the approximate magnetic resistivity Ap(T) for a series of C___uuMnalloys. A sudden AH will result in long time scale (~ log t) relaxation to a new metastable state as with the magnetization. relaxation effects have also been observed in the specific heat and heat flux (Nieuwenhuys and Mydosh 1977). This results in a negative temperature coefficient of the resistivity. lies at a temperature considerably below the freezing temperature (see fig. For yet higher temperatures. A theory due to Larsen (1976) relates Tm to the average R K K Y interaction energy. 26). There exists no definite indication for Ap or d(Ap)/dT of the spin glass freezing temperature. These excitations are highly damped. residual. a strong rapidly rising Ap roughly proportional to T is found. Ford and Mydosh 1976. First of all an estimate must be made of the non-magnetic contributions to the alloy's resistivity. The interplay in the resistivity between the Kondo effect and the spin glass interactions has been investigated via the application of high pressures (Schilling et al. Then an important component of the magnetic resistivity Ap due to the Kondo effect Ap~ o: . A theory of Rivier and Adkins (1975) has ascribed the low temperature Ap behaviour to long wavelength elementary excitations which are diffusive in character. 1974. there is a substantial residual resistivity Apo per at. Finally. Kondo scattering and at a certain temperature Tin.% of magnetic impurity. Pressure always causes an increase in TK while leaving the impurity-impurity interactions relatively unchanged. phonons and deviations from Matthiessen's rule. This scaling behaviour was predicted by Souletie and Tournier (1969) and Larkin and Khmel'nitskii (1970. By starting from the limit T->0. the maximum value of d(Ap)/dT. via T~:.3 K (Laborde and Radhakrishna 1973. single impurity. Ac o: f(c)j2/D. 1974). Laborde 1977). Larsen 1976.e. Resistivity The electrical resistivity of a dilute transition metal alloy is an easily measurable. For the temperature region about Tf. d(ApK)/dT < 0. yet difficult to interpret. SPIN GLASSES 121 trations. residual component. Ap(T. As the temperature is increased. quantity. Such general temperature and concentration dependences are typical for all the 3d spin glass systems (Mydosh et al. which characterizes the Curie or N6el temperatures of long range ordered substances.c)= cApo + A(c)T 3/2where A(c) decreases very slowly with increasing concentration. the specific heat scales as Cm/c =f(T]c. magnetic. 1971). non-coherent (independent) localized spin fluctuations which scatter the conduction electrons.H[c) over the entire temperature range. 1976. This signifies the dominance of the spin disorder scattering freezing-out over the Kondo effect. 0 0 i . Cu-16nt/. The arrows represent the freezing temperatures as determined by the susceptibility peak. Hall effect (magnetoresistance) The anomalous part of the Hall effect due to the spin-orbit coupling between the conduction electron and the localized moments may be used to study spin glass alloys.. 6..3at '/.J. Because of the logarithmic nature of the Kondo effect..8 % 300 T(K) Fig.. ..7. :.. . 2J. Overall temperature variation of the magnetic resistivity.. w ° o .f ' = i ".0" -2~. followed by a continuous fall-off as room temperature is reached.5x /~#" ...5ot%Mn ¢leeeao -ZS.~ -2~0 . N"~ x . consistent with the specific heat we have experimental evidence that correlations and magnetic clusters are progressively destroying the Kondo scattering and reducing the paramagnetic spin disorder scattering.Hn .5 x :" ° e -z o -ZB.5 • x xaXlmxxxxxx'maxxxaaN x a~ °° . 97 0t '/oMn *'0...:i ~' . . Once again. if. N I E U W E N H U Y S I I I 1 oeeo meee eoe e °°eQeeee e eee I ~o ° -z. Cu. This coupling results in an asymmetric or skew scattering for those .7ot ~2. there is a growth of magnetic short range order as Tf is approached from above.32.. Ap. Cu-2. 50-8. breaks many of the impurity-impurity interactions.122 J..2-. o °°°ooeee~eeeae°oo° o I3.. .'ii[ i 100 l 200 I I -7..Xn .Oo | 18....Mn Imxxx ~ ./. '.. .0- " 17.. Here the strong thermal disorder. the maximum in Ap at Tin... In other words.5° Cu.. ~xlmx N ImXxm 18. • . The large changes in Ap for T >> Tf means the average magnetic scattering is constantly varying.A.O.5 ~ lES12..:-'" 13.4 .. After Ford and Mydosh (1976). 26.. . this negative slope tail in Ap can extend over a wide temperature range especially for these larger concentrations. .o" Cu.4 o e .. kBT. MYDOSH A N D G. for six CuMn alloys.S t/ I z.0- ~ Q..O" °°lee < 12.. xl. /~o° ~ Cu.7~ Y.. They measured the temperature dependence of the Hall effect in different external fields.16 % Fe ~. Thus. In fig.020 T • 0. .b). 2 7 . The sensitivity of this transport 2°r 1. however. Since the normal Hall coefficient (the linear Lorentz contribution) is at least 10 times less than the anomalous part. At Tf. a transverse voltage is developed which reflects the degree of alignment in the magnetic field (Fert and Friederiech 1976).050 T -". After McAlisterand Hurd (1976).: ' X . The low magnetic fields are necessary to avoid smearing the spin glass freezing. lO0 T ° I0 m 1. Here the applied field is not strong enough to produce significant deviations from the random freezing directions. the thermal disorder randomizes the local moments and the skew scattering is small.~ ' ' .O 0 I0 I 20 . At high temperatures. I 30 I 40 . 80 TEMPERATURE Fig. Good and consistent agreement of the freezing temperature obtained from Hall measurements exists with the other methods of extracting Tf. SPIN G L A S S E S 123 moments aligned with a magnetic field perpendicular to the current flow.~ I I :i+/ 0. 27 some of these measurements are shown.5 ~C -.5 ' . Note. O. Hurd and McAlister (1977) and McAlister (1978). For a random arrangement of moments there is no average skew component.D I L U T E T R A N S I T I O N M E T A L A L L O Y S . I f. I I I Au+8. A definite similarity appears between the anomalous Hall resistivity and the susceptibility x(H).0 Z I. the skew scattering effects may be followed down to low temperatures and fields. there is a clear drop in the skew scattering due to the random freezing of the moments.I T [1000 G]. 0 I 20 I 60 (K) .% Fe. A series of such experiments on a variety of noble metal alloys has been carried out by McAlister and Hurd (1976a.' ~ ' ~ F'E o 0. Temperature dependence of the total Hall resistivity divided by the applied field strength for Au + 8 at.. the substantial broadening effects as the external field is increased to 0. roughly concentration independent. When these effects are combined with the electron diffusion and phonon drag contributions. 8 0 I60 240 K Fig. e. Little recent experimental effort has been devoted to magnetoresistance measurements in the spin glass alloys. is opposite that from ordinary potential scattering. in indicating the freezing process is due to the smallness of the non-magnetic contribution~ For the Hall effect the normal component is negligible. The sign of Q due to the magnetic scattering.g. . Thermoelectric power dependence on the temperature for four AuFe alloys. After Cannella and Mydosh (1972).. Thus a strong negative rnagnetoresistive effect is observed which demonstrates the alignment of the local moments in an external field and a reduction of the fluctuations and spin disorder scattering (Daybell 1973). Thus.A. resistivity and thermopower.J. 0 i I f I ~ I i I B I ~ I i it J o -8 o -10 -12 0 :. the magnetic component usually dominates the others making a qualitative analysis possible. Li and Paton 1976). Similar behaviour is observed for the higher concentration spin glass alloys where the very large external fields (8-13T [80-130kG]) distort the random orientations and give gradually varying temperature and field dependences (Welter and Johnen 1975. MYDOSHAND G. Q. Fortunately. Q becomes a rather complicated quantity. (1977). Thermoelectric power The most sensitive of the transport properties is the thermoelectric power. and phonon or electron diffusion (which greatly dominate the total resistivity and thermopower) do not play a role.. when compared to the others. The magnetoresistance is an important property in the Kondo effect where an external field destroys the Kondo state. peak in IQI near TK (Daybell 1973).124 J. 28. A similar comparison was performed for Z_LrMnby Jones et al. NIEUWENHUYS property. Dilute Kondo alloys exhibit strong anomalies with a large. the overall magnetoresistance character may be related to the magnetization M(I~H/k(T + 0)). 1970. However. 1977. There exist thermodynamic relations which relate the temperature dependence of the sound propagation to the specific heat. (Moran and Thomas 1973. we can discuss the general thermopower behaviour. SPIN GLASSES 125 Using A_uuFe as a prototype spin glass. This theory treats the sign changes and maxima in Q and derives a scaling in c/T for Q when interaction effects are present. .6T[6kG]. but only for temperatures below Tf. Tlolm~xis always much greater than Tf. Extended and systematic investigations of the many different spin glass systems is presently lacking Nevertheless with the now available data. still they permitted a consistent (with other measurements) determination of the freezing temperature. Figure 28 illustrates the temperature dependence of Q for four concentrations of A__uFe (Cannella et al. Other spin glass alloys which have been studied. where the maximum in IQI is distorted into an obvious change of slope at T ~ Tf. An example of these general trends is the A_uuCrsystem (Ford et al. show similar behaviour allowing for certain changes in the overall sign of the various contributions to Q. The magnitude of Q at TIQImaxremains relatively constant until about 1 at. For A___u_uFe. 1973). For typical magnetic ordering (long range).2 at. 1976.DILUTE TRANSITION METAL ALLOYS. Ultrasonic experiments Ultrasonic measurements are very sensitive to magnetic phase transitions and have provided much useful information regarding the critical behaviour. There was no sign of anomalous behaviour in the longitudinal wave sound velocity at 30 MHz as the temperature was varied through Tf in zero external field. By employing the high resolution (1 part in 107) of this technique.6 and 11 at. C__u_uMnand A. Cannella and Mydosh 1972). for A_.a noticeable change of velocity occurred for an external field variation 0 ~ 0. we may draw the following conclusions: (a) There is no indication of the freezing process from the thermopower*. small deviations from background did o c c u r at Tf. AuMn (MacDonald et al.___uuMn. 1962) and C_uuMn (Kjekshus and Pearson 1962). a sharp maximum in the ultrasonic attenuation and a clear minimum in the ultrasonic velocity have been observed at To or T~._qCr (c = 4. 28). These minima required the utmost in sensitivity to detect. *Very recently Foiles (1978) has proposed the temperature at which the thermoelectric power reverses sign to indicate the freezing temperature.% there is a rapid increase. this maximum in IQ[ is at first slowly shifted to higher temperatures.% Cr). Hawkins et al. above which it decreases (see fig. Both of these statements are fully consistent with the interpretation and results of the resistivity measurements. As the concentration is increased and spin glass effects appear. and (b) The high temperature peaks in IQ[ suggest the presence of correlations and interactions among the spins well above Tf. due to the presence of additional scattering mechanisms. Hawkins and Thomas 1978). the spin glass freezing for different systems has been studied by Thomas et al.%. Above ~ 0. An interacting pair description of the thermopower has been given by Matho and B6al-Monod (1974). with T~oIm~around 100 K. 1965). 1967. 1970). 1970. none were at that time able to resolve the question of a magnetic transition. The one feature common to all these measurements is a sharp transition temperature (Window 1975). Two conclusions are indicated from these experimental results.A. Additional systems were investigated with a variety of M6ssbauer isotopes 19~Au and H9Sn in order to further probe the magnetic ordering (Borg and Pipkorn 1969. This would further suggest a corresponding maximum in the specific heat at Tf.the freezing process is plainly evident from the ultrasonic velocity. there are certain field dependent excitations which exist for T < Tf and they clearly affect the magnetoelastic coupling down to the lowest temperatures.126 J. Window 1969. canted) ordering to occur. 4 K. the M6ssbauer studies showed that a clear hyperfine field splitting occurred at a distinct temperature. Additional measurements are needed to better resolve the ultrasonic-spin glass situation. While the early macroscopic methods all exhibited certain anomalies in the low temperature properties.s e e fig. The low temperature (T ~ Tf) M6ssbauer studies have also given information regarding the local spin arrangements within the ground state. Window et ai.2. the spin alignment (ferro. to those observed for long range ferro. Significant departures from randomness were observed due to the application of an external magnetic field (Borg 1970). Such a study by Craig and Steyert (1964) showed a peculiar type of antiferromagnetic (weak. the anisotropic part of the exchange interaction between nearest neighbour Fe atoms determines the direction of the magnetization of these Fe moments.or antiferromagnetic) can not be distinguished in a M6ssbauer measurement without using an external magnetic field. and an M(T) functional fit was obtained which did not differ much from that of pure ferromagnetic i r o n .AuCr c ~>4 at. Window 1972) focused upon the nature of the magnetic ordering. MYDOSH AND G.2. yet quite rounded. The main thrust of the present day M6ssbauer work is towards exotic . A comparison with computer simulation signified this anisotropy to be of dipolar-like form (Window 1972. This hyperfine field can be related to the local spontaneous magnetization. Window 1975). Secondly. Firstly. N I E U W E N H U Y S The general shape of the minima was similar. Gonser et al.or antiferromagnetic phase transitions. 1973). for a particular alloy . Borg 1970. Ridout 1969.J. An unique freezing temperature was found which coincided with the Tf extracted from the low field susceptibility (Borg and Kitchens 1973. At low temperatures a random distribution of magnetic moments was determined on the basis of the intensity ratios of the M6ssbauer hyperfine spectrum. Here the important result is that for AuFe. However. Microscopic properties M6ssbauer effect The M6ssbauer technique measurements were the first to indicate the existence of "magnetic transitions" in AuFe and CuFe alloys (Borg et al. 3. Nevertheless. 29.% . A number of other M6ssbauer investigations (Violet and Borg 1966. 1963. I O. however.1 to 1 at.8 1.9 --~-~'ff'----~---~.DILUTE TRANSITION METAL ALLOYS. .3 I 04 I 0.% Mn) over a wide temperature range. 29. especially the rare earth M6ssbauer elements. After Borg et al.3 0. It would be worthwhile to perform one last very sensitive measurement through the freezing transition to test the sharpness and consistency of Tf.5 I 0.9 I 0.5 7.I ~.4 10.~ 0. Nuclear magnetic resonance Up until recently it has not been possible to follow the temperature dependence of an NMR signal for a typical spin glass alloy.9 tD TITc Fig.0 v v 0.1 O.~ 0. The former linewidth result was interpreted as being in disagreement with the notion of a cooperative freezing at Tf of spin orientations. A difficulty with these experiments was the necessity of performing the resonance in .2 I 0.6 I 0. There were.8 I 0.2 0.4. decreases in the longitudinal and transverse NMR relaxation times and a gradual variation of the resonance intensity through Tf.7 II * • • 11. while the latter results indicated important modifications of the impurity spin dynamics for T > Tt. Normalized temperature dependence (To = Tf) of the hyperfine splitting (proportional to the /flagnetization)determinedfrom the Mossbauer effect for five Fe concentrationsin Au. 0.C 0. The first of these investigations by MacLaughlin and Alloul (1976)at the lower end of this concentration decade reported no abrupt increase in linewidth below Tf. systems. (1963). SPIN GLASSES 127 I. In the past few years the host NMR technique has made available linewidths and relaxation of 63Cu in dilute C___quMn (0.8 0.7 I 0. here a spin glass state is indicated at very low temperatures. This new and highly sensitive technique gives a measure of the direct magnetic dipolar fields and the contact field from the RKKY polarized conduction electrons. Also a dramatic decrease of the spin echo transverse decay time constant. distribution of hyperfine fields which are static on a time scale of 10-4 s.b. The temperature dependence of the local fields showed a significant difference between a 0.2 and 0. in contrast to the giant moment ferromagnetism (no negative oscillations in the *New measurements by Alloul (1979) have studied the formation of the spin glass state in C__u. 1976. A = (%+T2*)-j.b) extended their experiments to include these higher concentration alloys. The appearance of local fields causes A to increase via additional depolarization. was observed at Tf. i.28at. There are also field cooling effects giving a large constant depolarization rate below Tf. A series of A__u_uFeand C__uuMnalloys have been studied in this manner by Fiory and co-workers (Murnick et al.% Mn in Cu.6 at. . static spin configurations over the characteristic time of measurement. particularly when the macroscopic measurements X.% Fe sample. Fiory 1976).% Fe and a 0. Here definite evidence was found for a low temperature frozen configuration of Mn spin. certain nuclei were lost from the observed resonance. 7"2. and this presented a further problem with the data analysis.uMnby field cooling the sample and then performing NMR with the field set to zero. Positive muon spin rotation (I~+SR) The precession of polarized muons can be used to determine the distribution of local fields within a spin glass alloy.A. and good agreement was obtained with Levitt and Walstedt. Thus. MYDOSH AND G. Furthermore the temperature width of the transition increases with applied magnetic field. (1977a. along with indications of short range order and fluctuation slowing down in the region around Tf.e. N I E U W E N H U Y S external fields* larger than 0.1/xs. In fig. Very recently Bloyet et ai. At the lowest temperatures the extrapolated limits of A are consistent with random.128 J.8kG] which will greatly smear out the freezing process. In addition.18T[I. MacLaughlin and Alloul (1977a. (1978) have reported NMR results which indicate a well-defined Te below which all impurities interact and behave collectively. 30 IX+ depolarization rate and A data for A__.c) have further used the/z+SR technique to probe the conduction electron polarization in PdFe. More recent measurements of the inhomogeneous broadening of the Cu NMR linewidth were carried out by Levitt and Walstedt (1977) on a higher concentration ~1 at.J. Nagamine et al. O.% C_p_uMn alloy. where ~/~ is the muon's gyromagnetic ratio and T~ is the tx + depolarization time. here ~ 0. This then leaves open the question as to why such a drastic change in the NMR behaviour occurs between concentrations of 0.015 at. The reason for this change in behaviour was attributed to conduction electron spin oscillations of the RKKY in the lower concentration alloy.u_uFe are shown as a function of temperature. Note the abrupt change in A near Tf as determined from the low field susceptibility. Cm show nothing unusual in this concentration regime. ~t÷ depolarization rate. Tr is 7. 30. o • 8 5 Oe fc 330 Oe fc 1 8 9 0 Oe fc 1 8 9 0 Oe z f c ~3 O O f~- qo 0 n 0 o . expressed as a line-width in Ga-ss.7 K for CuMn and 11. °1 A ~" o A 85 oo . (1976). . 8 1'2 r (K) {6 ~o o t'kt. plotted against sample temperature for several values of applied magnetic field. respectively.6 K for AuFe. After Murnick et al.57. 8_. fc and zfc mean field cooling and zero field cooling.[ I AuFe 1.DILUTE TRANSITION METAL ALLOYS. SPIN GLASSES 129 o I o o- CuMn 07% o g.c 1 8 9 0 Oe fc O 0 4 8 12 16 20 r (K) Fig. J. : 04 ~-1 I I I .L 52-*3~\ . Also included is the low field ac susceptibility X(0).1. The broad line was interpreted as due to the fast relaxation process of single spins.. ii / i' 1. .130 J. We begin first with the high temperature (T>> Tf) measurements. two quasi-elastic lines were found with different linewidths (Scheuer et al.2.0 ' i I I '~ ×(o) 3. f=16 Hz i 56 / .. MYDOSH A N D G. Neutron scattering With the availability of very high flux reactors.A. By using diffuse scattering of unpolarized neutrons in AuFe with zero external field.% Fe in Pd sample. Both iinewidths have a Korringa-like linear T-dependence (with different slopes). After Murani and Tholence (1977). Wave vector dependent susceptibility x(q) as a function o f temperature for a C u + 8 at. 1977a.\K\\ "~ \\ o-~ % : 0. See section 3.00e \=. the problem of neutron absorption in the noble metals has been alleviated and neutron studies on the most typical AI!Fe and CuMn spin glasses are now on hand. N I E U W E N H U Y S conduction electron polarization) of the 0. etc.0 / ~" -. but as the temperature is lowered towards Tf the intensity of the slower (cluster) linewidth grows at the expense of the faster one.0 o constq : 0 2 ~ \\ a .08 A O) o v X 2.28 at.% Mn alloy.b).0 / . triplets. 31. averaged collectively). 4.o H<2. while the narrow (or slower) one represents the effect of spin clusters (pairs. I 50 ~00 T(K) )50 200 Fig. e. low field and frequency (ac) susceptibility. Yet the q = 0 susceptibility gives a Tf = 40 K. the static wave vector dependent susceptibility x(q) may be obtained as a function of temperature. the intensity is then proportional to x(q)T with a fairly long measurement time constant .DILUTE TRANSITION METALALLOYS.SPIN GLASSES 131 A series of neutron scattering experiments by Murani and co-workers (Murani and Thoulence 1977. has a typical time constant of 10-2 s. The results show a maximum in x(q) which is especially clear for the lowest . Since Tf ~ 40 K. On the other hand. the static susceptibility has its very long measurement time and is particularly responsive to the largest of the magnetic clusters. at T ~ 2Tv Again such behaviour is fully consistent with the other high temperature measurements in suggesting local correlations and the building of magnetic clusters.1 0 -3 s. % Mn spin glass. the integrated quasi-elastic. 1976b) have focused directly on the temperature region near Tf. _ _ _ ~ u + 10 and 13 at. while the neutrons are mainly responding to the smallest and fastest of the spins. this behaviour indicates a diminution of the fast relaxing spin component. Murani 1976. X(0) detects the freezing of the largest clusters at Tr. By properly calibrating the scattering cross-section. Of importance here is the strong q dependence of X. while the elastic cross-section begins to increase below this temperature. paramagnetic spins. these latter spins are too small in number to adequately contribute to x(q). elastic and total cross-sections have been determined at various temperatures for a Cu + 8 at. Here the cluster growth rate and relaxation time play an important role. Here the temperature variation of the small angle scattering intensity is determined for various values of q. The results show a smoothly decreasing quasi-elastic component as the temperature is reduced under about 80 K. The best neutron determination for the temperature of the maximum is 50 K with q as small as possible. there is no indication of the freezing process. i. Figure 31 illustrates this x(q. T) dependence.08 A. The reason for this temperature difference is intimated by the various times of the two measurements. By assuming the observed scattering to be mainly quasi-elastic. By employing time-of-flight spectrometry and a separation analysis. the very fast neutron scattering will see the fastest or non-interacting spins. Also included in fig. and the 10 K difference between the two types of measurements may be considered as a wide temperature range slowing down. the scattering cross-section and x(q) are insensitive to these magnetic entities and will drop. Once these become correlated (dynamic-correlation times greater than 10-" s) with sizes greater than 1/0. Thus. % Fe. while for the neutron scattering the instrumental energy resolution sets the time constant scale at about 10-I~ s. a maximum starts to appear in X.Tc)/Tc region that is normally found. So it would seem that the freezing process represents the cooperative "locking-in" and growth stoppage for these largest clusters. afterwards it falls off with further reduction of the temperature. Another neutron scattering investigation (Murani 1976) has been the small angle measurements on A . This results in a rather smeared "critical phenomenon" with a much larger ~ = ( T . Therefore. However as q is reduced. 31 is the static q = 0. At T--->Tf.At large q-values (very small regions of real space). the ac x(q = 0) using audio frequencies. Murani et al. deviations from linearity appear and result in a low T concentration dependent minimum with AH still increasing at the lowest temperatures (~--1K). while there are small entities (single spins or localized excitations) which can contribute to x(q) at a lower temperature. AgMn. Nevertheless a systematic investigation and connection with theory of ESR effects in simple spin glasses is presently lacking. In a complete experimental review.. Although there are certain difficulties with the "bottleneck" effect. etc. Such behaviour. A wider series of neutron studies on lower concentrated alloys would be most useful. There is fair agreement between the values of the freezing temperature for the x(q -~ 0) maximum and the low field a. indicates a change in the spin relaxation rate to larger values due to spin-spin interactions as T-~ Tf from above.J. showed a weak minimum and a line shift became apparent. Electron spin resonance ESR measurements on the magnetic ions in CuMn. The first results indicate the presence of magnetic excitations in a spin glass for T ~ Tf. some very recent diffuse inelastic neutron (time of flight) measurements. MYDOSHAND G. susceptibility (see Soukoulis et al.c. have been begun at the lowest temperatures (Scheuer et al. It would seem that the temperature and concentration variation of AH exhibits the same general form for many spin glasses. This suggests non-propagating (dto/dq = 0) localized modes. He found a welldefined maximum in the signal amplitude at a temperature where the ESRlinewidth. but for these rather high Fe concentrations (beginning of the mictomagnetic regime).This range of temperatures indicates that the largest clusters freeze out first.g. 1977c). once this is broken. there is the usual Korringa thermal broadening AH ~ T. A continuously variable temperature spectrometer was used by Griffiths (1967) to obtain the complete temperature dependences for CuMn. it is most difficult to carry out an exact comparison of the various samples and measurements.A. e.2 meV = 49 K > Tf = 27 K. By estimating a characteristic temperature from the x(T) maximum. AuMn. The preliminary analysis shows little dispersion with to being constant for three different q-values. Taylor (1975) has discussed the general area of ESR for magnetic ions in metals. % Mn sample at a rather large energy hto = 4. a shifting of the ESR ling to lower fields below the "ordering" temperature along with hysteresis and field cooling affecting the ESR results. as the temperature is reduced. the smallest q-values give the largest Tm~x. This "characteristic:' temperature is well above the freezing temperature determined from other measurements. AH. (1978c). At high temperature. A final point regarding microwave frequencies has to do with the frequency . However. offer another method with which to study the spin dynamics of a spin glass. often referred to in the literature as "ordering effects". Finally. a direct study of the interacting magnetic impurities becomes possible.132 J. (1957) already contained many indications of spin glass behaviour. For an alternative description see Verbeek et al. 1978). The early work of Owen et al. Much more work has been carried out on the rare earth ions. NIEUWENHUYS q-values. A well-defined excitation peak was found in a Cu + 5 at. additional work is necessary to pinpoint the mechanism for this frequently occurring and often postulated anisotropy. e. a good spin glass.dom. .anisotropy. we can collect the previous survey of experimental results into a phenomenological description of the *Currently. and 6°Co in Pd. (1976) were carried out on PdHMn and PtMn. this unequal population produces an anisotropy in the y-ray radiation pattern.SPIN GLASSES 133 dependence of the low field susceptibility X(to). 1979).e.the frequencydependenceof the lowfieldsusceptibilityis the subjectof intenseinterest(see Dahlberg et al. Thus. This suggests that. Nuclear orientation At very low temperatures (inK). the nuclear sub-states are unequally populated. Further NO investigations by Thompson et al.The authors found it necessary to assume a distribution. the hydrogenation greatly increases the strength of the random freezing. Flouquet et al. 1978) and Thomson et al. H~er= Hext+ H~. 3. At present there has been no X(to) experiments from the audio frequency range ~10 2 Hz through the radio bands up to the microwave frequencies 10j° Hz. (1976. the spins do not freeze into a fully random array. i. In a series of nuclear orientation experiments using 54Mn in Pd and Au.DILUTE TRANSITION METALALLOYS. A strong decrease in Hen. From macroscopic measurements (Mydosh 1974) we know the same to be true for PdHFe and P_ddFe. but that a local anisotropy exists and gives the spins a preferred direction. The freezing process Before proceeding with the theory of random alloys. random in direction and Gaussian in magnitude for the local field on the Mn ions. Such a study would be most useful in determining the spin dynamics and relaxation of a spin glass near T~'. on a microscopic level. This distribution of radiation is proportional to the local magnetic hyperfine field which orients the nuclei.2. and thereby probes the field seen by the atom or ion. a preferential nuclear spin ordering axis was found in the absence of an external field. The method of nuclear orientation (NO) may be directly used in very dilute Mn spin glass alloys or it may be employed as a hyperfine field probe of other interacting impurities. Upon the radioactive decay of certain elements. the NO studies showed that although both PdHMn and PdMn are spin glasses at sufficiently low T and c.3. Certainly. Such spin glass effects were clearly seen below 10 mK for as little as 10 ppm Mn and as little as 3 ppm Fe parasitic impt:rity. The distribution half-width was four times larger with hydrogen charging than without. This indicated the presence of the random spin glass freezing which prevents a full alignment of Hhf.g. Mn in the former system was much more difficult to orient (a greater misalignment) with an external field at low temperatures than unhydrogenated p_ddMn. due to local misalignments of the hyperfine field axes. occurred at low temperature.For PtMn. (1977. 54Mn and 6°Co. 1978) have measured the temperature dependence (~-3-25 mK) of the effective field He~ = Hhf+ Hext from the y. TB. and does not represent the well-defined "chemical particles" of N6el super-paramagnetism. e. the various spin components begin to interact with each other over a longer range and the system seeks its ground state configuration for the particular distribution of spins. a "window glass". For a distribution of EB's or TB's. Now there . as the temperature is lowered from T >>Tt. Here the statistical mechanics of phase transitions may be invoked. show a wide range of behaviour depending upon the particular space or time region. 1978). ~'m). at which these domains cannot overcome an energy barrier. Transitions over the barrier require thermal activation. as is required for the spin glass case. will give no clear indication of the freezing process. such as the specific heat and the resistivity. governed by the anisotropy energy and the interaction with the external field. it is frozen. and various critical phenomena and exponents for the thermodynamic quantities can be calculated near Tt. The first model (Tholence and Tournier 1974. rm. Experimental techniques which are not sensitive to these clusters. 1977) extends the N6el description of superparamagnetism to the random metallic systems. Domains are formed and the freezing is a result of a distribution of blocking temperatures. the maximum TB determines Tf. A final model which we propose here for the spin glass freezing would draw heavily upon comparison with the solidification process of real glasses. The anisotropy is basically provided by the dipolar coupling. As T ~ Tf.A.J. MYDOSH AND G. EB. The second approach (Edwards and Anderson 1975) replaces the randomly situated moments and the oscillatory RKKY interaction with a regular lattice of spins which have a Gaussian probability of exchange interaction strengths P(J). which essentially determine x(q. to) and thus the response as a function of r and t. although cluster shape anisotropy could also play a role. Luttingen 1976. although this model might easily be adopted to the dynamical cluster case. More exact and sophisticated treatments based upon this starting point have been recently obtained (Sherrington and Kirkpatrick 1975. 1977). The exact nature of the freezing process is presently unresolved. EB(TB) = k~TB ln(const. The application of the N6el theory to spin glasses and a review of its fundamental concepts has been recently discussed by Guy (1977a. We note that this cluster growth process is strongly dependent upon the alloy randomness and the temperature. 1976. Thouless et ai. A unique feature of the spin glasses seems to be the wide temperature and concentration regimes within which the spatial and temporal correlations are varying. and there are three main schools of thought which focus on this problem. This means a favourable set of random alignment axes into which the spins or clusters can lock. NIEUWENHUYS freezing process. The freezing takes place in both the spatial and time dimensions with the largest and slowest of these dynamically growing clusters responsible for the sharp effects at Tf. many of these randomly positioned and freely rotating spins build themselves into locally correlated clusters or domains which can then rotate as a whole. If the domain is blocked for a time greater than a typical measurement time. The remaining loose spins serve to transmit the long range interactions between the clusters.134 J. First. The neutron scattering measurements. Harris et al.g. %] I I IIItll I l I Illlllio 0 loo AuFe f domplng J l 1 x ~ -0. etc. as the molten liquid is cooled into an amorphous solid.Om 1 Fig. At present there are no direct references or detailed comparisons on the possible similarities of these two "glass" systems. 32.. density. volume. SPIN GLASSES 135 is no distinct phase transition. After Larsen (1978a). but a gradual change in the behaviour of the viscosity. A first test of such behaviour would be to measure the low field spin glass susceptibility near Tf as a function of various cooling and heating rates. dT/dt. Collection of characteristic temperatures for AI!Fe alloys over the complete concentration range.DILUTE TRANSITION METAL ALLOYS. I 10"e l t0 °s C I 10"1 I I0 "l . beginning both above and below Tf.00 J~C) M6ssbouer spectroscopy 0 • A x 01 10"s I 10"s r. Most important in this model are the irreversibilities and the dependences of the experimental properties upon rates and directions of the temperature variation. . I o oool i i i i!iill o ool i I lilil[ o ol i I I I i11111 I I i illill o1 Io Io Fe FRACT[0NAL CONCENTRATION lot. Since the process of cluster growth has now stopped.! g < Susceptlbiht y maximum Resistivity maximum NOISe |1. most measurements exhibit irreversibilities and relaxation time effects. At the lowest temperatures T ~ Tf. These localized modes are probably related to quantum mechanical tunnelling through the energy barrier. A.136 J.. The solid lines represent . 1978a. Tf(c) can be evaluated for the entire concentration range. After L a r s e n (1978b).. --y.. the model of N6el super-paramagnetism can be used to describe many of the frozen spin glass properties. A _ _ _ u _ u F eand C__u_uMn.b).1}z/2{~. M Y D O S H A N D G.p~P J 1 _- ~ 10 = . Figures 32 and 33 illustrate the results of Larsen. magnetic excitations involving diffusive.A... In addition to this classical energy barrier process. highly damped spin fluctuations are also present.: Z o SuSceptibility moxlmum O .i 10 .iA2.- 0~ I ~ ~SIStlVlty N0fSe mOxl~m 1178 A c l scotlerlng • ~//// Neulron N e I0 "6 ! 10 -5 I 10 -4 I 10-3 C l 10 -2 I 10-1 o~ Fig. A collection of freezing temperatures for the two most-studied spin glasses. (self) damping e . This calculation begins by relating kBTt to the RKKY interaction envelope A(r)~ 1/r ~ which is consistent with the Edwards and Anderson expression for the freezing temperature kaTf = ~{(2S+ 1)4 . and the effect of fluctuations in the nearest neighbour distances. r=0 1100 100 FRACTIONAL CONCENTRATION lol %1 co...~ of the RKKY interaction. Collection of characteristic temperatures for CuMn alloys over the complete concentration range. 33. By considering the mean free path.J.} I/2. N I E U W E N H U Y S I 0 0001 i I I IIIiii 0 001 I = ~ la~J=l 001 ! Mn ¢ i ~ITBJl 01 1 : I rl~l:[ 10 J [ t IIl~...and a theoretical model to calculate the concentration dependence of Tf have been given by Larsen (1977. • • . e. due to 17 at. Another theory of Larsen (1976. we do not in principle exclude orbital momenta). Jo = J(ro). the M6ssbauer effect and neutron scattering. The results of this "noise" theory give an additional set of data points for Tf in figs. SPIN GLASSES 137 the theory with a scaling parameter r(c) which may be obtained from the experimental residual resistivity. 4. The measured Tf-points are determined from the susceptibility maximum. then the Hamiltonian (without external magnetic field) can be written . It is obvious that such a thorough treatment is beyond the scope of the present article. and. finally. Furthermore.1.. their direct and indirect interactions among themselves. This J~i is assumed to depend only on the distance between the magnetic moments.u_uFewhich has TK = 0. Theory of random alloys A complete survey of the theory of dilute giant moment systems and spin glasses should contain a description of the existence of the magnetic moments in metals (i.5). the theoretical description of the ordering phenomena is fairly complicated due to random positions of the magnetic atoms in the host matrix.2 K and thus shows a significant depression of Tf below this Tg. % (see section 1. its "percolation limit" is -~45 at. so that there is little competition between Kondo and spin glass effects down to the lowest concentration. In the first we will describe a random molecular field theory which gives the magnetic phase diagrams of ferromagnetic/spin glass alloys. If the spin operator of the magnetic moment i is denoted by S~ (S instead of the total angular momentum for simplicity. In the second part we will give a limited review of the important literature on the theory of these alloys.the Kondo temperature is very low (~-10 -2 K). For C__uuMn. denoted by J~j. deal with the atomic physics in a metallic environment). Since the long range magnetic order in C____uuMnis of the antiferromagnetic type. Even if the interaction between "good" magnetic moments is known.DILUTE TRANSITION METAL ALLOYS. and which roughly describes the experimental phenomena. and there are no deviations at the high concentration limit. Larsen et al. 4. In order to make this theoretical section consistent with the lines used in the experimental sections. The opposite is true for A_.% percolation for ferromagnetism. R a n d o m molecular field model In this model it is assumed that the bare magnetic moments exist and are stable. an upward departure from the theoretical line results at the high concentration limit in AuFe. we shall divide this section into two parts. the ordering phenomena due to these interactions. their interactions with the itinerant electrons. 32 and 33. Due to direct and/or indirect correlations there is an interaction between each pair of magnetic moments i and ]. As can be seen by comparing these two figures C____u_uMn is a well-behaved spin glass over the full 5 orders of magnitude of concentration. 1977) connects the temperature of the resisistivity maximum with the freezing temperature. A. This technique (Marshall 1960. This probability is then given by P ( H ) dH. and z is the effective number of neighbours. To obtain results from this Hamiltonian one should go to better approximations.J. Another approach to the spin glass problem (called at that time the dilute alloy problem) has been made by Klein (1968).~ equals ZJo and J = J~/z.1) The zeroth order approximation to the solution of this Hamiltonian is the molecular field approximation. We reproduce this phase diagram in fig. One is due to Edwards and Anderson (1975) in which they treated the Hamiltonian assuming a Gaussian distribution of J.138 as J. (4. Then. have appeared since then. 34. N I E U W E N H U Y S = -~ i>j 2J(rti)S~ • Sj. based on the Random Molecular Field Approximation (RMFA) introducted by Marshall (1960). Two important approaches have been suggested in recent years.# according to P(J. Many theoretical papers. according to which the alloy may become a spin glass or a ferromagnet depending on the ratio between J0 and J. leading to coupled integral equations for P ( H ) and the magnetization. On the basis of this distribution of J0 they could (via a replica technique and applying the n -->0 trick) derive an expression for the free energy and found that a phase transition occurred at T = J]kB. where . It should be noted that P ( H ) is temperature dependent. Sherrington and Southern (1975) and Sherrington and Kirkpatrick (1975) investigated a mixed ferromagnet]spin glass system by using a slightly different distribution function 1 / and these authors derived a phase diagram. since it depends upon the direction of the magnetic moments. but it will lead to wrong results in the case of a spin glass because of the oscillatory character of J(rij). including a quantum mechanical version and computer simulations (see next section). Klein and Brout 1963) has been more recently applied to giant moment alloys by Korenblitz and Shender (1972) and by Nieuwenhuys (1975). investigating the so-called Edwards and Anderson model.'i)oc exp(-J~/2j2). which must be calculated via the P(H).. In this approximation the probability is calculated that a magnetic moment (taken to be at the origin) senses a molecular field between H and H + dH. M Y D O S H A N D G. This approximation may give a solution for ferromagnetic ordering with J(rij)> 0. the Hamiltonian is written as i where 171 = ~ J(r~)(Sj). In order to characterize magnetic alloys it would be sufficient to calculate the . Afterwards the total interaction can be formed by incorporating the direct short range interactions.3) Bearing in mind that the parameters entering the phase diagram are given by ZJo and J'k/z. Obviously.3).25 0. Therefore.DILUTE TRANSITION METAL ALLOYS. however. Recently.0 PARA 0 SPIN GLASS i 0.50 I 0.00 0. an effective interaction range has to be defined. 34.25 I 0. For the itinerant electrons with intraatomic exchange enhancement the susceptibility can be calculated according to . multiply these by z and X/z respectively to obtain J0 and Jand compare these values with the phase diagram given by Sherrington and Kirkpatrick (1975). P(Jii) curve. which may be considered as a free electron gas is given by the RKKY formula (see section 1. deduce the mean value and the width. (4.0 0. Klein (1976) showed that if one calculates the P(H) on the basis o f the distribution P(Jii) as used by Sherrington and Kirkpatrick (1975) and then calculates the properties of the system by the RMFA. After Sherrington and Kirkpatrick (1975).75 JoIJ 1.ZJo)2~ 2zj2 j. SPIN GLASSES 139 1.25 Fig.50 0.25 kr/Y 1. the results are identical to those obtained by Sherrington and Kirkpatrick (1975) using the n ~ 0 expansion. and then to use the mean and the width to deduce its location in the phase diagram. Phase diagram of spin glass/ferromagnet. since the major part of the mutual distances is relatively large. If ferromagnetic ordering prevails the molecular field distribution at T = 0 as found by Klein (1976) is given by P(H)=~ 1 exp - { ( n .0. Unfortunately. it might be sufficient to calculate P ( H ) at T = 0 for any given alloy. The generalised susceptibility of itinerant electrons.75 0. it is rather difficult to calculate P(J~j) even if the distance dependence of the interaction is known. The interaction as a function of the distance can be calculated assuming that the indirect interaction is governed by the generalized susceptibility of the itinerant electrons. and the resulting P(JQ will depend on the choice of this interaction range. the distribution will be sharply peaked at J~i -'.00 1. 0 If we let the volume of the system go to infinity. ~Jl~Jl = ~ 1 1 J(r. but we have to include its complete form 1 kF / F(q)= ~+~.8) Taking the limit for d H ~ 0 and writing e ipl~'u(r) as [1 .½d H < ~ J(r. the probability can be written as F(H) dn = (4~/V3" f. N I E U W E N H U Y S Schrieffer (1968) via the random phase approximation (see section 3.j)l~l < H + ½d S .(.6) The integration extends over the range of r values such that H . The term in the brackets may be written as V ( 1 _ D) f [l _ (l _ eiol. (4. We shall follow Margenau's paper.. J (4.. while maintaining the density ..elpl~'lJ('))r2 dr. M Y D O S H A N D G.7) this becomes (4.dr. f r~. The molecular field acting on a magnetic moment in the origin is given by ~. sin(½pdH) _ 1.5) Assuming a homogeneous distribution of n magnetic moments in a volume V.140 J . f + ~ . Since we are now interested in giant moment alloys as well as in spin glasses..4) Once the distance dependence of the interaction is known (after inclusion of the direct interaction) the P(H) at T = 0 may be calculated according to Klein (1968) applying a method developed by Margenau (1935).j)l~l.dr. x L ~ op p expt-.. .np +ipl~]~/(rij)]. A . the integration can be extended over the whole volume 1 (4 y P(H)dH---~\-f/ f .....l.+ ..._qq ~l_~k~ ) .1) the approximation of the Lindhard function for small q..)]r2 dr = _~_w~ 00 (4.J. (4.... (4..1). f r~.r~dr.. we cannot use (as in section 3.p{f [1 -(1 - eipl~11('))]rz dr}".. J By using the Dirichlet representation of the 8-function.n 12k---f=-~_ 12kF+q' ql._.9) where D = 4zr f (1 .( 1 -eipl~'lS(r))] P(H) = ~-'~\--Q-] 1 (4~-3" f -00 do e_. r~dr. Fig. Then. N. SPIN GLASSES 141 nl = n / V constant.~ 'f do e -i~°-~'D. we reach lim n-oao ( 1- = e -nm° +¢o thus P ( H ) -. In fig. The calculated mean value (f H P ( / . on the basis of eq. is shown for several values of the Stoner enhancement factor.10).DILUTE TRANSITION METAL ALLOYS. As can be seen from the graph the freezing t. respectively. Note that no adjustable parameters have been used in this model. 36a we have used the lattice spacing and Fermi wave vector for AuFe. We have calculated the generalized susceptibility within the random phase approximation (see section 3. ~~}v2). then determine the position of the alloy in the phase diagram. In fig. The results are shown in fig.9) and (4.4). 35.I ) d H . using eq. (4. (4. = ./ ) d H ) and width ({f t t 2 p ( I .1) as a function of 2kFr. by assuming J(r) to be proportional to this susceptibility. (4. for several values of the concentration (or density n0." the P ( H ) curves have been computed. The generalized susceptibility multipliedby (2kFr)3 as a function of 2kFr for three values of the Stoner enhancement factor. 35 this suceptibility.10) From this distribution function the parameters for the phase diagram can be calculated straightforwardly. multiplied by (2kFr) 3 for clarity of the graph. 36 for ~ = 1 and ~ = 10. Investigating the possible causes of this disagreement. NIEUWENHUYS temperature is proportional to c °52.. 36. .J. MYDOSH AND G.6 0.b) on PdFe 0..4 0.A. . ' "'"~'"f/~e 10 5 I ¢ . we conclude that the Sherrington-Kirkpatric phase diagram cannot be used with extensive parameters in the case of a "non-symmetric" P(H).12) where Bs(x) is the appropriate Brillouin function.% (depending on the magnetic quantum number).0 Fig. If n is the total number of magnetic moments then on the average there will be nt={n[l+(MIm)] --S= 2... Let the mean absolute value of the local magnetization be denoted m (m = and the mean value of the bulk magnetization by M.%.015 and 0.5 . For ~ = 1 the ordered phase is the spin glass one.~ I 2 J 4 I . a{.. for ~ = 10 the spin glass exists up to about 0.. Clearly. In order to improve the calculated phase diagram we have to go one step backwards. In fig. the spin glass phase exists up to rather high concentrations of impurities.8 at. so that combined with the second one. The first fact gives us some confidence in the calculation of P(H). S= dO Pd-based . 36b the parameters have been chosen. which is in fair agreement with the results from experiments. (1977a. for this limited concentration region. .142 J.3. in contrast to the experimental observation.6 at.°/. (ii) The form of the P(H) obtained for the Pd-based alloys differs considerably from that used by Sherrington and Kirkpatrick (1975). Then the equations for m and M read (Klein 1976) +~ --o0 +co f xlG 3 20 I ' I ' I ' I ('.25 at. corresponding to the properties of Pd-based alloys. see section 3. The calculated phase diagram for (a) an alloy (AuFe) with ~ = 1 and (b) for an alloy (P___~Mn) with ~ = 10. it can be noted that: (i) The calculated ratio of the width of the P(H) and its mean value is in fair agreement with the results obtained with the help of /z÷-depolarization by Nagamine et al.°/ol. in that it is not at all symmetric about the mean value of H.2. I 8 J I 0 ¢ > 02 0. The calculation of P(H) may then be based on the following approximation. A transparent and mathematically simple model has been developed by Takahashi and Shimizu (1965). that between 4d electrons and the localized moments by or.n t D ( o ) .14) Equations (4. Restricting ourselves to low temperatures.14) can be solved numerically to obtain an improved phase diagram (Nieuwenhuys 1978).DILUTE TRANSITION METAL ALLOYS.11)-(4.1 the ferromagnetism in giant moment alloys is obviously correlated to the large susceptibility of the host materials.(M/m)] in the downward direction. Giant moments The magnetic phenomena in giant moment alloys have several aspects: the ferromagnetism at low concentrations (far below the nearest neighbour percolation limit). the random molecular field model is potentially able to predict a wide range of properties of alloys from spin glasses to giant moment ferromagnets. spin waves.1. and the occurrence of the giant moment itself. Noting that D(p) changes into D ( . (iv) The bare moment is localized on the dissolved atoms and the induced polarization is uniform over the alloy. In conclusion. small concentrations and weak .13) where D(O) = 4~r f (1 .ei°"O~r))r 2 dr. and (c) short range interactions. Survey of additional theories 4. 0 (4. P ( H ) will be given by +oo P(H) = ~ do exp{-iHo . if the sign of the interaction changes. the influence of direct interactions. Then the energy of the 4d electrons is given by E = IxB(aMi + IMd + Be~) where M~ and Md are the magnetization of the localized magnetic moments and of the 4d electrons. The interaction among the 4d electrons is denoted by I. (ii) Direct interactions between the dissolved magnetic atoms can be neglected. 4. This section has therefore been divided in the following parts: (a) ferromagnetism and spin waves. (a) Ferromagnetism and spin waves As explained in section 3.2. (iii) The interaction among 4d electrons and between the 4d electrons and the magnetic atoms is independent of the composition of the alloy. (b) the giant moment. respectively. and Bex is an external magnetic field.n t D ( .p ) } (4. These authors began with the following approximations: (i) The rigid band model can describe the 4d band.p ) .2. SPIN GLASSES 143 moments pointing in the upward direction and n~ = ~n[1. NIEUWENHUYS external magnetic field. leading to an expression for Tc identical to eq.17) Combining eqs. the agreement is much improved. Herring 1966). This is obviously due to the assumed uniformity of the polarization.16) where XP is the Pauli susceptibility.A. we may write . If instead of X0 a function x(r) is used.g.22) showing that a2X0 may be regarded as an effective molecular field coefficient in a localized picture.+ Bex) (4.a2Cx0)" (4. (4. the total susceptibility diverges. The same duality is found in the description of pure ferromagnetic metals (see e. we may write Mi = N~gI~BSBs[glsBS( o~Md+ Bex)/ ka T] Ma = Xp(IM~ + ctM~. This model put forth by Takahashi and Shimizu (1965) contains the main features of the static properties of giant moment alloys.15) (4. where p ~ = gI~B{S(S + 1)}2/2(1 + axe) (4. MYDOSH AND G.16) and (4.18) (4.J. The model of Takahashi and Shimizu does not solve the itinerant/localized duality of the magnetic ordering phenomena.144 J.18) one may derive M~ = C{B~x(aXo + 1)+ a2xoM~}/T (4. as shown in fig.19) When the denominator of this expression vanishes. For small arguments of the Brillouin function we may write for M~ M~ = C(aMd + Bex)/T where C = N~2I~ 2S ( S + 1)/3ka.IXP). lim(Md+M~)/Be~. On the other hand.21) which is the expression for the giant moment used throughout this present paper. (4.19) can be written as NipPy. From the last equation it can easily be seen that for zero Ni (no impurities) the susceptibility will become X0 = Xp/(1 . where r is some mean value of the distance between the magnetic impurities. (4. indicating a transition to ferromagnetism.16) and (4. The transition temperature is then given by Tc = N~g21~S(S + 1)a 2Xo/3kB. It is interesting to note that from eqs. is found to be C(1 + aXo)2 X = Xo+ (T . and Ni the number of magnetic ions.20) The numerator of the second term of eq. as Bex-->0. except that the absolute value of the transition temperature appears to be too high. (4.20). 19. It also withstands remarkably well a comparison with experimental results.18) the total susceptibility. (4. (4. x ( q ) exp{iq(ri -. As a criterion for itinerancy of the magnetism they used the ratio of the magnetic moment deduced from the measured Curie-constant and that obtained from saturation experiments.{I + Ca2/T}xp + 1 Bex. Therefore. However. Kim (1966) has calculated the properties of the ferromagnetic alloys based on the interaction Hamiltonian: ~int = J X tr(Xj)S~ (~ is the spin density operator and J is a parameter measuring the interaction between the d-electrons of the local moment and the itinerant electrons). Their conclusion is that P___ddFeand P_ddCo should be treated as itinerant (intermediate) magnets. (4. 145 (4. (1974) and by Star et al. PdCo and PdMn alloys should be treated as localized magnets (Nieuwenhuys et al. 19 and the one used in section 4.3 at. we have to conclude that low concentrated PdFe. the susceptibility to be incorporated in eq. the itinerant criterion for ferromagnetism will be given by Xp{I + Co~2/T} = 1 (4.x ( r = 0) or more exactly Ni ~.20) (using a = 2J/Ndg21~2). He then uses a canonical transformation to eliminate ~int. He extended the Anderson model (Anderson 1961) to the many-impurity case.1. leading to an effective interaction among the delectrons of the host plus the RKKY interaction. (4. Long and Turner (1970) have pointed out that in calculating the effective molecular field acting on the ith magnetic moment. (1975). ~. For itinerant (intermediate) magnetism it is larger than 1.% Ni). which diverges at a temperature Tc again given by eq.1) have made clear that such a critical concentration exists (here 2. From here he calculates the susceptibility of the band. His conclusion is that as soon as the alloy obeys the AndersonWolff-Clogston criterion for the occurrence of localized moments it will also (4.23) Defining {I + Ca2/T} as an effective d-d interaction. 1978). including also d-d intra-atomic interactions. Experiments on PdNi alloys (see section 3. For localized magnetism this ratio is of order 1. The localized/itinerant duality has been the subject of a paper by Rhodes and Wohlfarth (1965). This problem has been treated theoretically by Kim (1970).rj)}. if we apply the same criterion to the experimental results obtained by Chouteau et al.SPIN GLASSES Ma = 1 .20) should be x ( q = O) .24) which again results in the identical expression for To.25) . q i~i These authors obtain smaller values for the transition temperature via a procedure similar to the one used by us to calculate fig. one should be careful to exclude the field due to the polarization induced by the ith moment itself. Later.DILUTE TRANSITION METALALLOYS. So far the occurrence of a lower critical concentration for magnetic order has not been mentioned. O-)opt = gOopt Long and Turner (1970) have calculated the electrical resistivity due to spin waves. they arrive at the conclusion that for very low concentrations D should vary exponentially with c. Korenblitz and Shender (1976) have obtained an expression for D based on a model with essential ingredients: the random position of the magnetic moments. t . For the appropriate ranges the spin wave spectrum is characterized by wa¢ = D c q 2.( E k -.A. is given by qm~. J is approximately 2. and by o -. a low frequency acoustical one and a high frequency optical one. to) = N d k w -. Considering the experimental values of D. According to Stringfellow (1968). It should be noted that for w ~ 0 eq. To obtain the enhanced susceptibility. e. where tOopt = J M ~ + 2 J M ~ .I M ~ . Using percolation theory ideas.26) (leading to the Lindhard function for a parabolic band) X becomes (ignoring exchange-enhancement for the moment) I_.% P___d_dFevalues . N I E U W E N H U Y S order magnetically. On the basis of a molecular field approximation the resistivity is found to be proportional to T at temperatures just below To. Note that the model of Doniach and Wohlfarth does not possess the restrictions necessary for the Takahashi and Shimizu approximation. The dynamic properties of giant moment ferromagnetism have been treated by Doniach and Wohlfarth (1967).L~ fk.Ek+q) . Their starting point is again the Hamiltonian ~ = J ~'i cr(xj)SJ. = M d / 2 E F N a . respectively. Cole and Turner (1969).2 J M ~ (4. Recently.15 eV] in the case of PdFe.27) is similar to the one used by Kim (1966). while for the higher concentrations a linear dependence on c should be found.27) where M~ and M~ are the reduced magnetizations of the d-electrons and of the localized impurities. w ) = N d k W -. where D is the spin wave stiffness constant. From the calculation of the susceptibility. The borderline qmi. rather different results have been deduced from the various measured properties. and an exchange interaction between these moments falling off exponentially with distance.( E k -. After solving this Hamiltonian and including the d-d intra-atomic interaction x ( q . for 1 at. Doniach and Wohlfarth (1967) conclude two spin wave modes. This latter conclusion is in agreement with those of the other calculations mentioned above.J. (4. and obtained results proportional to T 3/2. So there is no lower critical concentration for magnetic ordering. ~ x ( q . since a distinction has to be made between the ranges of q-values because of the polarization of the Fermi sea.g. and Long and Turner (1970).fk+q.4×10-~Sergs = 0.Ek+q) (4. Cole and Turner (1969) have pointed out that the results of Doniach and Wohlfarth (1967) for the acoustic mode are only valid for q "~ qmin. but rather one for the appearance of localized magnetic moments (see also Chouteau 1976). the usual random phase approximation has to be applied.4x10-2°J [=2.146 J. M Y D O S H A N D G.Ooptq 2. Note that XPa also governs the spatial extension of the moment. Later Hirst (1970. a reasonable agreement with the predicted results is obtained. Long and Turner 1970. 1970.F. Williams et al. Similar results have been obtained by Giovannini et al. 1962). They showed that the magnitude as well as the range of the induced polarization decreased with increasing total magnetization of the itinerant electrons. (1962). Doniach and Wohlfarth (1967) derive. With the existence of the localized moment established.DILUTE TRANSITION METAL ALLOYS. considering the concentration dependence obtained by the different workers. tr(r~e)S~ (4. T. Nevertheless. within the linear response approximation Ix = glzBS(1 + aXPd) (4. The Virtual Bound State (VBS) model (Mott 1949.t = J ~. Kim and Schwartz (1968) have gone beyond the linear response approximation by considering the susceptibilities of the spin-up and spin-down electrons separately within the random phase approximation. This VBS picture has been translated into mathematical models by Anderson (1961). Skalski et al.1 (a) and Clogston et al. Zuckermann (1971) has added an extra term flXJocto 1 + aXpd.28) where rEe is the lattice site of S~ and tr is the spin density operator.2. Star et al. SPIN GLASSES 147 between 2 x 10-42 J m 2 [= 2 x 10-31 erg cm 2 = 15 K ~k2] and 10-4° J m 2 [= 10-29 erg cm: = 700 K/~2] have been reported (see Stringfellow 1968. Smith et al. In the case of large host susceptibility this polarization can be much larger than the bare moment itself. Williams 1972. Blandin 1973). representing a local extra enhancement of the host susceptibility due to the presence of the magnetic atom. Williams and Loram 1971. Wolff (1961) and by Clogston et al. From this Hamiltonian. 1971) suggested that these calculations might overemphasize the itinerant character of the localized moments. 1973. 1975). Friedel 1958) has provided a sound framework for the understanding of the existence of localized moments. the interaction with the host metal may be denoted as (following Doniach and Wohlfarth 1967) ~i. Suhl (1975) interprets the occurrence of giant moments within the Landau- . (1964). (b) The giant moment Throughout this article it has been assumed that the giant moment could be described as a localized bare moment due to the magnetic impurity which polarizes the surrounding host. 1970. A theoretical basis for this picture emerges by treating the localized magnetic moment and its interaction with the surroundings. This result explains the decreasing moment per dissolved Fe-atom with increasing concentration in PdFe. Reviews on this subject may be found in the fifth volume of Magnetism (Wohlleben and Coles 1973.29) where ot = 2J/Ng2l~. Takahashi and Shimizu (1965) (see section 4. Colp and Williams 1972. 1971. From this calculation. the calculations by Moriya provide a basis for the "giant moment" phenomenon and its spatial extension. This completely neglects possible negative values of J (e. and to predict a smaller but positive polarization of Mn in Pd. The results for 8M appear to be essentially independent of the choice of the starting model (Anderson or Wolff) and of the shape of the density of states. (c) Short range or direct interactions In the foregoing paragraphs it has been accepted that the indirect RKKY-type interactions are the main cause of the magnetic ordering in dilute alloys. giving an antiparallel polarization. Thus. the antiferromagnetic coupling between Mn-pairs dissolved in Pd or Pt is . In addition there is of course the usual exchange interaction (always positive). This is in agreement with the antiferromagnetism of Cr and Mn and the ferromagnetism of Co. The number of d-electrons in the host metal and impurity atom determine for the major part the sign and magnitude of 8M. MYDOSHAND G. giving a positive polarization. Moriya generalized the Anderson model for the case of a five-fold degenerate d-orbitals.J. However. and the other due to the admixture between the band and the impurity levels. The conclusions are that atoms with nearly half-filled d-shells couple antiferromagnetically for any value of the magnetic moment. Based on the investigation of the "two localized moment" problem by Alexander and Anderson (1964) and by Moriya (1965a). NIEUWENHUYS Ginsburg theory of second order phase transitions. as thermodynamic fluctuations. the latter being confirmed by experiments (Star e t al. From his calculations Moriya (1965b) was able to explain the giant moment of Fe and Co in Pd and the negative polarization in PdCr. From this calculation he obtains results similar to those of Kim and Schwartz (1968). Moriya reaches the conclusion that the indu6ed moment equals a constant 8M times the generalized susceptibility. 1975).g. (1962) have ascribed this interaction entirely to exchange effects. As mentioned above. Clogston et al. PdMn have shown that direct interactions can play a role at concentrations larger than 1 at. Kondo effect). but this is expected to be a minor contribution to the total interaction. experiments on. The origin of the effective exchange interaction J has been discussed by Moriya (1965b) and later by Campbell (1968). e.148 J. Alexander and Anderson (1964) and Moriya (1965a) have treated the problem of two neighbouring localized magnetic moments. The effective exchange can then be calculated as due to d-d covalent admixture. it again appears that the chance of ferromagnetic coupling increases with increasing number of d-electrons. The constant 8M is determined by two major terms: one due to the energy shift of the impurity levels. the heavier atoms (with nearly filled d-shells) couple ferromagnetically..%. he treats the interaction between the host and the magnetic atom as due to covalent admixture. Fe and Ni. (4.A. Moriya (1965b) has further treated the induced moment problem by incorporating into the Anderson model (Anderson 1961) or into the Wolff model (Wolff 1961) a five-fold degeneracy of the impurity level and the intra-atomic exchange interaction of the host metal.28). The starting point is also the Hamiltonian given in eq.g. implying J to be positive. For alloys in general. This order parameter is different from the usual phase transition order parameter. The magnetic properties which are easily obtained from the MRF approach are similar to those derived from the EA free energy solutions. A second theoretical model is based upon a random site representation for which J~i depends upon the atoms at the end of the bonds (Mattis 1976. Binder 1977a. is defined as q = ~ where ( ) and ~ represent a thermal and a configurational average. Thus.2.3). see section 4. Aharony 1978). As mentioned in section 3.~. ~-gtXBH~.iSZi where the distribution of the Jii is random.[kBT)]} dJ is rather difficult and has been the subject of various methods of calculation. Writing J0 as J~i~j where ~ = 1 for an A-atom and e~ = -1 for a B-atom.2.DILUTE TRANSITION METALALLOYS. Luttinger 1976. Spin glass alloys The stimulation of an intense theoretical interest in the spin glass problem began with the Edwards-Anderson (EA) (1975) model. Co or Mn and the Pd-atoms is ferromagnetic and that between Cr and Pd-atoms is antiferromagnetic. respectively (see section 1. we have the Hamiltonian = . a finite freezing temperature is found instead of Tf = oo as with earlier MRF calculations (Riess and Klein 1977). and exactly soluble spherical and ring diagram models. So even this completely localized picture accounts for the observed giant moments. These involve such techniques a s the replica trick. Anderson 1977. which emphasizes the insensitivity of the sign of the induced polarization to the band structure. When a cut-off of a nearest neighbor distance for the closest approach between two impurities is invoked. a simple Hamiltonian results: ~ = .SPIN GLASSES 149 explained. i.'~u and Hi =. Aharony and Imry 1976).e. mean field and renormalization group treatments. Tf. In these treatments the order parameter which appears at the freezing temperature. i d J i j S i . Remarkably.1) approximation has recently been extended within the framework of the EA model (Klein 1976).HEi. Fischer 1977. and thereby causes non-ordinary critical phenomena and exponents. 4.1 this coupling is responsible for the spin glass behaviour at higher concentrations. going one step further. These authors replaced the random occupancy of lattice sites coupled via the oscillating RKKY interaction by a model of a regular lattice with random bonds or interaction strengths.X J4 " sj - X i By transforming to a new spin and field variable Tu --6i. The mean random field (MRF) (probability distribution model.~ . P(Jij) is a Gaussian. it appears that the coupling between Fe. A number of review papers have appeared which elaborate the mathematics and methods of the EA model (Sherrington 1976. The solution for the free energy F =~ = f P(J)F(J) dJ = f P(J) {-kaT ln[Tr exp(. (Si). the . b). However. MYDOSH AND G. This was followed by a review of the salient experimental features which manifest themselves and which lend support to our picture of giant moment ferromagnetism and spin glass freezing. Binder 1977a. Conclusions and future directions In the preceeding sections we have introduced the important concepts and physical models used to describe the two different ways in which magnetic ordering can occur in dilute transiton metal alloys. which is especially suitable to the "randomness" of the spin glasses. Using the EA Gaussian P ( J ) .3. a f__erromagnetic phase will appear. Yet there is still much to be accomplished before a complete theoretical description of the spin glass phenomenon is attained.b. This specific sampling is chosen with a probability exp(-U/kBT) (where U is the interaction potential). The choice of these "importance" points according to the above probability is made from a Markov process in which a chain of points is constructed using a transition probability W consistent with the detailed balance condition. Binder and Schroder 1976a. is that of Monte Carlo computer simulation.1. A final technique. The computer simulations which are primarily based upon the EA model give a better agreement with the experimental results than the analytic calculations of the same properties. Finally an introduction was given to the random molecular field m o d e l . in order to better determine the accuracy and degree of convergence. Furthermore. Basically the Monte Carlo method amounts to a numerical determination of the thermal average of a given physical quantity.150 J. Then for a sufficiently large number of these points. and the spin glass phase is possible. but lel -. many of the spin glass properties have been calculated by Binder and co-workers (Binder and Stauffer 1976.A. with equal concentration ~i = 0. Then a survey was presented of the various systems in which such ordering appears.J. This leads to a master-equation-governed probability that the system is in a particular state at a particular time.)l. the dynamics of the physical quantity into equilibrium may be followed via the Monte Carlo steps (Binder 1974). In addition. exact solutions of the above Hamiltonian are accessible to give the full thermodynamic behaviour. Thus. a time is associated with the steps in the Markov chain. The problem is now to choose an appropriate W for the given physical situation.j i For unequal concentrations of A or B atoms (~i ~ 0). Here the usual integrals are replaced by a finite sum over an "importance" sampling of points in phase space. a good approximation can be obtained for the thermal average. 4. Here the order parameter is the ordinary one (~-i)= I<s. NIEUWENHUYS Hamiltonian becomes an ordinary Heissenberg Hamiltonian in a random (updown) field i.a very useful theoretical method to calculate the general properties of . While there exists a number of older theories describing the giant moment formation and the low temperature behaviour. Within the framework of this model and by using realistic. Presently the spin glass problem is receiving enormous attention especially from the theoretical side and it is impossible to mention in this article all the recent calculations and methods. Here additional work is needed and hopefully a synthesis of these two magnetic states will be attained via percolation theory. see fig. the magnetic ordering phenomenon can be nicely discussed within a percolation representation which is very similar to certain spin glass models.l gives a complete listing of measurements performed on giant moment alloys and their most characteristic parameters. The experimental situation is moving into a second generation of highly sophisticated and accurate measurements. infinite cluster or chain is formed. A very recent experimental discovery has been the transition of giant moment ferromagnetism into a spin glass state by reducing the temperature in an alloy of constant concentration (Verbeek et al. e. the extension of the critical phenomenon or phase transition theories while focusing upon the freezing behavior has only begun to include the very low or very high temperature regimes. The spin glass freezing required random orientations within the infinite cluster.g. distant-dependent exchange interactions J(r) much of the experimental behaviour may be simply obtained. The results of these studies will certainly stimulate the theoretical progress and offer ways of distinguishing between the various models and calculations. which also contains the rare earths as solute. it fails to meet the requirements of a sharp freezing and dynamical cluster growth above the freezing temperature. In addition. On the other hand. 5. .DILUTE TRANSITION METALALLOYS. 1978a)~ This effect seems to be a general property of magnetic alloys. Present attention is centering on dynamical and time dependent effects employing the most modern of techniques. There is further a great deal of controversy concerning which of two general approaches is most suitable for the spin glass behaviour. In brief both the giant moment and spin glass problems remain a topical area of magnetism and a better understanding will continue to develop in the coming years. The convergence in the description of these two types of magnetism is now underway and we might shortly expect a consistent and complete picture of the dilute magnetic component alloy. so a ferromagnetic. neutron scattering.SPIN GLASSES 151 random magnetic alloys. It must then be left to future investigations to resolve these spin glass disputes. Although the phenomenological super-paramagnetic model gives a good description of the low temperature spin glass behaviour. The main difference is that for the giant moment case J(r) strongly favours parallel orientations. The Appendix with table A. a summary of other theoretical approaches and some of the modern techniques were briefly described. where at a certain concentration there will be paramagnetism ~ Tc ~ ferromagnetism ~ Tf ~ spin glass transitions. Iz+SR etc. % (or in parts per million if indicated). d Ap/dT: temperature derivative of the electrical resistivity. means nuclear orientation experiments. If one wishes to calculate the magnetic moment per unit of volume. max. respectively. As in most cases with dilute alloy systems.M. p the density of the alloy and M the molar mass of the alloy.022169 x 1026kmole -I [6.1.: Tc determined applying the Weiss-Forrer method.~BNpc/(lO0M).: T~ defined as that temperature at which AC or d Ap/dT attains its maximum value. respectively.%. Arrott: T~ determined by means of an Arrott plot. sucs. knee: T~ defined'as that temperature where a knee can be found in the resistivity versus temperature curve. where /-¢B= 9.: Tc determined as that temperature at which Ap starts to deviate from a straight line as a function of T with increasing temperature.: specific heat. the magnetic q u a n t u m n u m b e r and the effective g-value are collected. F. Some alloys. instead of S.1 ("other alloys") the alloy composition is given in first column. magn. In spite of this difficulty we have included these alloys in the table for completeness. .: T~ determined from Weiss Molecular Field model calculations.J. The magnetic quantum number J is obtained from specific heat experiments by evaluating the magnetic entropy and assuming it equal to cR ln(2J + 1).274096 x 10-24jT -I [9.022169 x 1023 mole-I].152 J. spin glasses) is not sharp. in order to facilitate comparison between the alloys.: ferromagnetic resonance. c the concentration in at. From magnetic measurements this quantity is obtained by fitting the experimental data to a Brillouin function. The magnetic quantum number and the effective g-value have been omitted here. N. in a number of cases Tc should be read as Tf.h. In the last part of table A.M. Therefore.g. A table of the saturation moment and transition temperature of Fe dissolved in "Ni3AI" and in "Ni3Ga" can be found in section 3. fifth. res. the spin glass freezing temperature.274096× 10-21 erg G-I]. the saturation moment per dissolved magnetic atom. N is Avogadro's number = 6.I. sixth and seventh columns contain the values reported for the transition temperature in K.F. units. one should remember that this is given by i~l. The meaning of the abbreviations are: M6ssb.1 data on the transition temperature. the borderline between giant moment alloys and other alloys (e. and the fourth and fifth columns list the transition temperature and the magnetic moment. The first column gives the concentration of the magnetic atoms in at. an abbreviation of the experimental method.R. The fourth. We have used the "unit"/~8 for the magnetic moment per dissolved atom. In the third column the reference is given. MYDOSHAND G.: magnetization measurements. intl.3 (table 6).I on the main properties of "giant moment" alloys In table A. s.: electrical resistivity. NIEUWENHUYS Appendix A: table A.O.A.F. W. and the second column./~ is the number of Bohr magnetons per dissolved atom. which exhibit the phenomena of a giant moment do not order ferromagnetically at any of the concentrations under consideration. for the total magnetic quantum number J and for the effective g-value gef~.: M6ssbauer effect. model: Tc determined using model calculations. W.: susceptibility measurement. for the saturation moment/~ in/~B. 1: ~ ~ .. t~ o ° .:. . `3 ~ ~ o .4 U3 . ~ - ~.< [.. ~ O4 .z ~4 . o ~ • ° o o~ c~ _0 . o 0 o - .~ ~v o . _'2 "2. .. . 00 ~ ~. SPIN G L A S S E S 153 ..o ..-.. . . v v o . e:a v o o ¢.o ~.~ ~.~ o ~. .t..3 o c.-.va • v .~ ~ ~ . . °~ "7.D I L U T E T R A N S I T I O N M E T A L A L L O Y S .J t~ .3 o o . J.~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 0 [J c~ 0~ m W m ~I C~ • • cO ~J ~o r0 j • (3 • u~ ° ttl • O~ u~ • u'l • .154 J.A.~ ~ .~ . MYDOSH AND G. NIEUWENHUYS o~ • ° (/} ~. DILUTE TRANSITION METAL ALLOYS.~ o ~ v v v o o v .. . _ cA ~ cA . o .N cA .o u'3 I:I o o~ • o o'~ eq cA eq 0 ~ .. ~ - ~ ~ ® . .q e~ •. . SPIN GLASSES 155 ¢.o o o 0 ~-~ ~ 0 0 r..) I cA 0 ~ . o o o o.ID a0 0 • o ¢nl u~ ~ @ o o "0 I .. N I E U W E N H U Y S cxl u~ . o o o .156 J.0 o o o o..J. MYDOSH A N D G.A. SPIN GLASSES 157 ~.DILUTE TRANSITION METAL ALLOYS.~ g 0 "0 "0 0 0 "~ . a o. • ° .4 • ° ° ° . N I E U W E N H U Y S I ....158 J.o . E-~ 0 I "C- • 4.J.A. . . .. : .. . . I:: ~ii °. .a ° 4.-. o ~ _. MYDOSH A N D G. 0 00~ "' o u ~ov O3 CO -.'t • ° o Qw =o o E I11 Y=. 0 . SPIN GLASSES 159 ¢.DILUTE TRANSITION METAL ALLOYS. 160 J. ~ ~ ~ ~ ~ .. N I E U W E N H U Y S t:t O -or .. ~ .~ ~ o.. M Y D O S H A N D G.t~ f.A.4 ~ eq eq eq eq 04 eq tB v gt4 .7..ff 1.J. . .i o ~ ~ . o4 o= o~ ¢m r'r~ O0 e~.~ . . O CO to tt~ ~ v o ta. o. 4 . i m m t~ ~ ~ e3 ~ . v o. . o4 .-4 co qo • co ~ oo • eq oo t0 ~ . ~ o4 . o4 .~ • o . o4 . to f~ to ~ to to o. o4 .~ no o ~. SPIN GLASSES 161 tt~ • t ..ta t~ ~ . . ..DILUTE TRANSITION METAL ALLOYS. 162 J.J.:/ o ~ o c. MYDOSH A N D G. ~ o ~°~ gfl o . N I E U W E N H U Y S .A. o o ¢.-~ o I ~ ~ ~ ~ . .o • ° o . ~ ~ ~ co .: .o ~ ~ ~ " ... ~1 ~ wD ~ 1~1 ~1 o~ ~1 ~ o ~.: ~ ~ ...... v . ~o & MI P~ 0 v .~ .0 . " .. .a ~ ~ CXl o . I. .. 0 c~ ~ ' ~.. SPIN GLASSES 163 i~ 4.DILUTE TRANSITION M E T A L ALLOYS..a r~ .-... I.~ ~ ~ ~ ~ ~ ~ - ~ ~ ~ ~ ~ ~ r-- ~ ~ ...... 0 o~.. )... t 0-.. .o ..4 t)-4 m I... . N I E U W E N H U Y S t. "8 P o v • • ° • ° . MYDOSH A N D G.)..164 J...A.J. .DILUTE TRANSITION METAL ALLOYS. o .t o I I '~ ~ . ~ o ~ o I-i o o o I d.. ~ .. .. o~ ~ ..... .i 0~ . . SPIN GLASSES 165 . tta ~ v .4 ~ ~ ~ .7 . . ... ~ o4 'q..~ ~ . "2. - .~ ~ - . A. c~ ~5 c5 c5 c5 o o o c~ c~ o o o o ~ . o ~. .- . . .~ v ° o • . N I E U W E N H U Y S o~ ~ • v ~ v • ~ ~ v .- ° • o 0 if3 ~ v ~ v . .J. MYDOSH A N D G.166 J. ~ C v v 0 v c~ c. a¢~ t-q ¢*-1 o t-o .) t~ tu .DILUTE TRANSITION METAL ALLOYS. o~ o ~ o .-i . o~ ~.~ ~ • ~.o to • o v . ~ • _ ~t o tJ o ~ o ~ o v t~ g to ..4 •~ • t~ eo o O t..iJ •. SPIN GLASSES 167 t~ e~ ~ ~ E c-4 tr~ ¢o ¢o .. O e~ oJ O~ v O O O ~ ~ 04 t~ ee~ o'~ .o • ° * o .~ -~ .. M Y D O S H A N D G.168 J.-..J.5" .A. N I E U W E N H U Y S t~ o~ ¢~ eq J o~ • o~ g v . SPIN GLASSES 169 m ~ .. e~ g v v • v v • v v ~ & M & ~ :~ m v v ~ ~ ~ =~ ~ ~ m ~ ~ X ~ o3 to m 0 ~ 0 ~0 ~ ~.DILUTE TRANSITION METAL ALLOYS. ~ 0 ~1 ~1 t"e) u-I u'~ .~ 0 e. h.A. ~ ~ ~ . v .. %. ~ ~.-4 0 0 o a~ o o ~o t.~ "I. M2dDOSH AND G.~ ta to "o o o - ~.J.170 J. %. N I E U W E N H U Y S v o~ o v o I i ~ o ~. ~ g o. .q~ .¢ o~ ::= ~ o r.o ~ 03 <2. ~ tO • tO • tO V tO "%'.--4 • ~ o. ~ .. ~ ~ ~ 0~ ~ ~ o ~.4 ¢¢ r~ O 04 ° ~ ° .~g o o ~ ~~ ~ 7 o 7. o.-4 . r~ ~ ¢q ~. .4 O °. co ~ ~- ~ ~o ~ t~ tt3 ~o • co • ~ 00 ° o~ ° o'3 ° ~ ~o • tt3 ° tt~ • 03 ° . r~ "X r.~ ~ eq ~. ~ to g ° to ° ~ ~ O~ ~ ° ~ o. t4.DILUTE TRANSITION METAL ALLOYS.~ o ~ o . SPIN GLASSES 171 ~.. J.. . NIEUWENHLIYS .A.172 J. o ° ° • ° I t0 0J v v v O O N N g g .:I ~ ° .--4 . MYDOSH AND G. SPIN GLASSES 173 • • ~ ~ ° o O (~ 0 0 0 .DILUTE TRANSITION METAL ALLOYS. v c.4 0 o "* ¢D v .:.A. v .:.174 J. NIEUWENHUYS ~ e 00 • tt't J t'q • tt~ e I e~ t4.J. MYDOSH AND G.E . o d eel . 1969.. Solid State Commun. 55.S. 1970. 2282.A. 1972b. in Low temperature physics LT-14. Phys. A. 295.. Phys. Tournier. Phys. J.E. Bull. Schr6der.M.W. B3. Blandin.A. Rev. Phys. Burger.. P. K.W. Hansen. 193. Physique Lett. Lett. D.D. 213. Taurian and J. Anderson. Solid State Commun. 41. J.J. N.T. AIP Conf. Hoare. 1971. Davis and J. 13. Soc. G. R. K. Trans. JETP Letters 8. J. Wolff. Aharony. 1976b. 1978. Bagguley. Souffach6. Amamou. Pilon.. J. A 257. Compton and J.T. Lecoanet.D. Phys. Bozortb. and J.. 3 (M.P. Thesis. Ribault..P. Bloyet. 23. 57A. Lett.I. Anderson. A.W. (G. D. Chapellier. Alekseevskii. 211. Stringfellow. Rev. F4. and J.P.. Rev. Physik B 26. 603. Souffach6.W. ed. A. J. 22. Magnetism V (H. A. and J. R. Binder. R. Beck. M. J. S. D. Lett. B1. Bancroft. J. 1972. J. K.J. Kreisler and J.. Budnick. Anderson. J. K. and Y. 40. 1963. Burger. Beck. .. P. Costa. J. Physique 9. Appl. eds.N.. voi. D.S. Borg. 124. M. 1964. Delyagin. 4659. P. 27A.C.. J. 1966.W.N. 1974. SPIN GLASSES 175 References Aharony. New York) p. Imry. 1966. 516. Magnetism in alloys (P.H.A.A..J..) (TSM-AIME. Phys.S.. 307.H. Adv. Rev. Suppl. F 6. Beck. Boerstoel. 1971. Benoit. Phys. Schr6der. O. Mallfert and B.. K. McLachlan. 1976. 1977b. and G. R. 1978. J... Skalski..M. Phys. F 5. P. Bagguley.. 1968. 26. Davis. Rev. Burger. 1093. Vibet. 1961. J. O. Amsterdam) p. O.. Beck and J. Cannella and T. Less-common Met. Robertson. G. and J. Phys. Wernick. 917. 397.D. 20. 1973.) (North-Holland. 1976. Rev.I. Varma. B-I. Phys. Butch. Solids 34. Met. Robertson. Wernick.J.. Rev.J. A1594. A.P.E. D. B. Treusch. Binder. Phys. Kir'yanov and V.A.P. 1975. J. D. 1957. Burger. Binder. AIdred. Mat. A. Alloul. Mag. If. Yerzinkyan.. Rainford and M. 1483. Kitchens. and P. 1973.B. 1970. R. 49.I. J. Solid State Commun.E. Yu. 349. Loegel. F. 1323. Braunschweig) p. R. Phys. 278. 1974. Hasegawa. A.. Sadoc and J.P. Avenel and M. Japan. Booth and C. Physica 86-88B.. 265. Tsebro. Flouquet. Lett. Zwart. 1394. Phil.L Tholence and R. P.P. 1974. V. Kreisler.M. 3834. 1975.A. Lechaton and S. A. Balbanov. Stauffer.M.T. 1972a. 1. Friedt. Benoit. 1969. Z. Binder. Mat. S. Proc.) (Vieweg. and D. 1961. 2. Magnetism liB.M. 1131. Caudron.H. Alqui6. J. Appl.. Res. Suhl. 1977. 42. Physica 57. H. Rev.. A. Preston. J.. Sanchez and J. 198. Alexander. 11. and D. J. 2142. 2015. 17. Chem.L Tholence. 1978. Borg. JETP 28. Phys. 1970. 721.A. 1563. Klein.DILUTE TRANSITION METAL ALLOYS. 1973. Boucai. P. 7. P.P. Amorphous magnetism H (R. lg. J. Bozorth. Boerstoei. Borg.M. B. 28. 35. Solid State Commun. Arrott. Phys.M.E. J. P. Flouquet. and Mag.. Bremer. Senoussi and B.I. Phys. M. 899. 112.. J. ed. 1977. J.J. E. 1965. 897. Samerskii. Mag. 464. Suhl. Anderson. B 14.W. 1361. 2597. 1979. A. 108. A. and T. New York) p. Arrott. Rev. Soy. Borg. Rev. 25.S. Arrott. P. unpublished. Lett. 16. Burger. Phys.W. 1968. R. Chouteau. B. McLachlan. 1157. Roy. Alqui6.L. J. eds. A.A. 1960.J. V. Binder. J. 1962. eds. Anderson. Phys. Phys. G. Ann. B10. 122. F. vol. Phys. Budnick. 250.) (Plenum Press. 1976a.S. R. V. Krusins and M. D. M. All. Shpinel. University of Leiden. Halperin and C. 1972. Vuorio. Varoquaux. Lett.P. B2. Advances in solid state physics. 487.. 18. W. Phys. 1976. E. Phys.. Phys. Phys. Levy and R. A.D. Phys. B. 5. Gautier and B. Festk6rperprobleme. 133. Gallop. and K.. 1974. 405. Rev. and D. XVII (J. N. 177. Burger. Perfenova and V. Soc. 36. Phys. Budworth. New York) ch. 1970. 2371. 1964. Berglund. B.A... E. 40. Beille.) (Academic Press.M. Weber.. 345. Binder. Violet. 250. A. A.. Rev. 403.A.) (Academic Press. L69. 1970. 1.. Rado and H. R. J. Less-common Met. 1977a. Proc. Rev... C. New York) p. 1974. Taurian. eds. 339. and K. 549. Pipkorn. K. 1976. Proc. Nieuwenhuys.L.F. 1969. F 5..) (Academic Press of Japan) p.A.A. 1962. Fourneaux. 1970. Dahlberg. Saint-Paul.R.. London) p. 1971. 12.V. Crangle. 1975. 1002. 136. Physica 8411. and L. 606.J.R. J. V. E. Wollan and W. Taxi and H. 1965b. 565... Lederer. Rev. 10. 1975. Souletie. 1974b. C4--38. Fourneanx. B. and W. Clogston. Campbell.. Schinkel and J. and R. R.176 J.. Phys. Rado and H. 769. Solids 35. Physique. Chouteau. Child. and J. Costa. Mag. C 2. M.. Steyert. Kawatra. 2.O. De Pater. P.J. Proc. 331.C. Cracknell. 4220. 895. 1969. J. J. Hardiman. 1973. Kandra. E. R.. Daybell. in Low temperature physics LT10. du Chatenier. New York) p. in Low temperature physics LT-12 (E. B6.P. Wilson. 24A.E. Canneila. B. Cable. Phys. Tournier.. Mydosh and J. unpublished. Cable. Proc.M. Phys.R. Lett. J. Koehler. Thoulouse and R. Kandra. De Chatel.E.. Mydosh. M..W.. 1971. J. Rev. 1049. R. 1974a. Taylor. E. 1971. Rev. Sherwood.T. Mozer and R. 165. 40. 1964 (IPPS.J. 2120.C. 737. De Boer. AIP Conf. 2599. Phys. Chouteau. Physica 48. P. H. Lett. Rev. Turner. and H. P. Matthias. T. 1970. P..P. K. ed. 14. 1969.. 18. Phys. 24. M.A. Phys.25. R. 802. C 32. C. Mag. Coles. David.D.R. 41. 1977.S. Chouteau.W. I. M. Cottet. Chouteau. 1689. Rev. MYDOSH AND G. P. Appl. 1974. Phys.A. Appl. 401. P.J. Moscow) p. J.F. vol. and J. Phys. von Molnar and R. 380. Colp. Tournier. Perisho. J.A.J. Nagle. 464. Phys. vol. Phys. V. C. B.. R. 42. Tournier.D. Cariow. H. 335. W. J. Craig. B16. R. vol. de Boer. V. M. A1460. 1525. C 1. G. J. 1972. R. Tholence and R. $308. and F. 1967.E. 13. Physica 25. Careage.L. Mydosh. and R. Costa-Ribeiro. 1977. Phys. 1973.. Loram. S. Phys. Fourneau× and R. Segnan.) (Plenum.B.D. Tournier. University of Geneva. Rev. M. Steyert.. 1971. G. A. 284. 1972.R. 74.J. R. Lett. 1976. Mozumder and R. R. J. B.A.J. 1968a. Phys. Int. Jamieson. J. 521.) (Academic Press. S. 1968b. Tournier. R. Biesterbos. vol. B. Rusby. Rev. 24. Tournier and P. Rev. IV (M.J. Coles. and R. NIEUWENHUYS 1965. Timmerhaus.. Chem. 9. 1967. 1968. J. and W. Taylor and A. Butch and J.A. Phys.S. Budnick.P. Meads.A. Lett.. Steyert.A. Steyert and R.A. AIP Conf. ed.H. 5. V. Cole.E. P. Chouteau. Phys. J. J. Loegel. Craig.T.R. 1960. J. 21. in Low temperature physics LT-12 (E.R. P. Rev. M. F. Budnick.F. Physica 86--88B. Hammel. J. O'Sullivan and E. 167. Cable. O'Sullivan and E.H. 833. G. W. Proc. D. in Low temperature physics LT-13.P. 1965a. New York) p. Corenzwit and R. Cannella. A. BS.. 1971.. J. Phys. ed.D. Coles. Conf. 1974. Phys.. Coles..I. V. 42..C. Tari. B. 1421. J. V. 138. De Boer. 10. 2 (K. 1974. Mydosh and M. 38. Cannella.. F 5. Van Dijk and G. H. B. eds. F. Lett. (Pubi. 719. Weil. Lett. and R. J. Cannella.A.) (Academic Press of Japan) p. 40. Appl. House Nauka. 969.F. 1959. Gallop and G. 1082. C. G. W. Phil. 1623. Solid State Commun. De Noble. 1965. Timmerhaus. Phys. Mollard.D. . Craig. Mydosh.W. 124... Dreyfus.. Williams. C 3. Jamieson.R. 25A.P. Choutean. L58. Waszink and J. Cannella. Physique. and W. Clark. Mydosh. 651. G. Rev. New York) p. and J. and G. J.P. 185. C. 1977.C. 414.W.A. J. Williams. J. Peter. J. Daybell.C. Caudron. 1973. Crangle.. Lett. J. J. C 2. Rev. Phys. 1970. in Magnetism V (G. R. De Mayo. 297.R.) (Plenum. and J. Biesterbos. Phys. in Low temperature physics LT-13. Tournier and P. A755.) (Moscow) p. B. and F. 1964. AIP Conf. Phys.. Cannella. Phys. Meads. Tournier and L. 1965. 125. Proc. Malkov. Phys. 1974. 193. eds.H. Gohrecht and R.E. Mag. 1968. Appl. J. Proc. V. 1962. H.J. 921. Int. Segnan and W. J. 541. Rev. 2 (K.D. Coey. Phys. AIP Conf. Suhl eds. Scott.M. Phys. I-Iammel.E.J. Craig. 1975.. Thesis. B.I. Rev. 20. 687. 785. 138. Gambino. Cannella. Phys. G.A. Conf.D. 1979.J. 1966. Lett. D. Schinkel and J. Mod. Orbach and J. B. Phys. D. Gonser. 197. G. 1968. Muir and H. Swallow. Sanchez and J. Sol.. Phys. 442.E. A. 978. 1967.G. 1974.J. 31A. Franz. F. 813. Foiles. Heir. de Graaff. R. 1964. C. 541. 1970a. 1964.J. 1978. 765.. Lett. Griiner. 207. Campbell. McNiff. Ericsson. 1969. J.A. Fiouquet. Tholence. Conf. Rev. J. 241. M.R. W. S. Proc. C4. 965. 665. S. Rev.L. Mydosh. Phys. Peter and J. Duff.A. 351. Phys. Graham. T. J. Phys. P. Grtiner. Electrochem. Phys.T. M. Langer. G. Taurian. Phys. Essam. Cooper. 2083.B. and J. A460. 3. Sierro. 1977. 1973. Rev. Schreiber. Ann. 20.. J. 90. Phys.C. 1967. Physica 84B. New York) p. J.F. Mydosh. 1973b.W. Fischer.D. and D. 41. 941. Thoulouse and R. Fischer. 5...L Tholence.J. Grassie. K. 13. 4154. Giovannini. vol... Mydosh. Appl. SPIN GLASSES Devine. Z. J.. Roy. Gerstenberg. Moscow) p. D. O. 541. 1206. A. Schreiber. in Low temperature physics LT-14. Phys. 1973. J. Hooper and A. D. A. Reivari. R. Taurian. Adv. and D. Berlin) p.. 2124. 1965. Soc. 1.) (North-Holland. Tournier. T. 17. H6hler. F. A 296. Graham. 1975. and J.J. S. Griffiths. 1974. 2 (C. Phys. Hr. AIP Conf.) (Academic Press. eds. Wohlfarth. Phys. 1976. F 7. 11. Kankeleit.J. Metal MeLalloved 40. 161. M. Rev. Phys. O. T. T.. Ford. and V~ Cannella. unpublished. Wohlfarth. Solid State Commun. J. 492. 1970. P. L 285. 37. J. . SLat. 38. Devine. 1974b. J. J. L. Soc. Steiner. 46. and R. Foner.J. 1971. and O. and O. Rev. 1970.S. 1976. 287. Grube. 963. (G. F.J. and Mag. 370. 31A. 1974a. 1972. BI8.A. Frossati. eds.W. 719. M. 3 (M. Narath. Green eds. Hirvonen. vol. Ribault. Ford.L Tholence.) (Springer. B. K. V.. unpublished. J. 736.S.K. Meecham.P. Phys. Rev. WincHer. 33. and J. 6. 129.C. and LA. Lett. Proc. G. 10.. Friederich. Japan 19.T. and E.E. 1970b. Hiifner and E. Williams and J. 857. 1976. 1966. Fiory. J. Hirvoren. Proc. and A. D. A. P. 236. and J. 1497. Litterst.B.Z. in Low temperature physics LT-12 (E. 1976. 54. 1977. Appl. 2. Schrieffer. 1973. 52. Friedel. Men'shikov and S. 177 Flouquet. Vuorio. Doran. Phys. J. Gallop.M. Phys. Rev. in Amorphous Magnetism (ILO. and P. C. Amsterdam) p.. 1978. K.. Doran. 765. Rev. J. Wiedersich. Edwards.M. 67A..) (Plenum. P. N.. J. S. 1971. 54. 40. 155.W.S. Solid State Commun.P. J. Foner and A.C. K. 461.. Du Chatenier. 1967. Phys.. Chapeilier and J. G. 397. Guertin. University of Oxford. Gainon. Thesis. Phys.C. Thesis.M. and D. G. 81. and I. Doclo. Dunlap. 214..DILUTE TRANSITION METAL ALLOYS. University of Leiden. Edwards. in Springer tracks in modern physics.. Lett. Katila and P. 1976.. and A. G.. BS. 36.W. 1964.M. Jungfleish and J. D. 23. and J.M.A. Sanchez. Phys. Dash.L.. Zawadowski. Fiz. 2057.. 1976. AIP Conf. D. Kandra. Proc. Kalvius and P. 8. 229. in Phase transitions and critical phenomena. J. and D. Ericsson. 19. Phys. Solid State Commun. New York) p. P.A.. Ehara. Fischer.. S. Lett. Phys.J. Ford.M. Physica 86-88B.. Schilling. Sellmeyer. 12.A. R. 5.. 707. Duff. 1974b.A. Grant.T. Mathon and E. Prog.G. E. Katila and V. and J. J. House Nauka. B14. ed. B. Phys.S. G. B3. ed. A. Phys.J. Proc.. Rep. vol. Soc. M. Krusins and M.L. and V. Erich. 650.S.K. Symko. 1977.D. K. 1968. F 3. 980. 1968. Fisher. Phys. Dorofeev Yu. J. Physique 35. Gierisch. Mag. Anderson. 1977. Nuovo Cimanto 7. U. Mag. Tournier. S. J. Fert. Lett. 79. G.. 14. 1976.J.G. Solid State Commun. J. AcLa 43. 1313. LD. Doniach. F 6. 1935. 1975. Ford. Sidorov. Phys. J.D.J. Gallop. Canneila. A. B13. 1958. G6ring. Solid State Commun. 2.. Koch. W. Domb and M. 1974a. 29. J. Phys.E. 1969. 466. 1970. Mat. Typpi. Pro¢. Frossati. Appl. Rev. 39.J. (Pubi.J. 831. Rev. 1958. 1970. M. Ford..C. Lett. 1973a. Int. Symko..P. Tholence. Lett. Phys. Mydosh. 18.) (Academic Press of Japan) p. Phys. AIP Conf. Thoulouse and R. vol. R. Loram. D. M.A. Klein. 1956. ed. 1957. New York) p. Proc. Guy. Phys.L. Katayama. Magnetism IV (G.. Hoare. J.. 429.A. T. and W. eds. H. vol. J. 1505. Phys. 1965.. Lett. 1972. Brout. Manchester. Madden. Kandra.P. Symko and J. Rev.N. 1977. Hirst. 5008. Symko and J. Hodges.N. M. Low. M. T. 1969. and W. 397.A. 45.) (Academic Press of Japan) p. New York) p.J. 1968. J. 45. C.F. Yates.. Hirschkoff. 255. Kondo. 23. Turnbull and H. Skalski.C. Phys. Taylor. Schwartz. 1977. N. Thomas.M.. Proc. 1971. Walling. eds..C. 1962.B.E. Mydosh. Shen. Phys. and R. 221.M. AIP Conf. Shimizu. 1970. Proc. Rev. Hicks. Kobayashi. 1966. Watson and H. and J. Phys. Itoh. Suhl.C.W. 2293. Rev. and Zuekerman. Rev. 1964. Rado and H. Mydosh. Roy. 1966.G. K.) (Moscow) p. Mathon..J. Phys. 1969. M. Rev. Heeger. 101.178 J. $. BI6. 201. 20. M. Kim. Matthews and J. vol. Chen.C.W. 40. S. Phys.L.. 1968. 94. A. Phys. M. eds. A. Phys. Phys. 485. A 240. Hawkins. Rev. Can. Appl. 136. 1970. in Solid state physics.. Kittel. A.A. Phys.P. 9. N. Shanaberger. 1977a. C 1. Budnick. E. 24. G. F. Gubser.. Appl. in Amorphous magnetism II (R.. Hurd.P. Theor.A.E. New York) p. Prog. Kim. Kato. and F. Wheatley. Seitz. 1202.) (Plenum.. Turnbull and H. Appl. Klein.. J. Wheatley.C.F. 1972. and S. 27. J. in Amorphous magnetism II (R. Mod.J.C. 283. . J. BI. 1975. J.J. 41.P.C. 1972. M.A. Hawkins. Japan 40. Hake.) (Academic Press. J. 1966.R. J. N. 1177. Seitz. Kato. 1971c. Phys.C. 1976. Prog. Klein. 173. Turnbull and H. 188. T. Phys. Phys.I. 323. Guy. Rev. Levy and R. Kitchens. Phys. 545.) (Academic Press. F 2. Phys. Itoh. C. I. J. Kumagai. and L. 1.G..C. Soc. 1972. Budnick and J. Physica 8688B. Kondens.I. 1966. BS. 1977b. 1174. and S.N. T. O. in Solid state physics. and D. Koon.A. Materie 11. Klein. Koon. Phys. Kohara. Phys. T. Ehrenreich. E. T. L.E. Hoare.W. Budnick. 1627. B2. Int. Rev. Phys. Guertin. A 1156.W.W. Phys. Hasegawa.U. 1971a. J. J. Phys. eds. 917.R. 877. and M. Symko and J.) (Plenum. G. Nadler and R. Low Temp. 3953. S. 34A. Asayama.. Phys. 1972. Budnick and B. Kjekshus. Hasegawa.A.C. Shanaherger. in Low temperature physics LT-12 (E. I. L. Kobayashi. 47. C. 434.. Harris. MYDOSH AND GJ. VI. Kobayashi and J. Phys. Guy. 483. Japan.A. 216.. 169. Rev. Thomas.G. 415. and B.L. eds. Phys. 65. 36. I ~ w Temp. L and S. Ehrenreich. R. and D.. Ehreureich. F 6. New York) p.P. C.D. Phys.A. T. 117.) (Plenum. Phys. B $.N. Guy. 3725.F. Rev... Guy. Jamieson. Lin. Soc. and B. 138. C.J. A 552. 155. Hirschkoff. Proe.J.. 1970. 1970. T. M. C.) (Academic Press. T. S. 773. Hasegawa. Kawatra. Phys. and R. 149. L.. Foner. Campbell. Jones. Thomas... F. Rev.. eds. M. Malkov.. 5. 1959. BS. Rev.C. 1973. 1977. D. 22 (F. 1975. C.. M. Loe.L. M. Japar~ 21. H.L. Steyert and R. New York) Ch. McAlister.B. H. 33.. R. Lubensky and J. A 167. 235. ed. 241. Seitz. 1963.N. S. AIP Conf.. 1971h. vol. Hirst. 23 (F. Rev.D. Kawatra.. Rev. Howard. 1976. 1953. 1969. J. 1.C. J. M.W. Phys. K. 1978. Kasuya. Hirschkoff. Huq. D. Proc. O. Roy. Kim. 1968. New York) p. Soc. J. F 8. 1587. 1968. Morgan and R. 2412. Herring. AIP Conf. 16. M. 49. Harris. Sano. 86-88B. New York) p.-H. 363 Kawatra. Phys. F 7. in Solid state physics. D. Phys.. J.W. (F. in Amorphous magnetism II (R. 574. F $. Wheatley.. TJ.I. J. 18. 42. eds. Lett. 1976. Pearson. Kawatra. 1976. Kirkpatrick. 302. 502. C. NIEUWENHUYS Itoh. 29.) (Academic Press. Phys. Moody. Phys. and J. Mag.W. J. 1974.P. Phys. 1968. 1977. J. M.E. 1976. K. 132. A 933. Rev. 1977. E.C. 183.G. 528. Klein. O. J. Phys. 1970. 44. Phys.. 1978. Rev. Soc. D. Soc. 1969..P. Morgan and R. Levy and R. Physica. R. A.G.R. Mydosh and LI. Klein. Z. J. Hasagawa.. J. in Low temperature physics LT-10 (M. Theor. Phys.B. Holden and G. Asayama and J. 61. Ehrenreich. Levy and R. D..T. 186. L242. Lett. Montgomery. H. Hawkins. G. BI4. J. 1973.E. Swallow.) (Plenum. Fiz. Rev. 56A. and R. and R. Proc. Soc. J. Kouvel. 2 (K.D. Phys. 881. 1158. Maxwell. Phys. 1977. Laborde. Alloul.P.I. 458). Lovesey. Low. Korenblitz. 1971. Kossler. Proc. Manuel.L. 1975. Fiz. University of Grenoble. 110. McAiister. Phys. in Amorphous magnetism II (R. and D. 85. 8. 819. R. H. Hammel eds.R. 1972. G. Hicks. Luttinger. 329. Paton. and C. Phys. 1973. l. Husemann and H. and experimental references therein.P.E. Rev. 1976. 1967.C. O. 1972. Phys. Lett.G. F 3. 1973. Khmel'nitskii.L. 133.A. J. R. 1968. Medd.A. in Low temperature physics LT-13. G. . Malozemoff. The theory of thermal neutron scattering (Clarendon Press. Z. vol. Mfssbauer. 1969.. Burton. and R. and H. Maley. 788. JETP 35. 36. 37. 421. F 3. Mills.. Phys. 1616. 1970. Levy and R.G. and C. Laborde. Phys. Larsen. MacLaughlin. BI4.) (Plenum. and H.E. Hurd. Budnick. 846 (Sov. McDougal. 49.. Chem. P. Levy. R.S. B3. (IPPS London) p. 60. 57. Phys. McAlister. Shender. 1977.. 225. Int. M. D. (Publ. 38. 178. Margenau. Phys. Jamet. Radhakrishna. 68.J. Phys. Int. W. 1965. and J. J. 837. Radhakrishna. 1977a. and R.. Mag. 1973.E. A 676. H.... MacDonald. Lett. Kouvel. Phys. Phys...J. B8. A 266.. 39.P. 1865.J. G. Ford. S 127. 1976. F 6. MacLaughlin. Eksp. Rev.I. Rev.. Marshall.J. B9. 1966. P.S. Rev. and P.E. O. R.C. P. W. and H. Phys. Marshall.S. 37. Phys.E. 53A. Moscow) p.. Schindler. 56A. JETP 44. BI8. Ber.958). Solid State Commun. Low. A.A. 1976. 795.. Mattis. Low. Instr. Phys.S.. Alloul. 1085. 1249.I. 1977b. 1974. Phys.. Phys. Thompson. MacLaughlin. 475. Grayson-Smith. J.A. J. 19. A. D. Long. Rev. 1731. N. 1960. R. Sov. Larsen. and G.C. J. K. 1970. Phys. J. I.. 1974.I. 1970. Mag. Beal Monod. Kouvel. 1973. J. Appl. Alloul. J. J. Appl. and B. McDougal. Rev. Mydosh. Grassie. W. and T. Lett. Adv. Turner. Lett. Levin. 1975. Phys. Chem. 1926. 778. J. Solid State Commun. Soy. 1960. P. 1519. 1977.M. Loram. 1977. 39. Bass and K.S.L. Mehlmann. Physica 86-88B. Rev.A.D. J. and M. Li.W.S. 3060. 48. House Nauka.E. Paul and J.L. Rev. Appl. H. Lederer. J. 4241. Phys. C 3. and A. Phys.G. Rev. D. Solids 24. 311. 1961. Rev. 1976a.H. 31. Rev..W. M.E. U. Schindler and D. Lett. 22. U. 179 Loram. 1970. 1971. Manuel.. J. Soc.D. 118. Soc. 1978. O. Taylor and J.Ya. Brodowsky. J.K. A. and E.J. Sci. R. 1425. P. Conf. JETP 31.P. B5.P. Phys.A.B. Levitt.M.J. Hasegawa eds.-fyss. and H. 1648. D. 1972.J.F. 1971. 1976. Teor. 134. 1954. Phys.. and S.T.F. Rev. 371. 147.J. White and A. 1297. S. Pearson and I. Physik 250. Roy. Maartense. 553. J. N.DILUTE TRANSITION METAL ALLOYS.F. 1978b. 1017.. F 3.. and J. 38. Phys. 1789 (Sov. 1976. 143. and A.. A 112. Phys. 4. Larsen. 82. C 3. Williams and G. Lindhard. Proc. 1977. Phys. 1965. Watstedt.C. E. 119. Chem. Rev. J. Schilling and J. Lett. Larkin. Ling. Liddell. and P.C. 165. Phys. 5257. Zh. Mat. Appl.I. Conf. 697. S. Phys. Solids 21. Phys. A. Timmerhans. Danske Videnskab. Phys. Roy. 38. and D.P. Koon. and E. Proc. D. JETP 33. Street. 58. and J. Lett. Lett. New York) p. Rayne. Eksp. Bunsenges. LI21. H. 755.W. and D.. 1974. J. Maletta.C. 1972. Phys. 1972. Oxford). and A. Larsen. Laborde. 181. Khmei'nitskii. U.M. D.. W. 1963. Phys.J. Larsen. AlP Conf. 1964. 36. Hurd. 1962. Phys. Kgl. 77. Templeton. 36.M.C. Larkin. Proe. U. Matho. Phys. 24. 1976. 5014. Korenblitz. Shender. Lutes. Phys. McLennan. J. O.. P.J. 161. B6.. Williams. 1017.Ya. unpublished. 1976. Rev.L. 839. 3659. M. S. Mills. Selskab. Schmit. U.M.A. 1968. 1978a. Rev. 89. MeAlister. Rev. W. Zh. O'Sullivan and E. Phys. B6. Bennemann. Teor. Maletta. SPIN GLASSES Koon. Rev. D. and T. vol. 4356. K. 961. Proc. Rev. Phys. 28. Lett. G. New York) p. I.. J. Holden. Phys.. 1935.I. Phys. 1976b.D. 18. Thesis. 8. Solid State Commun. Levy. Phys. to be published. 450. F 7. 1976a. G. and H. R. Phys.. Proe. 1976. A. 157. Levy and R.S. Solid State Commun. Murani.P. J.J.. J. Chem.D. and P. Nieuwenhuys. Lett. Ruderman. Verbeek.K. Phys. T. J. A. 1973. Phys. Raiuford. A273. Rapp. B. R. 329. Verbeek and J. Mydosh. Yamazaki. Whall. Murani. 1977b. 33. series B. 1265. 1978. Olsen and R. Nishida and T. Rev. Taylor. G.A.J. P. Phys. Prog.. Phys.. and C. Phys. A. J.. 67A. N. 1346. 43. B15. 49.A.R. J. Temp. 1969. 167. Phys. F 4.J. Murani. 1745. 2222. G. Mydosh... 33. 1977. O. 22. in Low temperature physics LT-14.) (North Holland.P.C. Mishra. Mydosh. 66A.. D.J. 99. 1978. Lett. G. Phys.P.r. 37. 25. R. Arp and A. 95. Paris 269. Hasegawa. M. Mydosh. Lett. 489. eds. 1977. M. Phys. Burch and V. Phys. R. Beck. Boerstoel and G. Ch. Univ. and P. Phys. Nagle. J. J. 86--88B. 1957. Hashimoto and T. Fiory. 346. M. Riess. J.J. 1973.A. Appl..F.P. A. Murani. Skalski and J. Nishida. Phys. 1966. 1976. Coles.J. 1975. J.A. Wohlfarth. Murani. 1976b. Kossler. Nishida.J.J. 1978. Mydosh. J. 17. 1977c.P.. A.E. O. C. Sablik. Tholence. 1972. 278. Mydosh. 1975. . 7. 22.P..T. K.H.D. F 4.. Rev. 1977a. 37. 1973. 29. Rev. and Mag.. Tari and B. 36. 1974. G. Jr. Phys. Nieuwenhuys. Nagamine. J.P. Lett. Less-common Met. P. J. Emerson and D.. K. Physica 62. 1258. Phys. 1963. in Amorphous magnetism II (R.D. 1974. 96. A. Yamazaki. N.M. Phys.P. Roshko. J. 1979. A. Mukhopadhyay. Roy. Solid State Commun. Sacli. 1962. J. G. Proc. Rizzuto. Coles.I. B.880. Shull and P. Sci. A.. Phys. Rado. 1965. Phys. hebd. J. 69. Phys.A. K. A. 125.A.P. 1965a.A. 1973. Mydosh. 1977.L. Murani. Budnick. 1769. 267. 33A. N. 19. D.. Murani. Nieuweuhuys. 630. Solid State Commun. 1977.. 237..I. Budnick. 1970. 147. Phys. 733..E. Japan 28. Phys. 1974. N. B8. Mat. 237. Roshko.L. Solids 2. A 19. Phys. 1978a.J.K.J. Ododo. Boerstoel. 25. Prog. 21. Appl. 1976. Craig.J. Magnetism V (Academic Press. G. Thomas. Rep.. M.. Nagamine. S. Nieuwenhuys.. Soc. 1977. and J... J.. Goelt and K.F. Low. S. Mukhopadhyay. 38. G.D. Phys. A. 1067. van den Berg. Proc. G. 147. Lett. C. Roth. 1977a. Stat. 2845.I. Cochran. AIP Conf. T. New York). Mydosh and E.R. 1976.P. Kawatra and S.W. Rusby. 85. eds. Adkins. 24. 416. Mag. J.M.D. Fromhold. 221.. Rev. Mat. Lett.. J. 1949.C. P.J. Rev.. A. Owen. 1975. Wohlfarth. Mezei. 1974. Williams. A. Rev.. Sol. Radhakrishna. G. Vuorio.F.180 J. eds.E. A.A. Prog. Ridout. 1497. Rao.D. 6001.S. Skalski. Rev.. Beck. and R. J. Ibel. Reivari. and G. 490. S159.V. P. W. van den Berg. and Mag. Lett. Phys. Burger. Phys. 1975. 1978b. C.J.A. P. Nieuwenhuys. A. B. M. R.J. Phillips.J. Krusius and M. 425. 3. Rault. A 62. 413. Rev.) (Plenum. J. B 10. Coles. Rev.A. Rev. and E. AIP Conf. C 2. Phys. H.H. Mag.E. 829.. Barrett.. 1965b. Moran. Kip. Roy.T. Murani. Murnick.M. G.L. T. Williams. and J. J. 45A. and K. 144. Johannesson. S~anc Acad. Boerstoel. B. Zwart. Cannella. Phys. 428. Nagamiya.R. Rhodes. 5. Suhl. Phys. Nieuwenhuys.. 1975. Kittel. S. 5. Physica 86-88B.. W. and J. Rev.T. Moriya. 1974.. F 6. Theor. J. J. B. 247. O. Proc.. 1562. Kawatra and T. and M. Nieuwenhuys. and G. 99.J.M. Lett. G. H.F.J. R. Zwart. 1969.A. 29. 34. A1649. Soc. Phys. Narath. Nagamine. 25. Rev. Physica 69. Yamazaki. A. Dokter and G. Hayano and T.E. Parks. J. 1978. Proc. Phys. J. J. 239. Klein. (M. Phys. Nieuwenhuys. M. Theor. J. Phys. F 5. 1974. 1973. Physica 86-88B.. Rev. MYDOSH AND G. Brown. 1969. D. T.R.P. and E. Brewer. 1974.J. 119. Nagasawa. Ford. N. and B. V.P. Amsterdam) p. S.A. 1685. 1000. Wiss Z. and B. Phys. Adv. 29. Beck.. Rivier. 138. 274.A. M. 1085. Phys.. J.P. Phys. 16. 1954.M. I. 50. AIP Conf. Tari and B. D. vol. A. N.A.. 1970. Budnick. Jones. Pikart. Lett.P. 1970. 515. C 2. Physica. Moriya.F. K. 1968. 425.. Goeltz and F.P. Dresden 23.J. Murani. Rivier. Ibel. K. P.A. Solid State Commun. 100. NIEUWENHUYS Nieuwenhuys. Lett. Mort. Tech. 1972. 1604... New York) p. to be published. 1171. . and R. 1971.D. 181 Smith. Smith. 1974. Star. H.P. 77. 1972.. and R. FS.A. G. J. AIP Conf. 115. Tholence. Schilling. Wernick. 1967. Shen. 3613. C6. Phys.S. Smart. Loram. Loewenhaupt and W.E. on Phys. J. 20. 1976. Tholence. Lett. Sherrington. 1976. Solid State Commun. Levin. Williams.. Kikuchi. New York) p. Phys. J. and B. J. Soc. Grest. Schmatz. Tansil.L Nichols. Schindler. J. Mackliet. and R.J. Seidel. and J. J. 1976. Kirkpatrick.F. 257. J. Loewenhaupt and J. Phys. Solid State Commun. 2148.J.. Phys. Kawatra. Thesis. 1974a. 1978. 1975. R. H.W.C. Rev.J. 1970. Lechaton. Gierisch and G.H. 1155. D.. S. Rev. Rev. Smith... Phys. Takahashi. 1976. Phys. W. 1974. J.E.. 160.H. J.L Cock and C. Mydosh. 562. BI0. 1973.E. Phys.A. 1974b. Ford. Skalski. F. CI. Rev. D. Kitchens. Trainor. 1977a.I. 1977. Jr.. 1968. Schinkel. J. J. Schilling. Rev.S. 2034. Adv. Suppl. G.... Phys. A. Phys. AIP Conf.W. Star. 4.L. M.. 6. Gardner and H. W. 2796. 35. Thomson and P.M. Czjzek..W. J.R. Phys. 20. Scherg.S. Appl. 1974. Lett. 2976. 1949. and Mag. U. Woolley. Proc. F 4. Loram. AIP Conf. Peter. McCoilum. Phys. 642. 342. Phys. 135. and R.J. Hammel. Grassie and J. and J.. Physica 86-88B. Schaikwijk. BI2. 136. in Amorphous magnetism II (R. Sarkissian. W. 1976. and D. J. New York) p. Kalvius. Arko. Southern. Segnan.) (Plenum. eds. M. 28. M. J..C. Phys. Phys. Physica 86-88B. R.R.B. A245.. Sato.M. G.L. 95.D. S.I. Tournier. 1977. Mydosh.M. 1972. C. unpublished.. Tournier. 1968. J.J. A404. Budnick and J. (W. 3. 100.W. 39.J.W. Phys. 224. S. 179..W.H. Phys. Rev.B. LA9..H. Phys. J. 1964. Appl. Rev. Thomson. Physique 35. F..P. Smith. 1975. Rev. 1267. S.A. Solid State Commun. 24. Phys. and C. 26. I. C.S. Phys.J. J. Proc. G. de Boer and J.J. Mag. Phys. J. J. 593. 512.E. W. 1. F. vol. Tournier. 2980. eds. 29. and S. D. 229. Effective field theories of magnetism. 1975. R. J. Scheuer. Shaltiel.W. Mag. 1968. Rev.L.. 511.F. Swallow. F. Schinkel. Nave and T.. 4368. 1977. 1968. Rev. 217. 1977. F 4. Craig and T. O'Sullivan and E.269. E. J.R. Rev.DILUTE TRANSITION METAL ALLOYS.568. Palmer.F. Wernick. P. J. University of Leiden. 942. and R.. J. Wassermann.. 1965. Street. Thomson. Rev.A.A. J. Anderson and R.H. G. and R. Physica. 15. AIP Conf.M. L266. 2 (K. Phys. 337. Lett. J. D. Scheuer.. 1975. Biesterbos.W. F. B. Rev. C. Rev. B.. 1977.A. A62.A. Thompson. Physique 32. Thouless. and J. Tournier.A.J. Tissier. Foner and E.A. S. Sherrington. and K. Ford. C4. Lett.. 1977. Senoussi.M. H.O. 169. Montgomery. Shimizu.. H. B6. Soukoulis. Skalski. 1969. Tang. Phys. Smith. 84B. 593. 1978. 1968. Smith. P. J. A. 1975. D. Soc. 2690. Thomson. C 1. Toulouse..R. Hasegawa.C. Suhl. and J. Levy and R. BI0.. BI4.. Timmerhaus. 1971.S. D.W. Schreiber and A. Grassie and J. and D. M. Proc. 35. Physique 35. Phys. Tholence. 2. Proc.I. .. G. J.R.. 875. 1974. 527. Phys. B2. BI3.C. M. Loewenhaupt and W. J. Shaltiel. 1975.O. Shaitiel. Phys. 21. Taylor. L243.R. 501. 1977. Phys. Stringfellow. 20. Taylor. London). F 1. R. 11. Smith.O. 1977c. Williams and M. J. Appl. Larsen and J. 29. Swallow. H. D. Tournier. BII. 965. 1966.W. P. Mydosh and J.V. Budnick. Proc. 8. 1971. 997. U. S. M. 1977b. F. and E. 95.S. 39. Rev. Just..J. 1967. B9. A. W. P. Huray. Appl.G. Phys. 1964. Suck. R. 1699. Larsen and J. 41. F. Phys. P.G. J. M. Phys. Saunders. 34. and R. Williams. Mat. 681. Rev. Smith. 3581. 26A. 13.. in Low temperature physics LT-13. Phys. Phys. 1974. T. Litterst. Souletie. SPIN GLASSES Sarachik. L. J. 873. Tournier.A. Sherrington. 1974c.895. 1971. H. and M. Mat. 605. 1975.L. J. 1975.J. A1346. 3. Rev. 1969. J.. 1974.. BI1. Comm. Phys. Physica 86--88B. Scheuer.. 38. McNiff. D.. 18. Phys. Phil.D. Tholence. Rev. J. F. Japan. J. Obenshain and G. Lett. S 370. Schrieffer. Campbell and A. 842. 1792.A. Fert.. and Mag. 1970. Brommer. D. Mag. Phys. G.B. Thompson. Low Temp. F 5.P. F 5.) (Plenum. T. Phys. Solid State Commun. F 1.. p. Physica 86--88B. Williams. Rainford and A. Volkenshteyn. Phys. Rev. 1970. Phys.A. and F.W. W.E. 1973. 3863. Solids 17. A442. Phys. Swallow and J. Williams.A. 9. 893. Zimmermann. P. AIP Conf.D. 1970. Chem.. G. B. Tholence. T. Rev. Zweers.517. 1973. AIP Conf. 237. Yamazaki.K. Swallow and J. G. J.E. 1969. Res. Loram. Gorter. and G. Rev. Kramers. 90. Rev. Hoare. 52..W. Private communication. Swallow and J.A. Window. 1977.E. R. Window. Lett. G. Woodhams. D. Lett. and P. Appl. Phys. Weiss. Rado and H. Rev. 236.F. 1979.. and M. 11. Grassie and J. 1976. New York).J. J. New York) Ch. G. Appl. G. Verbeek. Nieuwenhuys and J. and P.. J.. Loram.J..W. in Magnetism V (G. Phys.. Stat.E. Nieuwenhuys and J. Crystall. Proc. 1977. B. 194. M.J. eds. G.W. Proc.) (Academic Press. Rayne. 1926. Rev. Window.P. J. in Amorphous magnetism (H. Phys. Wenger. C. Yosida. Wenger. B. Williams. Phys. J. Murani. Thesis. Johnen. M. Forrer. Longworth and C. Wohlleben. Solid State Commun.W. Rev. 106. J. Borg. Mydosh. Mydosh.P.E. B. B. 540. van Dijk. 1975. Williams. B. Trousdale. 1976. Solids 31. Loram.. Meads and J. Proc. F 5. 45. Phys. Phys.E. H. Rev. B. C.H.M. 1961. 135. W. Zuckermann.V.W. 821. 1971. 1973. Verbeek. 1975. MYDOSH AND G. Mat.. Bll. 20.J. Van Dam. Phys.434. 1075. 2156. 1969b. 162. Thesis. Tustison. 841. Phys. 1967. 1976. 135. 1975. 3497. Physica 86--88B.S. Hooper and A. and P.213.L.H. L. Johnson. 1827.W. Keesom. Rev. Phys. Metals Metallog. 1966. unpublished. 4053..J. 1978b.. 1978a. (USSR) (English translation) 19. 1975a. Phys.A.. 1261.A. W.. and R. J.J.A. Cryogenics 15. Beck. 1977. 19. Rev. NIEUWENHUYS 1964. Williams. 1967. T. J. Amsterdam) p... Violet.J. 1957a. Williams. Sol. Pelt. 1. Phys. C 2. 7. G. 1978.. 396. 1030. 529. 21.G. and B. G.A. Tustison. Loram. G. University of Leiden. Phys.A.J.A. 1967. G. 2380. Ann. 1966. Williams. Appl. Tsiovkin. Loram.. 23A. 1976. Phys.H. Wheeler. 107. 922. and J. Coles. 1971. 38. Yu. B...O. R. J.. 1975. R. R. 922. 419. Verbeek.) (Plenum. J.C. P. Mydosh..N.J. and J. and P. J.A. Veal. 344.H. and R. 153. Phys.J. Sci. 24. C. unpublished.. 4 (C.R.W. Phys. in Progress in low temperature physics. L. 1965. Swallow. Carlow.. Van Dam. 801.. Rev. 1. Verbeek. de Physique 5. J. 837. Phys. C. G. Solid State Commun. Williams. H. Soc. Chem.J.C. B. J.H. K. Solid State Commun. Violet. 1978c. Window. 1053.W. Solids 30. Stocker and J.S... Tustison. Wiebes. B. van den Berg. B5. 40.. . E.E...H. 1969a. 1972. Wilding. B. 124. Rev. Williams.A. and F. 11. 1970. 167. Phys. J.A. Phys.A. Wolff.) (North-Holland. Rev. Loram. Welter. K. Bll. 229. G.A. ed. B7. 1957b. and J. Window. Beck.E.. G. Phys. A3. 28. C2. C6 918. G. Verbeek. J.A. G. Nieuwenhuys. 1969. J. Solid State Commun. C 3. Borg. 1975b. Van den Berg.E. Suhl. Hulscher and H. A. F. and LW. 1971. B. Williams. 447.T. 19. Zweers.182 J. van Dijk.A. 1964.W. 555. Keesom.H. University of Leiden. 1976. Wassermann. Phys. C 3.E. Phys. G. Phys. B3. 257. G. Loram. J. 1960. BI3.E. and N. Longworth.D. vol. 587. J. Chem. G. Kitchens and G. eds. and J.W. Phys. 637.L.. and Mag. 149. and G. 11. Phys. H. 1964. Physique 39. Mag. 1970. J. van den Berg. G. 29. 1861.M. de Graaf. Solid State Commun. 1973. 608. Yosida. chapter 3 RARE EARTH METALS AND ALLOYS S. Vol.P. 1980 183 . IA 50011 USA Ferromagnetic Materials. LEGVOLD Ames Laboratory-DOE Department of Physics Iowa State University Ames. Wohlfarth © North-Holland Publishing Company. 1 Edited by E. . . . . . . 3. . . . . . . 2. . . . . 5. . . . . . . . . . . . . . .2. . . . . 5. . Gadolinium . . . . . . . . . . . Samarium . . . . . . . D y s p r o s i u m . . . . . . . . . . . . Introduction 185 185 190 197 208 21 ! 212 215 219 224 228 233 236 239 240 246 251 254 254 257 258 260 260 261 262 262 269 271 275 278 280 282 283 283 284 290 184 . . . . . . . 3. . . . 1. Magnetic properties of Sc. . . . . . . .3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. . . . . .5. Magnetic a n i s o t r o p y energy and m a g n e t o s t r i c t i o n . . . . . . . . . . . . . . . . . . . . . . . . .6. Tm base alloys .4. . . . . .4. 5. . . . . . 3. . . . 5. . . . . . . Fermi surfaces and electrical resistivity . . 5. . 5. . . . . 2. . .8. . . . . . . . . . . . . . . . . . . . . . . . . . . 5. . Ho base alloys . . . . . . Dy base alloys . . . . .2. . . . . Y. . . . . . . . . . E n e r g y bands. . . . . . . . . . . . . . . . . . . . . . . 2. . . . . . . . . . . . . . . . .3. . . . 1. . . . . . .5. . . . Thulium . .2. Magnetic properties of Eu. . . . . . . . . . . . . . . . Scandium . . . . . . . N e o d y m i u m . . . . . . . . . . . . . . . . . . . . . . . . . . 2. . . . . .5. . . . . . . Ytterbium . . . . . Tb base alloys . P m and Sm . . . . 4. . . . . . . . . . . . . . . . . . L u t e t i u m . . . . .4. . .2. . . . . . . . E u r o p i u m . . . . . . . . . . . . . . . References . . . . Magnetic properties of Ce. . .5. . . . Er base alloys . . .CONTENTS . . . . . . . . . . . . . . . . . . Yttrium . L a and Yb . . . i. . . . . . Nd.7. . . . . . . . . 1. . . . .4. . . . . . . . . . Lu. . Tb. Er and Tm . . . . Terbium . . . . . . P r a s e o d y m i u m . . . . . . . . . . . . . . .1. . . . . . . . . . . . . generalized susceptibility and spin w a v e s .4. . . . . . 2. .1. . . . . The indirect interaction. . . . . . . . . . . . . 3. . . . . . . Eu base alloys . . . . . . . . . . . . . . Pr. . . . . . . . . . . . . . . . . . . . 2. . . . .1.3. Ho. . .6. Gd. . . . . . . . . . .3. . . . . . . . . . . . .3. L a n t h a n u m . . . . .1. . . . . . . . . . . 4. . . . . . . . . . . . . . . . . Light rare earth alloys . . . . . . . .1. . . . . . . . . Erbium . . . . . . . . . . . . . . . . . . . . . 4. . . . . . H o l m i u m . 5. . . . . . . . . . . . . . . . . . . . . 6. . . . 4. . . . . Gd base alloys . . . . . . . . . .7. . . . . . . 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cerium . The crystal field . . . . . . . . . P r o m e t h i u m . . Epitome and tables . . 2. . .2. . . . . . . . . . . . . . . . 2. . . . . . . . . . . . . . . . 3. . . . . . . . . . . . Binary rare earth alloys . 1. . . . . . . . . . . . . Dy. 4. . . . . . . 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Similarly. otherwise 3"= L + S. I. Strong evidence to support this view c o m e s f r o m the o b s e r v e d spin polarization of the conduction electrons. or lanthanides.1.S. La. 185 . (iii) For less than half filled shells J = L . Their magnetic properties s t e m f r o m unpaired electrons in the 4f shell. Strong spin orbit coupling for the 4f electrons leads to low magnetic m o m e n t s for the early (or light) m e m b e r s of the transition group. The elements which exhibit ferromagnetism are Gd. an indirect e x c h a n g e m e c h a n i s m via three 5d-6s conduction electrons is invoked. for these elements the total angular m o m e n t u m q u a n t u m n u m b e r is J = L . T o a c c o u n t for the o b s e r v e d magnetic order in the rare earths. l quantum numbers then the "lowest lying" electronic state has (i) the maximum multiplicity. Dy and H o h a v e the highest magnetic m o m e n t per unit volume for all the elements. Tb. Dy. U n f o r t u n a t e l y this high m o m e n t is attainable only at low t e m p e r a t u r e s and along the e a s y magnetic direction in single crystals. Er.S where the spin quantum n u m b e r S = Ei si. exhibit only typical conduction electron Pat~[i p a r a m a g n e t i s m . fcc Pr and fcc Nd. high magnetic m o m e n t s are associated with the h e a v y rare earths for which J = L + S. 2S + 1. Also included in the discussion are the closely related trivalent *When electrons are in an incomplete shell and so have the same n. allowed consistent with the Pauli exclusion principle and (ii) the maximum L consistent with this multiplicity. Introduction 1. the orbital q u a n t u m n u m b e r L = ?Et ml and the sums o v e r the 4f electrons are made in a c c o r d a n c e with H u n d ' s rules*. In m o r e picturesque language N o b e l L a u r e a t e Van Vleck (1932) wrote that 4f electrons are " d e e p l y s e q u e s t e r e d " in the atom. which has a full 4f shell. b y the three 5d-6s valence electrons. T h e latter are relatively closely bound to the nucleus and so are shielded b y the eight 5s2-5p 6 electrons and. This m e a n s that 4f electron w a v e functions are confined close to the nucleus and that w a v e function overlap with neighboring a t o m s in a lattice is vanishingly small. the magnitude of their magnetic m o m e n t s is o v e r fifty percent larger than that of iron. of these rare earths. H o . T h e r e f o r e direct H e i s e n b e r g exchange does not occur. are the trivalent 4f shell transition metals. to s o m e extent. Epitome and tables The rare earths. which is the f o r e r u n n e r to the rare earths and which has an e m p t y 4f shell a n d / " Lu. 8247 1.207 -5.7740 5.6482 12.989 4. In the following pages the intention is to give a reasonable accounting of the magnetic and transport properties of rare earth metals and their alloys.6290 4.8041 2. Several reviews have been published. the magnetic structure sometimes involves sublattices.753 18. hcp= hexagonal close-packed Rare earth metal La Ce Pr Nd Pm Sm Eu Gd Th Dy Ho Er Tm Yb Lu Sc Y Crystal Latticeconstants (•) structure ao co dhcp fcc dhcp dhcp dhcp rhombt bcc hcp hcp hcp hcp hcp hcp fcctt hcp hcp hcp 3. ** Data for coordination number 12.804 20.5915 3.904 19.8214 1. LEGVOLD elements Sc and Y.041 19.248 20.260 7.243 7.5494 5.6406 1.3000 1794 1529 3273 3230 2567 2700 2868 1950 1196 3402 2836 3338 Z 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 21 39 * After Beaudry and Oschneidner (1978).894 6. For more details on the theory and the experimental data. Liu has reviewed lanthanide electronic structures while M c E w e n (chapter 6) has treated the TABLE 1 Room temperature physical properties of the rare earth metals and their melting and boiling points*.981 19.006 18.186 S.5592 3.1610 3. fcc = face-centered cubic.900 8.6336 3.229 8. bcc = body-centered cubic.3088 3.6582 3. dhcp = double-hexagonal close-packed.7318 Metallic Atomic Melting Boiling r a d i u s volume'* DensRy point point (.7740 1. the most outstanding of which is the singlet ground state configuration found in pure samples of Pr. A wide variety of magnetic structures are displayed b y the rare earth metals and their alloys.145 6.8012 22.066 9.5850 5.843 17.7462 1.5052 3.603 20.007 7. Because of the low magnetic moments of the light rare earths it is possible for electric crystal field effects to dominate the magnetic exchange interaction.5778 3.312 19.7833 1.5827 3. More recently.7566 1. there is the volume "Magnetic properties of the rare earth metals" edited b y Elliott (1972). in chapter 3 of Gschneidner and Eyring (1978). These range from simple ferromagnetism to complex sinusoidal and/or helical ordering. t Rhombohedral is the primitive cell.6966 5. This leads to a number of interesting observations.6055 3.469 918 798 931 1021 1042 1074 822 1313 1356 1412 1474 1529 1545 819 1663 1541 1522 3464 3433 3520 3074 .698 20.7661 1.7810 5.0418 1.5375 5.840 2.6721 3.4848 3.65 26.781 15. it m a y be necessary to consult the references.7966 11.8013 1. .773 7.8326 11.965 9.65 3.8279 1.2680 5.795 9.321 6.7349 1.6178 5.584 20.450 18.6501 5.770 6.9392 1.5540 -5.8791 1. The close-packed layer stacking is ABABCBCAC with symmetries chhchhchh in nine layers. tt Low temperature form is hcp.550 8.124 24.001 28.520 5. In m a n y instances the magnetic ordering is incommensurate with the atomic ordering and this leads to sizeable physical property perturbations.~) (cm3/mol)(g/cm3) (°C) (°C) 1.171 -11.811 1. ." "'{D "'~..~:_.-"~"-'.._.. melting points. " A Ai • C ""~ ""~ /" . The rare earths exhibit several close packed atom stacking arrangements. In his book on soft magnetic materials Chen (1977) devotes a section to rare earth magnetism. 1... In many instances it is of importance to know the physical properties of the elements under discussion. e . The room temperature crystal structures.~. ¢ .. 1. lattice parameters.0 "./' .-~. These are shown in table 1 from chapter 2 of Gschneidner and Eyring (1978).i B • ~ . The theory for the electronic properties has been reviewed by Dimmock (1971). Close packed crystal structures found in rare earth metals. Some irregular features can... These are shown in fig. magnetic and magnetoelastic properties of the metals.1 / B A. e / . • At hcp -AXIS b-AXIS J .RARE EARTH METALS AND ALLOYS Aq f 187 C I.. metallic radii. A popular review has been prepared by Mackintosh (1977).. ". - B AI 3-:=~'---~ 7 • Samarium Fig. be seen at once. Reasonably smooth changes in the properties occur with increasing atomic number for the rare earths and the decreasing lattice parameters for the heavies heralds the "lanthanide contraction"._2~. " e / ' l C .~'___ . Eu and Yb have . densities. The heavy elements are hcp at room temperature while the light elements prefer the dhcp (double hexagonal close packed) crystal structure. however. A~ i I B 0. Rhyne and McGuire (1972) have reviewed the magnetic properties as have Taylor and Darby (1972).~ Aq fcc / "-. atomic volumes. . .. and boiling points are shown in the table. / ~ .. ~ 1) along side the latest observed value. It is convenient to use cgs units and to give the magnetic moments of the rare earths in Bohr magnetons.o E. the Land6 g value*. In table 2 we give an extensive listing of the magnetic and related properties of the rare earth metals.m : Fig.188 S. LEGVOLD low melting points and this is related to the divalency of the metals wherein one of the conduction electrons migrates to the 4f shell to half fill the shell for Eu and to completely fill the shell for Yb. by use of N e f f = Act®. S. Pm is radioactive and the boiling point given is an estimate. . \]/ ce Pr N0 _ _ Pm sm Eu / / \ o.1)J in the theory of the rare earths. The crystal structure of Sm is an unusual nine layered affair with close packed layers ABABCBCAC giving atomic nearest neighbor symmetries chhchhchh on the respective planes. 2. . The theoretical gJ values in the table differ from the observed values for the heavy elements because gJ does not include the conduction electron contribution mentioned earlier. L. their appropriately determined total angular momentum. their total orbital angular momentum. The saturation magnetic moment for light rare earths is hard to obtain because i i i i i f i i ~ i . Saturation magnetic moments per gram at absolute zero. these are shown in graphical form in fig. * g .1 + [J(J + 1) + S(S + 1) . This is now called the samarium structure.may be converted to the number of Bohr magnetons per atom N e f f .0/5585 where A is the atomic weight of the element. The table displays the total spin. The table also shows the theoretical saturation magnetic moments which are given by gJ.27409 x 10-24 Joule per Tesla. where /~B = 9.L ( L + 1)] 2J(J + 1) . J.0.27409 X 10 -2~ erg]Oe = 9. t~B. Since J is a good quantum number for localized magnetic moments.-. 2. the spectroscopic state designation. de Gennes (1966) proposed that the spin projection onto J should govern the magnetic interaction.° . of the 4f electrons././'-'\'-.1)2J(J + 1) (the de Gennes factor) for a comparison with the ordering temperatures TN and Tc in the next columns. Also shown are the values of S(S + 1) a n d ( g . this leads to the replacement of S with ( g . Plot of the theoreticalgJ saturationmagneticmomentsfor trlpositiverare earth ions in Bohr magnetons. or®.per atom.\ / _ Lo . and the theoretical paramagnetic moment g X / J . .. I I I I I I I o'~.~ I ~ I o~ r~ ~ .. ~ ~ r~ '4"- 189 .~ ~1..~ ~ Ot~i I l l i l l l l l ~D @ S I I ~S. .~ I ~ ~ I . 1.t. We begin with a total Hamiltonian /-/tot = Hcoul + Hexch + H c t + Hms+ Hz (1) where the Coulomb interactions of the conduction electrons appear in the first term as discussed in the band structure of the next section. H~xch is the indirect exchange or R K K Y interaction of concern in this section. This is one of the many interesting and curious magnetic phenomena associated with rare earth metals. Hot is the crystalline ionic lattice electric field energy of the 4f electrons. Very rough values might be forthcoming from neutron diffraction measurements.9 A). and spin waves In this section the contribution of the magnetic moments to the energy and magnetic ordering of rare earth metals is considered. H~o. Finally. happily. generalized susceptibility. In the indirect exchange model the 4f electron spin at Ra interacts locally with and polarizes the 5d-6s conduction electrons which then interact in turnwith the 4f electron spin at Ri.~ ~ ( R i -. References for this table will be listed when the individual elements are discussed. 5d and 6s electrons out to the Wigner-Seitz radius (3. The terms are written in order of decreasing strength. These correspond to the ordering of the moments on different sublattices of different symmetries for the dhcp allotrope.2. 3 which shows the radial distribution probability for the 4f. On the other hand. We note. We neglect it now in a discussion of the second term which gives the 4f electron magnetic exchange energy.S spin orbit coupling for the light rare earths./'/ms is the magnetostriction or magnetoelastic contribution to the energy of the metal and Hz is the Zeeman energy in an applied magnetic field. This approach is needed because the 4f wave functions have insufficient overlap to give direct Heisenberg exchange.-.1~ S. the last columns provide the paramagnetic ordering temperatures in the easy and hard directions for the heavy rare earths. This can be seen in fig. the existence of two N6el points for some of the light rare earth metals. is spin independent and therefore is not important for this discussion. The other terms in the Hamiltonian will also be neglected here even though we are aware that the crystal field term might be larger than the 4f exchange term for the light rare earths. in passing. the 4f-5d overlap (cross-hatched area) is adequate to yield a strong direct exchange between the local moment and t h e conduction electrons which can polarize the conduction band giving rise to an excess saturation magnetic moment and which. LEGVOLD of antiferromagnetic ordering. The leading term. The indirect interaction. Following Kasuya (1966) the interaction may be written in the form Hexch ---. although the relative importance of some terms varies because of the J = L .R i ) S i " S i (2) .8 atomic units or 1. takes on the appearance of direct exchange between local moments. Rj.0- 191 ~ 0.~)(g. (If more than one band is involved. After H a r m o n and Freeman (1974a). has the form 1 nk nk+..1 ) J i and work with the conventional form Hexch---.4- SPHERE RADIUS -~-. the shaded area shows the important d and f function overlap..0 RADIUS (out) 3.~ x ( q ) = -~ ~k Ek -. The procedure from here is to take the Fourier transform of the interaction function to get ~¢(q) = ~ a¢ (R. With this approximation one obtains for N atoms at(q) = (2/N)(g . However.I/ • J j (3) with R~j = R i .j]. the exchange matrix elements between states k and k' (such that q = k ' . At this point it may be recalled that the total angular momentum quantum number J is a good quantum number and proceed to use the projection of the spin on J as suggested by de Gennes (1966).RARE EARTH METALS AND ALLOYS i. Typical radial densities of S-like (F~ state) and d-like wave functions.k) are very difficult to work with and are frequently approximated as a constant or a simple function of q. 0 1. 3.4 1.k = q. where the 4f spin Si is located at position Ri and the 4f spin Si at Rj and a~(R~.Ek+q" (6) In the latter we have taken k' .0 Fig. J (4) This function can in principle be obtained directly from band structure calculations. the generalized susceptibility.8 ~ 06 0.~ a~(R.1)2.0 2. To accomplish this we replace Si by ( g .Rj) is the exchange interaction function.1)2I~xch(q)x(q) (5) where Iexch is the approximate exchange matrix element for the interaction and where x ( q ) . nk is the occupation number of electrons with momentum k and energy E~ in the conduction band. R.j) exp [iq. a band index with a sum on the index would be required.) Since the .21. /. If "nesting" occurs at q = Q. . so that x(q) plays the dominant role in determining magnetic ordering. LEGVOLD matrix elements are not easily calculated. =o: >~ - ~. then x(Q) will be a maximum and an antiferromagnetic (spiral or sinusoidal) type of ordering will give a minimum in energy. Before proceeding to the consequences of the effects of x(q) on magnetic ordering we examine the relationship between the exchange energy and the magnetic ordering temperature..x. 0 2 Io .192 S. . (3) with the thermal energy. . °'/7" Paramag. This suggests that the ordering temperatures should be proportional to the de Gennes factor (g . such geometry is called "nesting". 4 6 8 10 12 14 16 (g-I) 2 g(d*l) or S(SH) Fig. solid circles.~(Q)(g ...oo /J Ho /.1)2j(j + 1) (7) where ks is Boltzmann's constant and To is the magnetic ordering temperature. Hence kBTo = ]. When the maximum of x(q) is at q = Q = 0 the ordering is ferromagnetic. 4 the highest ordering temperatures for the heavy rare earths found in table 2 are plotted against the spin factors S(S + 1). This is obtained by equating Hexch from eq. • • . say at q = Q. For now we note the minimum in Hexchwill occur for a maximum in x(q). It is seen that the fit is better to I I I I I I I 300 • (g-I) 2 J(d÷l) • S(S4) Ordering ~ / / ' Gd 400 200 ( 300 F-° : -y o ~. In fig. The fit to S(S + 1) appears to be superior. .1)2J(J + 1). Highest ordering temperatures and average paramagnetic Curie points of heavy rare earths versus de Gennes factor and versus S(S + 1). This is discussed in the next section which covers the bands and Fermi surfaces of the metals. it is generally assumed that the matrix element 12 exchdoes not vary. -/. 4. solid triangles. i.oo I I .1):J(J + 1). It may be seen that those regions on the Fermi surface which make x(q) large would likely come from fiat parallel surfaces perpendicular to the c-axis (q is assumed along c here) so that many electrons could participate at a given q. . and (g . as well as ferromagnetic ordering. and get the results shown in fig. It falls off as 1/R 3 so has a somewhat limited range.sin(2kFR)] (8) w h e r e kF is the electron momentum at the Fermi level and m is the electron mass. We can likewise examine the relationship between the average paramagnetic ordering temperatures from table 2 and the spin factors. 4. Temp. I I 1 I I I I 300 • (g-l) ~ JlO+l) .L Porama. for small kFR. This is the Rudermann-Kittel-Kasuya-Yosida (RKKY) form for the exchange interaction. 5 where we show the paramagnetic Curie points for H parallel to the c-axis and for H perpendicular to the c-axis for the heavy rare earths as a function of the de Gennes factor and of the simple spin factor. g" 100 I I 0 2 4 6 8 I0 12 (g-I)= J(J+l) or S(S+l) 14 Fig. 5. We have in this simple case y (R ) = (mlll2/4~r3R4)[2kFR cos(2kFR). We see that in this case the fit to S(S + 1) is again superior. We examine next the form for ~ ( R ) when the assumption is made that the conduction electron band is free electron-like with E ( k ) = h2k2/2m (parabolic).. We note also that the first term in the bracket is oscillatory with R so it can give anti.)= 310pU-I-320pj. ~ ( R ) is proportional to -1/kFR so we get ferromagnetic ordering out to the first zero of the function in the bracket.. S(S+l) . We use 0p(av~. / " / ~ ' . 500 200 v -I == 0oo 200 = 0 d/y I I I I I Temp. . We s e e (~p perpendicular to c is nearly linear in the plot against S(S + 1). Paramagnetic Curie points for H parallel to the c-axis and for H perpendicular to the c-axis for the heavy rare earths versus de Gennes factor and versus S ( S + 1). This may be accidental because the possibility that ~ ( Q ) might be different for different elements has been neglected. • ~ / 7 400 . Gd. We explore this matter further in fig.RARE EARTH METALS AND ALLOYS 193 the simple spin factor S(S + 1). that within the hexagonal layers we have aligned spin factors and that J makes angle 0 with respect to q which is assumed along the c-axis of the hexagonal lattice. the planar spiral. For a planar spiral structure (Tb. The theory for this process is discussed by Cooper (1972). i. (12) If ~ ( q ) > ~ ( 0 ) then the exchange energy would be a minimum for 0 =2l~r. In part (a) of the figure the orientation of the moments for H = 0 are the solid vectors which tend to cluster around the easy b-axis directions and for a modest H are the dotted vectors. At higher fields there is an abrupt transition to the fan structure shown in fig. Then at even higher fields the pattern in (c) and (d) appears. The behavior of the moments when a magnetic field is applied to the planar spiral structure (Tb. Dy.and q = 0. 6b. Neither case gives a conical structure and so anisotropy energy and/or magnetoelastic energy is required to stabilize a conical structure. This comes about because of the difference in the temperature dependence of the exchange energy and of the magnetoelastic energies which both play a part in determining the magnetic ordering. For the ferromagnetic structure of Tb and Dy 0 = ½or. Ho) 0 = ~w and Ji~ = 0 with a turn angle again determined by q.1~ S. Dy. On the other hand if a~(0)>~(q) the exchange is a minimum for 0 = 0.• Let £ be along the c-axis.. This can be seen by examining the exchange energy per atom Eexch= -J2L~(q) sin2 0 + o¢(0) cos 2 0]. ~ along a line of atoms or a-axis in the basal plane and ~ along the b-axis which is _ 1 _to the a-axis in the basal plane. The components of J at site Ri are Ji~ = J cos 0 Jk = J sin 0 cos(q • R~ + ~o) Jig = J sin 0 sin(q • R~ + ~0) (9) (1o) (11) with g the amplitude and ¢ an arbitrary phase angle at R~ = 0. In the cases of Tb. Dy. This describes a conical moment structure (Er or Ho at low temperature) with the turn angle related to q = (2w/A)~. It is shown later how such fan structures affect the magnetization process in Ho. 6. LEGVOLD To examine magnetic order in greater detail we assume that the total angular momentum at site R~ is 3.e. Ho) is examined next. the c-axis is the very hard direction. It turns out that magnetic exchange alone cannot account for conical magnetic ordering. the ferromagnetic structure with the magnetic moment along the c-axis. Assume the magnetic field is applied along the b-axis in the basal plane. Large anisotropy confines the magnetic moment vectors to the basal plane. The magnetoelastic energy favors ferromagnetism and is greater at low temperatures but falls off more rapidly as T . Ho and Er there is a transition from an antiferromagnetic phase to a ferromagnetic phase as the temperature is decreased. Progressive stages showing what happens to the spins of several layers of magnetic moments in the spiral phase of Ho are shown in a projection onto the basal plane in fig. (c) Next the moments marked 1. The temperature range over which Dy and Ho are in the spiral phase is much greater.4. 5 bend toward the field in a weak field giving paramagnetic-like behavior. These explain the strong magnetic anisotropy associated with the rare earth metals other than Gd (which has a spherically symmetric half full 4f shell). (In the absence of crystal fields we have rotational symmetry about the z-axis as indicated. (d) at high fields the antiparallei moments move to give total ferromagnetic a l i g n m e n t .RARE EARTH METALS AND ALLOYS 195 (~ (o) (b) (c) (d) Fig. The 4f electrons have three units of angular momentum and for partially full or partially empty shells give aspherical charge densities as can be seen in the figure. (b) When the field is higher the moments marked 2. 7 polar graphs of 4f wave functions are shown. 4. (a) The moments marked 2. magnetoelastic and magnetic anisotropy effects which are observed.5 become parallel to the field. The planar spiral ordering in Tb exists over a temperature range of only 10 K and the spiral turn angle from layer to layer is small ~ 18°. A detailed discussion .) Indeed for one to three electrons in the shell the charge distribution is donut-like in shape. The diagram is appropriate for H along the b-axis of Ho at about 60 K. We turn next to a brief discussion of spin wave physics. When we invoke near neighbor Coulomb repulsion between such aspherical charge distributions one sees at once a simple basis for understanding the strong magnetostriction. 6.a n overall three step process. Cooper (1972) has discussed this phenomenon and has pointed out that the principal driving force for the helix to ferromagnetic transition in Dy and Tb comes from the cylindrical symmetry energy associated with the lowest order magnetostriction effect.4 jump to new positions creating a fan-like appearance.2. In fig. Development of the fan structure for helically ordered magnetic moments. increases than does the exchange energy which favors antiferromagnetic (spiral) ordering. In the latter case atoms are arranged in a lattice and interact via Coulomb forces making it possible for characteristic vibrations or standing waves to exist in the solid. the spins precess in a coupled manner and the spin wave propagates through the lattice. or magnons. is given by Mackintosh and Moiler in chapter 5 of the book edited by Elliott (1972). At absolute zero the magnetic moments are in their zero point energy state and we expect any disturbance of the ionic lattice to have a counterpart in the magnetic lattice. E(q)." Z m | ~~ //" ~£ mt~O Fig. i. The m~ = 0 distribution is noticeably different from the others with high concentration along the z-axis.. The frequencies in a solid are of the order of 1012Hz giving the disturbances a quantized energy hv of about 4 mev. The 0 dependence is uniform as sketched for zero crystal fields. For ml = 3 the distribution is donut like. This means that characteristic magnetic spin waves will be supported by a magnetic lattice.. which are reminiscent of phonon dispersion. The [Oim(0)] 2 probability orbitals for 4f electrons. It turns out that the energies of magnons are very much like those of phonons and the energy dependence on the q vector is also much like that of phonons so they have dispersion relationships. At low temperatures only long wavelength or low energy disturbances will be excited. . LEGVOLD z ml=3 .1~ S. In the case of magnetic systems the magnetic moments on different lattice sites are coupled by way of the exchange interaction of eq. arise is analogous to the manner in which phonons arise in the treatment of solids. (2). The name magnon is given to a quantized spin wave.. The manner in which spin waves.. 7.e. A step by step calculation of the energy added divided by the temperature gives the magnetic entropy. Short range order persists into the paramagnetic range so the specific heat levels off to the non-magnetic part (phonon and electronic) well above the ordering temperature. A thermodynami~ treatment of magnetic moments leads to a discussion of the entropy associated with the disorder generated by the spin waves. [~(q = O)-. The first term gives the ground state energy of the moments and the second gives the spin wave energy so the dispersion relationship is E ( q ) = hto(q) = J [ ~ ( q = 0 ) . We see from this that specific heat measurements are significant and useful in the study of magnetic systems. It turns out as suggested there that the Coulomb term in the Hamiltonian also plays a strong . Energy bands.al angular momentum quantum number. The term acoustic is used to identify the lower branch for which the A and B lattice site moments are in phase.RARE EARTH METALS AND ALLOYS 197 When the Hamiltonian of eq.3. 1. In this case Mackintosh and M¢ller get dispersion relations which show two branches. (I) was considered. so different curves for the ferromagnetic and helical phases encountered in the rare earths are expected. This term was discussed first because of its importance in explaining many features of the magnetic ordering in rare earth metals. When the phonon and electronic parts of the specific heat for a magnetic material are subtracted from the total specific heat the magnetic portion is obtained.~(q)]a~ag q (13) where a + is a creation operator for a spin wave of wave number q and a~ is the corresponding annihilation operator. essentially all spin waves which can be supported are excited and the contribution of the spins to the entropy is nearly saturated. while the term optical is used to identify the upper branch for which the A and B site moments are 180° out of phase. for q = 0. From statistical mechanics the total magnetic entropy Sm~ comes out to be Smag= R In(2/+ 1) (15) where J is the total angular momentum quantum number and 2 / + 1 is the spectroscopic multiplicity associated with the to*. (14) The problem is more complicated in the case of the hop lattice where there are two atoms per unit cell.A J 2 . By the time the order disorder transformation (Curie point or N6el point) is reached. ~ ( q = O ) + J ~. the energy takes on the form H = .. for small wavevectors. Fermi surfaces and electrical resistivity In the last section the exchange energy term in the Hamiltonian of eq. The dispersion relations depend on the type of ordering.~ ( q ) ] . (3) is second quantized and thermal disturbances are introduced in the case of a simple lattice. The points must be chosen judiciously to obtain accurate bands. Rj the position of the lattice nuclear (ionic) charge Z. This potential is spherically symmetric inside of non-overlapping muffin tin spheres around each ion and is constant outside the spheres. The bands of the related trivalent elements Sc and Y have been reviewed by Cracknell (1971). Since the rare earths are beyond the middle of the periodic table they fall on the borderline for the appearance of relativistic effects. One should certainly expect this because of the indirect exchange interaction wherein the 5d-6s conduction bands are intermediaries for coupling 4f moments to each other. Historically. R. pj the electron momentum. LEGVOLD and interesting part in the magnetic properties of the rare earth metals. APW and RAPW methods for calculating bands have been described by Mattheiss et al. Band calculations treat the conduction electron Coulomb term of the total Hamiltonian of eq. The most recent review of the band structure of the rare earths is given by Liu in chapter 3 of the book edited by Gschneidner and Eyring (1978). the second term the Coulomb attraction energy and the last term the electronic Coulomb repulsion energy. In the Born-Oppenheimer approximation the electron-phonon interaction is eliminated. By fitting the solutions at wave vector points in the BriUouin zone a set of basis functions is found for the approximations. Earlier reviews have been given by Dimmock (1971) and by Freeman (1972). Loucks (1967). We have p~ Ze 2 . (1).e. When the APW method is employed the wave functions for the Schroedinger equation are spherical waves inside the muffin tin spheres and are plane Bloch type waves outside the spheres in the interstices.. and e the electronic charge. A variational treatment leads to homogeneous equations in the coefficients which must have a non-trivial solution. 1 e2 Here m is the electron mass. (1968). The Hartree-Fock approximation using a Slater determinant wave function reduces the problem to an independent electron model which neglects electron-electron correlations of opposite spin electrons. Several approximations must be employed to make this many body system tractable. and Rk electron positions. The two sets of wave functions are matched at the sphere surfaces and this leads to linear relations between the sets of coefficients. Dimmock (1971) and by Callaway (1974). i. The augmented plane wave method with a muffin tin potential as suggested by Slater (1937) has proved to be effective in the band calculations for the rare earths. the electron moves in an average but periodic potential due to the ions and to all the other electrons. This approach automatically includes spin orbit effects. Some advantages accrue if a relativistic augmented plane wave method (RAPW) is employed to find the bands. The first term is the electronic kinetic energy. An average single electron effective potential is required. For N atoms there are then Z N electrons all told.198 S. the bands for Gd were calculated first by Dimmock and Freeman . Z b. Sketch of the pertinent energy levels for Eu and Gd. The much flatter bands above this near EF are d-like and these play a dominant role in the determination of the Fermi surface. Gadolinium has the hcp structure as do Tb. The original Dimmock and Freeman (1964) paramagnetic (above Tc = 293. Dy. The conduction electrons have some common qualitative features for all the heavy rare earths as well as for Sc and Y. lying about 8 eV (electron volts) below the Fermi level in the 5d-6s conduction electron bands for Gd and about 2 eV below for Eu.. It is seen that this occurs near T along F to K. Tm.. There are. and Lu.=. Energy bands are dependent on k vectors.I -32 xENON CORE ELECTRONS --'~ 4f . These differences are related to the positions of some of the flat d-like bands relative to the Fermi energy. some very important small differences which have strong influences magnetically. 9. Two bands intersect the Fermi level which is established when the three conduction electrons have been accommodated in the bands. The Brillouin zone for the hcp lattice is also hcp for which the geometric symmetry points are shown in fig. however. Ho Er.RARE EARTH METALS AND ALLOYS 199 (1964). By using a mesh of many points in the Brillouin zone the constant energy surface at Ep for such bands can be found. The general layout of the bands may be described as follows: Because the lowest energy band at F is broad in energy and rises in a fashion reminiscent of the parabolic band for nearly free electrons it is called an s-like band. which is essentially an atomic energy level. 8. . they are calculated along symmetry lines in the Brillouin zone and the energy bands are usually shown along these lines. The Dimmock and Freeman (1964) Fermi surface for Gd in the extended E=O -4 Eu Gd 5d-6s bond ]<-EF-)[5d-6s bond] 4f -E -12 -161 -20 "24 i -28 . A simple diagram showing the relative energy levels and conduction band for Eu and Gd (Gd is typical of the heavy rare earths) is shown in fig. The positions of the 4f levels below E~ (the Fermi level) are based on XPS data of H ~ l e n et al. (1972) and of McFeely et al.9 z £3 z l Fig.4 K) bands for Gd are shown in fig. 10. near K and near E along M to F. (1973).I (. 8. We see that the 4f electrons exist in a very sharp band. as might be expected since the conductivity comes from an integration of the electron Fermi velocity . 10. . The conduction electron energy bands for Gd calculated by Dimmock and Freeman (1964). . 9.n I" A Fig.9 hJ Z i.. The surface is found by folding the bands between F and A into the extended zone FAF.200 S. the trunk expands into arms or branches which extend out in the ALH planes and which exhibit a duck foot type of webbing between the arms near the trunk. It is an open hole surface and goes from one zone to the next with the states outside the surface occupied and the states inside empty. < / / f / / / . Both the trunk and the webbing play important roles in the electrical conductivity. The surface has a cylindrical tree trunk-like shape in the central FMK region which involves electrons in the steep bands of s-p character. I I I I\1 A H I L IS ~ . .u i I I I P . . Brillouin zone for the hexagonal close packed structure showing the standard symmetry points (an a-axis of the zone corresponds to a real lattice b-axis and a b-axis of the zone corresponds to a real lattice a-axis). . l lz \1 M -----6T' L o-oxis \ H b-oxis Fig. f : Kq~ . double zone scheme is shown in fig.~. 11. . . . . It is unusual that there are no other pieces or pockets of Fermi surface. Then going up or down along the c-axis. -0.4 O re" W >tv- _z >¢. . . . LEGVOLD L.. . Fermi surface of Gd as determined by Dimmock and Freeman (1964). P r and Nd. M o r e detailed discussions of these F e r m i surface f e a t u r e s f o r the hcp metals will be found later when the individual e l e m e n t s are treated.RARE EARTH METALS AND ALLOYS 201 K H K H K Fig. T h e Brillouin zone is hexagonal and the s y m m e t r y points u s e d are the s a m e as those for hcp as s h o w n in fig. as seen later in this chapter. Ce. I n d e e d the F e r m i surface g e o m e t r y explains the anisot r o p y f o u n d in the electrical resistivity. 9. Since there are f o u r a t o m s per unit cell in this situation there are f o u r bands which . o v e r the F e r m i surface. exhibit the crystal structure with A B A C stacking of hexagonal layers. l 1. This is a hole surface in the extended zone scheme with the states inside the surface empty and the states outside the surface occupied. On the other hand it is principally the webbing feature which exhibits a strong interplay with magnetic ordering b y w a y of the e x c h a n g e energy t e r m in the Hamiltonian and the effect this has on the periodic electron potential. T h e light rare earth metals. La. so they chose to display only some cross sections of the surface in high symmetry planes. The bands near EF are fiat and so have d-like character and are reminiscent of the bands for Gd. Since the RAPW method was used it was not possible for them to fold the bands out into the extended zone as for Gd. A K M l" Fig. Some cross sections of the Fermi surface of dhcp La with the high symmetry Brillouin zone planes as found by Fleming et al. LEGVOLD intersect the Fermi energy and thus contribute to the Fermi surface. The bands they found for La are shown in fig. 12. (1968). The problem is formidable. Relativistic conduction electron energy bands for La calculated by Fleming et al. 12.443~ RYD ~ ~= a2o I~ M K \y FA L H A ML KH Fig. (1968). r. even so the energy bands for La have been calculated by Fleming et al.202 S. 13. (1968) using the RAPW method. .60 - EF: Z 0. The Fermi surface they found consisted of many pieces and pockets. They noted that the webbing feature associated 0. Their findings appear in fig. 13. The point N is in the KxKy plane at the foot of the point P show~. 14.RARE EARTH METALS AND ALLOYS 203 with the c-axis direction is missing and suggested this might be associated with the stabilizing of the dhcp structure. Freeman and Dimmock (1966) calculated bands for bcc Eu by the APW method and Andersen and Loucks (1968) used the RAPW method. . It has been found by Bucher et al. Jepsen and Andersen (1971) made a RAPW calculation for hcp Yb and found the bands shown in fig. Briilouinzone with symmetrypoints for the body centered cubic lattice. 17. they noted that some of the surfaces depicted partially in fig. 16. it has been necessary to make a separate calculation for its bands. Since the metal Eu is divalent and exhibits the bcc structure. There is a large electron surface centered around H which has the shape of a rounded cube and around P there is a similarly shaped hole surface with ellipsoids tetrahedrally attached on four of the corners. On the other hand. (1970)and Kayser (1970) that the hcp structure is the stable form at very low temperatures. The fiat pieces of the hole cube provides the nesting required to explain the observed magnetic structure of Eu. The bands obtained by Andersen and Loucks are shown in fig. They also found that the Fermi surface consisted of a number Fig. 14. The Brillouin zone for the bcc crystal is fcc and has the shape and point designation shown in fig. The Fermi surface they found is shown in fig. 13 could lead to a nesting in directions perpendicular to c which might account for some magnetic ordering observations for these metals. More recent Fermi surface calculations by Kobayasi et al. The element Yb is divalent in metallic form and has a full 4f shell so it is only weakly magnetic. 15 and appear to be similar to the bands of the bcc transition metals. (1976) are in reasonable agreement with the earlier calculations above. of pieces and pockets which were hard to picture.-form) above 350 K. LEGVOLD %_ A ne .LIJ Z bJ y 1" H N P r N P H Fig. Fermi surface for Eu determined by Andersen and Loucks (1968). As might be inferred from the bands shown in the figure along F to K they calculated a high density of states at the Fermi level and they argue that this feature might account for the fcc to hcp transformation at low temperatures for Yb. 15.2~ S. 16. Energy bands of Eu calculated by Andersen and Loucks (1968) using the relativistic augmented plane wave method.9 n. which is dhcp. The element Ce is quite inscrutable from the band viewpoint. in the range . takes on the /3 form. The element is fcc (3. SUPEREGG Fig.2 (. Band structure.4 K H L 0F K M F A Fig. ~ is the relaxation time of the conduction electrons. A wide variety of conduction electron scattering mechanisms influence the conductivity of the rare earths. Reviews of the subject have been published by Meaden (1965. It should also be noted that at low temperatures the resistivity of magnetic metals should have a T 2 dependence according to Mannari (1959). The problem is usually treated by associating independent relaxation times with the different mechanisms so that the effective relaxation time for eq. Next a very brief outline of transport theory as related to the Fermi surfaces of rare earth metals is given. e is the electronic charge. The indirect exchange mechanism leads naturally to a close correlation of conduction electron transport properties to the magnetic properties of the metals.RARE EARTH METALS AND ALLOYS 205 EF F .Z .esistivity measurements. particularly the hcp elements. i. 50-350 K and collapses into a more dense fcc form (a) below 50 K. v~ is the component of the conduction electron velocity in the i direction at the Fermi surface and dSj is the projection of the Fermi surface element in the j direction. (17) has the form . the electrical resistivity exhibits anomalous behavior when changes in magnetic ordering occur. The usual Boltzmann equation treatment for determining electrical conductivity leads to e2 (P-~)ij = ~ f "rvidSj EF (17) where p is the resistivity tensor. the Fermi surfaces for the rare earths.. The f band falls close to the Fermi level and makes band calculations difficult. are anisotropic and this leads to anisotropy in the electrical resistivity of the metals. This makes it possible to determine magnetic ordering temperatures by way of electrical . 17. and (upper right) some features of the Fermi surface for hcp (low temperature phase) of Yb calculatedrelativisticallyby Jepsen and Andersen(1971). As indicated above. 1971).e. We recall that when the periodic lattice of ions (a Coulomb term) is introduced in free electron theory the wave functions take on the Bloch form and energy gaps appear at reciprocal lattice points. and Miwa (1963) such magnetically induced energy gaps lead to so called "superzones". ) in the one dimensional lattice whose atom spacing is a. vi. . particularly those which exhibit magnon scattering. (The resistivity is found to be isotropic in the basal plane so Pb = Po. In the case of helical structures which .) The ratio of the single crystal resistivities gives some information about Fermi surface geometry because (Pb -. Elliott and Wedgewood (1963). Here one notes that the spins of a ferromagnetic material would have the same periodicity as the ionic lattice so dramatic superzone effects would be missing. Of greatest significance for this chapter. Magnons are quantized magnetic excitations (spin waves) so T= arises from magnetic spin disorder scattering. The element Gd has a room temperature resistivity two orders of magnitude greater than Cu.OOb)/(Pc-. A similar expression gives pb in the basal plane b direction. 2. S. As suggested by Mackintosh (1963). Tp arises from phonon scattering and normally gives the low temperature resistivity dependence T x.g. The shape of the Fermi surface of fig.. these metals are poor conductors. We assume an average conduction electron velocity. It is therefore to be expected that the introduction of magnetic periodicity into the Hamiltonian by way of Hexchwould lead to additional energy gaps at or near magnetic ordering temperatures. if the magnetic lattice differs from the ionic lattice (as happens in most rare earths) pronounced effects on the conductivity are found. at n~r/a (n = 1. 3 . As might be expected in the light of eqs. T. For non-magnetic Y and Lu. however. (17) and (19) and the fact that the rare earths are transition metals with relatively high density of states at EF. However.206 1/~" = 11~'o+ l/~-p + l/~'m. e. LEGVOLD (18) Here T0 is due to impurity scattering and is related to the residual resistivity p0. + l/~'m f dSc) ~F (19) EF EF where A is a constant. Then in the case of hexagonal crystal lattices the resistivity pc along the c axis would have the form pc = A(l/~'0 f dSc+ l/~-p f d S . x = 2-5 along with linear temperature dependence at elevated temperatures and T= is related to magnon scattering. Hall et al.POc)= f dSc// f EF EF dSb (20) with similar expressions for residual resistivities and for the high temperature slopes dpldT of p vs. (1959) found resistivity ratios pa/pc of 2 and 2. .2 respectively from experiment. may be used. 11 makes the numbers look reasonable. . is the effect of the exchange interaction and magnetic ordering on the Fermi surface. RARE EARTH METALS AND ALLOYS 207 h a v e q along the c-axis and which are i n c o m m e n s u r a t e with the ionic lattice. Light lines are for the original Fermi surface and the heavy lines are the result of magnetic superzone effects with the onset of antiferromagnetic ordering.l/ K I P " g' M t" i I" M 41-1 A~ g r A~ I I|1 IIHI Al t K I k_ r 1 F I "--t/ A I" ~ L M Fig. I t. Some of the vertical cross-sections of the Fermi surface for Tm. 18. T h e y a s s u m e d a spheroidal F e r m i surface and used first order perturbation theory along with eq. H e r e M ' and M are t e m p e r a t u r e d e p e n d e n t m o m e n t amplitudes which m a y be found f r o m neutron diffraction data and ~b is a p h a s e angle. 18. (11) in the f o r m {J~) = M ' J cos(q . T h e e x t r a energy gaps wipe out a considerable a m o u n t of the F e r m i surface p r o j e c t i o n in the c direction. (3) plus eqs. After Freeman et al. . (9).E ( k + 21/)] 2 + 12 r2M211/2 ~xchJ ±X (25) where E ( k ) is the u n p e r t u r b e d e n e r g y o f an electron of w a v e v e c t o r k. the new magnetic energy gaps along the c-axis wipe o u t F e r m i surface areas with c-axis projections and this strongly influences the resistivity in the c direction. T h e m a n n e r in which the electrical resistivity is affected b y this p h e n o m e n o n has b e e n treated b y Elliott and W e d g e w o o d (1963). lc~ch is the e x c h a n g e matrix e l e m e n t of eq.R~) {J~) = M ' J sin(q • Ri) {J~) = M J cos(q • R~ + ~b) to get the position d of the magnetic s u p e r z o n e planes at (21) (22) (23) d = ½(n -. (5) and w h e r e M 2 = M 2 + 2 M '2 _ 2 M ' ( M 2 -F M '2) 112. A striking illustration f r o m w o r k by F r e e m a n et al. T h e y f o u n d the energy to b e 2 E ( k ) = E ( k ) + E ( k + 2~q) -+ {[E(k) . (1966) for hcp T m is s h o w n in fig. T h e e n e r g y gap f r o m this is (26) A = Iex~hJM +. (27) l-. (1966).q) (24) with ~/ a reciprocal lattice vector. (10). EF is the Fermi energy. #2. This is . Equation (16) treats the Coulomb energy of the three 5d-6s conduction electrons per atom in the ionic lattice. A2.F ( M 2 + M'2) 1/2 F = (3¢rlcxchJ/4EFkF) ~i [dil.½M2 . Such a term.M '2) 1 . the calculations for different crystallographic directions come out to be Pb = A1+ #1T + U~(1 . fcc) must be reflected in the description of the potential of the ionic lattice. The typical energy between the ground state and first excited crystal field state varies from 1 to 10 meV (10 K to 100 K) with the overall spread of all levels up to 20 meV.S and for which the exchange interaction is therefore small. The crystal field The first term in the Hamiltonian of eq. Strong L S coupling in the rare earths means that crystal fields may diminish both spin and orbital parts. (19) and (24-27). for which J = L + S. 1. The effect of crystal fields is most pronounced in the light rare earths for which J = L .) In the case of metals.½M2. U2 are adjustable parameters. This does not include the Coulomb energy of the localized 4f electrons on a given atom due to the charges of all surrounding atoms in the lattice. dhcp. to put it another way. The crystalline electric potential is of the Coulomb potential form. we know that the symmetry of the lattice (hcp. (In a metal this term is small because the conduction electrons move so as to neutralize electric fields inside the metal. the crystal field energy term is used to find the 4f wave function combination which will yield the appropriate energy levels. To find very large crystal field effects one turns to insulating or dielectric type compounds or matrices. and therefore also in the localized 4f electron wave functions. #1. LEGVOLD From eqs. (1) provides for the Coulomb energy of the solid.4. called the crystalline electric field term Hcf. kF is the electron wave vector evaluated at the Fermi surface and A~. (18). or. must be added to make the picture more complete.2#8 of 2. It is found that crystal fields have the effect of removing degeneracy and thereby diminishing (quenching) the orbital magnetic moment (recall that only 0.208 S. the exchange energy dominates the crystal field energy. These then dictate the magnetic moment of the system. Urn. It turns out that for the heavy rare earth elements from Eu to Tin. The fits of the theory to the experiments are just fair and appear later with the discussion of the individual elements.2#~ for iron comes from orbital momen0.M '2) Pc = (28) (29) (30) A2+/~2T + U2(1 . This should be compared to the exchange energy for Gd which is 25 meV. Now J is a good quantum number and one looks to the crystal field to find the proper mixing of the 2J + 1 degenerate mj levels. Here the sum is to be taken over all superzones which slice the Fermi surface. be calculated but are fitting parameters. For a cubic lattice only two parameters. Discussions of crystal field effects in the light rare earths appear in the sections describing the magnetic properties of these elements later in this chapter. for example. Group theory arguments show that because of lattice symmetries most of the coefficients of these harmonics are zero.B4(O ° + 504) + B6(O ° . 0.RARE EARTH METALS AND ALLOYS 209 expanded in tesseral harmonics which are directly related to spherical harmonies. 3' are Stevens (1952) factors. and W which gives the absolute scaling of the crystal field energy level scheme./3. (1962) have suggested that convenient parameters are x. are needed H a -. Her ": B 2 o0 20 + B 4 00 4 0 + B6 00 6 0 + B606 6 6 (31a) where the B's are parameters and the O's are operator equivalents. . Inelastic neutron scattering and magnetic susceptibility measurements have been used by Rathmann and Touborg (1977) and by Touborg (1977) for such studies. (1958). r is the radial distance.% Er in a Sc host and in a Lu host. namely. (33) In such cases Lea et al. (31b) Yosida (1964) gives a sample classical calculation where the operator equivalents are replaced by corresponding Legendre polynomials. When the d a ratio is ideal and a point charge model for the ionic lattice is used this expression reduces to Hcf = A4041 o_l_ A6[O61 0 + ~ O 6] (31b) where the parameters A4 and A6 could. which gives the ratio of fourth to sixth order anisotropy. 19. They got the hcp crystal field levels for 2at. Ampnm and gets Hcf = 2aA~(r2)j2p2(cos O) + 8flA°(r4)j4p4(cos O) + 16~/A°(r6)j6p6(cos O) + y A 6 ( r 6 ) j 6 sin 60 cos 6d~. For the hcp lattice and crystal field Hamiltonian of eq. They found the admixture of mj wave functions and the energy levels to be only slightly different in the two hosts. the brackets. As a typical case their results for Er in Sc are shown in fig. Baker et al. For a hexagonal crystal only four terms remain. The expression shows the anisotropy or angular dependence of the energy as it is related to the lattice geometry. (32) Here 0 is the polar angle from the c-axis and q~ is the azimuthal angle from the a-axis. They are given by B----54 = F B6 tl---c J x ] F6(J) B4F4(J) = x W (34. designate the expectation value for 4f electrons. many of which have been tabulated by Hutchings (1964). in principle. and a. See. Operator equivalents are used as suggested by Stevens (1952). the main difference being in the height of the upper crystal field levels. B4 and B6.21 04). 35) where F4(J) and F6(J) are specified constants for a given Z Most of the information about crystal field parameters for the heavy rare earths has come from studies of dilute alloys for which the exchange field is considerably weaker than the crystal field. ~ ~. ~ N ~ ~ . n e N ~.~ o ~ I 0 ~ ~.o < .~ .~-- .:)) AI|iUO.~?~ O O 0 0 0 O O O 04 0 . . .~ tt E~ 1 ....OlN f"" + ^ 0olo.~ "~ ~: ~ . ... ~ ~ ~ ~ c~. .-I~ 14- ~IN i+ ~l(~ 14" -IN +1 . ~ ..~. ~ .-~ (Olqg zOt Jod "S~.... . o~ ~ .----.4"o o~.. . .. .~.= =~ ~~ ~ ..210 S._ _~ ~ .~ o " o o" T / / ~ [~ . .. .IO~ ~0 + ^ ~ ~ • ¢) "~ ~ o~ . i ^ __..- :> • '-" l I ' l l l l l ..o m + ^ =1 ~ ~.-..I... +1 "~ @ "' II r. ~ ~-~ ~'~ ~ . ..~ ~ "-" ~ "~ .~ "~ o 0 o 0 o 0 o 0 0 o • 0 o 0 0 o o 0 0 .. L E G V O L D ~i~ 4- --IN + =t~ + [. . iJ.Ul u o ~ . ..~ - / ". GADOLINIUM TERBIUM DYSPROSIUM \ \ \ Ferr.4K 0 219.f. Er and Tm (see fig. A sketch of the magnetic structures of the heavy rare earths is given in fig. THULIUM II. Dy.:.4 K N6el temperature and the axis of the helix is along a (100) direction in the absence of an external field. . Ho.o I APO I" / 0 20 52 85K Ill T / '// 0 52 58K Fig. 20.RARE EARTH METALS AND ALLOYS 211 2. Er and Tm This section begins with a brief description of the magnetic structures of the heavy rare earth metals as they have unfolded from neutron diffraction measurements.. 7). The elements beyond Gd have strong magnetic anisotropy effects associated with the asymmetric charge distribution that goes with the 4f orbital electron wave functions which are donut-like for Tb and Dy and then become more complex for Ho. When a modest field is applied the axis of the helical spin structure takes the orientation of the field. The seven 4f electrons of body centered cubic divalent Eu have parallel spins (S = 5) which take on a helical configuration below the 90.~o Fer o Por. A review of this work has been prepared by Koehler (1972).~o 245 295. This implies that the magnetic moments are in {100} planes.5 25L5K 0 89 179K HOLMIUM ] " ERBIUM FT. Gd._ FeTro I 0 20 I 152K I ... Magnetic ordering in the heavy rare earths as found by neutron diffraction. 20. Magnetic properties of Eu. Tb. Experimental measurements show otherwise. 2. Why should this be so? The answer is found in differences (a) in crystal structure.2 K wherein four moments up along c are followed by three moments down. Below 219.84 times the full 9~B expected. As shown in fig. Like Eu it has the half filled 4f shell with seven parallel spins so S = 7.212 S. Below this temperature a conical ferromagnetic structure is attained with the cone angle about 30° so that the c-axis moment comes out to be 7. The divalency stems from the migration of one of the 5d-6s conduction electrons to the 4f shell so as to half fill the shell because this configuration is highly stable and energetically favorable.5 K the metal is ferromagnetic with the moments in the basal plane and with the easy direction along the b-axis. (b) in atomic spacing and (c) in conduction electron d-bands. Dy has magnetic phases similar to those of Tb with the helical form extending from 179 K down to 89 K below which it is ferromagnetic with the moments in the basal plane and with the a-axis the direction of easy magnetization.~ and that for .4 K Curie temperature. Just below the 132 K Ntel point the helical structure of Tb is found. Europium The rare earth Eu. Hence. This completes a brief survey of the heavy rare earths and we present next detailed information about the individual elements. From table 1 it is seen that Eu is body centered cubic while Gd is hcp. 20 Tb is helical from 230 K to 219. Then below 38 K the modulation of the c-axis component begins to square off and gradually takes on a strange ferrimagnetic like structure at 4. LEGVOLD Gd is a simple ferromagnet. The easy direction of magnetization lies along the c-axis of the hcp lattice just below the 293. atomic number 63.5 K with the magnetic moments in the basal plane and the axis of the helix along the c-axis. then at 20 K the moments take on a nearly conical ferromagnetic helical structure with a cone angle relative to the c-axis of 80°.1. it is quite different from its neighboring elements among the lanthanides. Starting with Ho a new magnetic phase develops. The atomic spacing for Eu is 4.6#s or 0. One might then expect Eu to have magnetic properties akin to those of trivalent Gd which also has a half filled 4f shell and therefore has the same spectroscopic designation of sS7/2. In the case of Tm the moments have a sinusoidal modulation of the c-axis component just below the 58 K N6el point so it is much like Er. This gives a net ferromagnetic component along c of one seventh the expected 7/~ or 1/~B at helium temperatures. Thus Ho has an antiferromagnetic moment component in the basal plane and a ferromagnetic component along the c-axis below 20 K. is a divalent metal and so has chemical properties like Ca.83 . 20 Er has an oscillatory (sinusoidal) c-axis component with an essentially random basal plane component below the 85 K Ntel temperature and down to about 53 K where some squaring off of the wave sets in giving a quasi antiphase domain magnetic structure which extends down to about 20 K. The easy direction moves away from the c-axis for T below 240 K. As sketched in fig. More recent neutron diffraction results on a Eu single crystal slab in an external magnetic field by Millhouse and McEwen (1973) corroborate the earlier findings and show that for fields H greater than 8 kOe the magnetic moments in domains move so as to be perpendicular to H .54/~B which is attributed to polarization of the 5d-6s conduction electrons. They found that the moments are ordered antiferromagnetically below 90.48ftB which is higher than the 8. (1973) on single crystal Eu at 4. in a study of Eu and Gd solutes in La. This helps to explain why Eu is found to be antiferromagnetic and Gd ferromagnetic. This shows the 4f electrons are much more tightly bound in Gd. They found from their data that the magnetic moment per atom was only 5.4 K to 292. q for the helical moment arrangement is then parallel to H. (1973) using (XPS) found the main peak for Gd at 7. Such a large negative conduction electron polarization is difficult to understand and certainly calls for further investigation.3 K or about 1 to 3.1fib per atom is required.7 eV below EF. (1972) found the main 4f peak for Eu to be 2. Just below TN they found that the pitch of the helix (the q vector period) was 3. This is nearly twice the positive 5d band polarization found in ferromagnetic Gd at low temperatures. (8). The magnetic moment of Eu in the form of small particles obtained by a filing technique was investigated by Nereson et al. (1971) found a moment of 8. the N6el point.3/~B reported by Bozorth and Van Vleck (1960). Legvold et al. and that the pitch gradually increased to 3.4 of the saturation value between 88 and 90. High field magnetization measurements by McEwen et al.1 eV below the Fermi level while McFeely et al.4 K. At 4.9/~n which is well below the expected 7/zB for the sS7/2 ions. If conduction electron polarization is used to explain the low temperature moment of 5. where a is the lattice parameter. both are high as compared to the expected g%/S(S + 1) of 7. A combination of the latter effect and the effect of atomic spacing explains the ratio of the Eu to Gd ordering temperatures which according to table 2 is 90.2 K the q stays in this orientation when the magnetic field is turned off. From X-ray photoemission spectroscopy (XPS) H6den et al. The divalent character of Eu as compared to the trivalent character of Gd means that fewer conduction electrons are available. The original helical arrangement returned when the sample temperature was elevated above 37 K.94ftB shown in table 2. locally for the indirect exchange. an antiparallel localized 5d moment of 1.4 K. This transition is second order with a precipitous drop of the moment from 0. (1964) using neutron diffraction methods. This gives a surplus of 0.RARE EARTH METALS AND ALLOYS 213 Gd is 3.2 K corresponding to an interlayer turn angle of 50°.6a at 4. The moments are parallel to a cube face of the bcc lattice so that the axis of the helix (the screw axis) is perpendicular to the cube face and is therefore along a (100) direction.9ftB as compared to the expected 7/~B. From magnetic susceptibility measurements in the paramagnetic regime Johansson et al.2 K show the moment is linear with field from 2 to 20 T with the .5a.63 A which is important in determining the magnitude of the exchange energy as well as the sign of the spin coupling from the RKKY interaction of eq. (1977b) found this effect was large. J" /. The specific heat of Eu has been reported by Gerstein et al.-. 21.. 6 are affected has not been determined. the N6el point. The cusp in the resistivity curve near 90.4 K in table 2 is about the mean of the literature values. The spin waves give rise to the rapid increase in the resistivity from 0 to 90. The result is the dashed curve of the figure which shows an interesting slow fall off to a constant value reflecting short range spin order-clustering or fluctuation effects up to 200 K. Electrical resistivity data for Eu obtained by Curry et al. (1960). Electrical resistivity of Eu as reported by Curry et al. As a general rule it is expected that electrical resistivity versus temperature curves will always bend down toward the temperature axis when the temperature rises past an ordering temperature because of the spin disorder saturation effect. 20 io . This is a nice example of the effect of spin wave scattering and of antfferromagnetism on the conductivity.-. 21. The dashed curve is the spin only resistivity. above which the spin disorder scattering saturates and approaches a constant." _ 1:t / I I TEMP~. (1967). One may extrapolate this linear "part back to the resistivity axis to obtain the total spin disorder scattering. .4 K.R~n~rURE.0 8o 7o I I I I I I '1 I I t I I I'1 I EUR~///' ! . (1960) are shown in fig.4 K shows the effect of critical scattering and is also typical of antiferromagnetism where Fermi surface superzones play a role as described in the theory section earlier. They expected the moment might saturate and reach the theoretical 7#~B at about 100 T (106 Oe).~ Fig. ". If we estimate and subtract the phonon part I00 9O . The slope of the resistivity curve at 300K arises from phonon scattering alone. Exactly how the Fermi surface pieces of fig.4 K N6el point with the curve tapering off gradually below the peak as the temperature is increased. Thus we have obtained a curve for the magnon resistivity alone for Eu by subtracting the nearly linear phonon resistivity. The N6el temperature of 90. LEGVOLD moment then falling below linear behavior between 20 T and 35 T (350 kOe) where the moment reached was nearly 5#~e per atom. As suggested earlier this proves useful in exploring for ordering temperatures.214 S. .--r-- e. Their results are shown in fig. 22 where we see a sharp peak at a temperature slightly below the 90. 2. The data of the latter and the results of torque measurements on single crystals by Corner and Tanner (1976) are shown in the . It is the only rare earth which is a simple ferromagnet. It marks the start of the heavy rare earths which have the hcp crystal structure.2 J/mole K.~~"I'~ I ]o 20 I 30 I 40 ~ ~-~J/mole I I[ I . 23. 22. (1963) measured the temperature dependence of the magnetic moment of single crystals at several internal fields and obtained the results shown in fig. has a half filled 4f shell containing seven electrons and so has the spectroscopic designation SSw2. using the ratio of 0. Nigh et al.. The Curie temperature is 293.RARE EARTH METALS AND ALLOYS 215 EUROPIUM 6C Eu 0a = 0. (1964) and by Cable and Wollan (1968) who found that Gd is indeed a simple ferromagnet and that the angle 0c between the c-axis and the easy direction of magnetization changes with temperature. (1967).4 K.71 Lu 0o 5O A J" ii ~/j/// . Gadolinium The element Gd. 2.50 60 70 80 T(K) /I I I ~K I 90 " I I00 I I10 " I 120 - Fig. These results are in agreement with neutron diffraction observations made by Will et al. Then as the easy direction moves away from the c-axis below 240 K the moment falls off to a minimum at 170 K and then rises at low temperatures. atomic number 64. This choice of Debye temperature (116 K) was made so as to obtain a magnetic entropy Smagfor the dashed curve equal to the theoretical Sm~g= R ln(2J + 1) = 17. For Eu Rosen (1968) obtained a low temperature 0D(0) of 177 K. The dashed curve gives the spin only contribution. As the temperature is lowered in an internal field of 100 Oe the observed magnetic moment rises sharply below the Curie point 293. The specific heat of Eu as determined by Oerstein et al.4 K (see table 2) and the direction of easy magnetization just below the Curie point is along the c-axis.7 for the Debye temperature of Eu to that of Lu we get the magnetic heat capacity shown by the dashed curve. Nigh et al.V a n Alphen measurements which explored the Gd Fermi surface extremal orbits have been reported by Schirber et al. (1975) give a saturation value of 7. Isofield magnetization data for Gd in the c-axis direction found by Nigh et al.2 K they found a saturation m o m e n t of 7.63/xB. in close agreement with the g X / S ( S + 1) of 7. 1977). LEGVOLD ® -. At 4. by Young et al.) De H a a s . (1963) was 7. Franse and Mihai (1977) found that the easy direction curve shifted downward when pressure was applied. 23. (1976. and by Mattocks and Young (1977). (The separated isotope was used because the slow neutron capture cross section for natural Gd is 46 000 barns. 23.216 S.94/~a. . the angle between the easy direction of magnetization and the crystal c-axis.oo -. (1963). The paramagnetic Curie temperature . (1975a) and by White et al. - o so ~6o ~o zoo z~o /\ \ .63/~B is attributed to polarization of the 5d conduction electron bands. The paramagnetic moment found by Nigh et al. More recent measurements on electrotransported single crystals with very low oxygen content by Roeland et al. The + and A symbols and the figure itself are from the work of Corner and Tanner (1970. Fermi surface and band calculations by H a r m o n and Freeman (1974a. ~'120 - . . The insert shows the temperature dependence of 0c.. T h e y were able to identify the orbits by fitting results to conduction electron spin up and spin down Fermi surfaces. .55/xa which is to he compared with the expected gJ of 7/~a. The circles are from neutron diffraction measurements of Cable and Wollan (1968). (1972) on a single crystal of 16°Gd. . (1963) found that the saturation magnetization followed the Bloch T 3/2 law from 50 K to 200 K and showed a T 22 fit in the temperature regime below 50 K. ..98/za. (1973). insert of fig. The surplus moment of 0. b) for ferromagnetic Gd have shown that the observed surplus m o m e n t is reasonable and explains the neutron diffraction form factor observations of Moon et al.'.~ ' ~ 320 0 40 80 120 160 200 240 ZSO T (K) Fig. 25 for different crystal directions and along the usual lines in the Brillouin zone. (1975) and their result (scaled to fit at A) is shown as the dashed curve of the figure. (1966) by Lewis (1970). The dashed curves are the spin only resistivities. 24.~l.o ~ /F / -AXIS I I I I I I I I J I I I IOO 200 TCK) 300 400 Fig. An ab initio calculation of the APW type has been made along FAF (c direction) by Lindg~rd et al.gu.l. (1970) to ferret out the magnon dispersion curves for Gd. (1954) by Voronel et al. Their results at 78 K are shown in fig.4~u cm c cm .c rn //1 i 'A o-A~u~_ e_res. The lower curve from F to M is the "acoustic" branch and it shows no gap at F and is well behaved. results are shown in fig. (1977) gave results much like those shown.RARE EARTH METALS AND ALLOYS 217 was 317K for measurements both parallel to c and perpendicular to c. (1963). There is a good correlation of the resistivity behavior of Gd with that of the specific heat as reported by Griffel et al. The spin only resistivity in the c direction exhibits short range order fluctuation effects for some one hundred degrees K above the Curie point. The dashed curve is the spin only resistivity obtained by the subtraction procedure described previously. The latter is from the work of Jennings et al.6 meV at F is the so called optical branch. (1960) and is shown here so that the phonon plus conduction electron part only for Gd may '%" I. .o eo ~ 40 t/// l/i. by Simons and Salamon (1974) and by Wells et al. The upper curve which has energy 14. The separated isotope '6°Gd made it possible for Koehler et al. Electrical resistivity of Gd single crystals as reported by Nigh et al.. Also the hump in the c-axis resistivity near Tc has been discussed by Zumsteg et al. (1975). 26 where we display both the specific heat of Gd and the specific heat of Lu. i COl" '3af"1~ "" -I mo b-AXIS . (1970) as a lattice parameter effect. 24." &i ~ XIS ~sd= 4.. Other measurements extending to 600 K by Maezawa et al. The temperature dependence of the electrical resistivity they found is shown in fig.'. The Griffel et al.' - -.' If. so paramagnetic Gd is isotropic as might be expected for the spherically symmetric 4f shell. b'A s :1 ~lze"'''" // 1/" 7 ~ P~-s~n c~ 80 j/// tf/. i ~O /t .o~ " P d . P ~. L E G V O L D o~_.~ °~ Q . _ -.( % N . e~ ~I O m CD ~I" ~ O ~0 ~D ~I" I O4 O o (^ow) AeU3N3 ..218 S..o O ..oj o o // I*' f o W o w > o ~_ ? t / o m.0 ... q" u //°' • o.. ~m O ~e~ 8 • = d 0. o~ o IE ./ /i ~.= U k O O O ..\ z 0 o i 1 ~ ~O. one beyond the half filled shell of Gd. 2O 10 I. The dashed curve is the magnetic contribution to the specific heat of Gd. Below 219. Debye temperatures for Lu have been reported by Lounasma (1964). 120 Smog = 17.. The external . It appears that at intermediate temperatures a Debye value of 166 K for Lu is appropriate. 2.--~ t ( 330 360 . be subtracted out to give an estimate of the magnetic specific heat for Gd which is the dashed curve of the figure. and by Wells et al. They found that the inter-layer turn angle in the heficaI phase is about 20° just below the N6el point and then decreases slightly with temperature to about 18° before rising again near the ferromagnetic transition at 219.2 J/mole K I I l . I 150 IBO 210 240 T(K) /! 1 i :)70 ~ 300 ~"'-. (1976). (1954) and the specific heat of Lu for comparison.5 K Tb is ferromagnetic with the moments in the basal plane. This single ion interaction leads to phenomenally high magnetic anisotropy and giant magnetostriction.2 J/mole K which we obtained by using a ratio of Debye temperature of Gd to that for Lu of 0. This means that a q vector wave spans between 9 and 10 c-axis lattice parameters or about 20 layers. 26. / 30 60 90 Fig. Terbium The element Tb has atomic number 65. The magnetic entropy computed from this curve turns out to be S. The total orbital moment is therefore L = 3. the N~el point.~g = 17.3.5 K. Neutron diffraction measurements on Tb single crystals made by Koehler et al.5 K to 230 K. (1960).95 LUTETtUM--~ . Specific heat of Od as reported by Oriffe| et al.RARE EARTH METALS AND ALLOYS ! I I t I I I I I I I ) 219 60 50 4O GADOLINIUM Lu Gd 8D 6'o = 0.3 J/mole K for Gd. crystallizes in the hcp structure and has eight electrons in the 4f shell. The latter is from the work of Jennings et al.95. the spin S = 3 and Y = L + S = 6 making the spectroscopic designation 7F6. (1963) showed that the magnetic moments formed a helical structure in the temperature interval from 219. The theoretical value Sm~ = R ln(2S+ 1) = 17. This orientation of the moments in Tb is not surprising in view ol Coulomb repulsion associated with the toroid like charge distribution for the 4f electron of angular momentum L = 3. if it followed the S(S + 1) factor. I t ¢ I I ! I I 230 I. . ! I ! I I i I .0/. 27 and is smooth while the one at 500 Oe shows a slight kink around the N6el point. This is also true for other heavy rare earth single crystals. The stability of the helical structure is tenuous on the basis of these and other observations including the very narrow temperature range over which the phase exists. i i I t ! 400 Tb b-AXIS CRYSTAL I ' I I00 so i . was found by Roeland et al.48/~. In this case it marks the onset of the helical magnetic structure as the temperature is lowered.42/~B if the moment scaled according to the de Gennes factor or 0.63/~a for Gd." I .tB shown in table 2. 27. Since neither one seems to fit it must be assumed that the higher atomic number or the addition of 4f orbital moment causes a decrease in the local 5d conduction I I ~ i . In an applied field of 50 Oe the magnetic moment versus temperature shows a sharp peak in the vicinity of 230 K which is typical of a N6el point marking the change from paramagnetism to antiferromagnetism.34/~a compared with the expected gJ of 9. Isofield magnetization data for the b-axis crystal of Tb as found by Hegland et al. Isofield magnetization data obtained by Hegland et al. Below 219. The same surplus moment of 0.5 K the isofield data show ferromagnetic behavior with the moment rising at low temperatures.0 80 120 160 200 II o I 240 980 ~90 ~0 O T(I~ Fig. The surplus is attributed to conduction band polarization and is down considerably from the 0. 27..tB.I. (1975a). T) versus T with T-~ 0) comes out to be 9. The saturation magnetic moment found by the usual high field-low temperature extrapolation method tr(H.2~ S.34/.. The isofield data at this field is shown in the insert of fig. The critical external field required to suppress the helical phase in Tb is about 800 Oe. T) versus 1/H with 1/H-~ 0 for several isotherms followed by tr(o0. One might expect at least 0. (1963). LEGVOLD field required to magnetize Tb in the c direction is of the order of a million to ten million oersteds and one must not be surprised if single crystal samples leave their moorings or suddenly suffer recrystallization in the presence of strong fields along the c direction. (1963) in the easy b-axis direction are shown in fig. ~='" tO 05-'_ "H/'~ o I ~ l I . (1963). T data of Hegland et al. (1977b).0' TERBIUM _ ~ c-o=is O p = S g ' ~ ' - . (1963).77/~B which is slightly higher than the theoretical 9. In the case of Tb the susceptibility in the basal plane is higher than that along the c-axis as can be seen in fig. We have subtracted the phonon part to obtain the spin disorder resistivities which are shown as the dashed curves. (The mhch higher field needed here to suppress the helical structure as compared to the 800 Oe field mentioned I I I I I I I I I I I I I I I I I I 4. T) lines are parallel and the paramagnetic moment found is 9. The dramatic effect of an external magnetic field in the easy b-axis direction on the electrical resistivity along the c-axis is shown in the insert. l I .RARE EARTH METALS AND ALLOYS 221 electron wave function overlap with the 4f wave functions. There is also the possibility that 4f orbital moment in Tb brings about a decrease in the 4f-5d interaction when compared with the spin only 4f band of Gd. (1963). 29. Their results are shown in fig. The electrical resistivities of single crystals of Tb have been reported by Hegland et al. One of the outstanding differences between Tb and Gd is found in the anisotropy of the paramagnetic susceptibility. 28.. The external field suppresses the helical phase and eliminates the superzone energy gaps near the N6el point...70~B.. The importance of this overlap was seen in the suppression of superconductivity of La by Legvold et al. The reciprocal of the paramagnetic susceptibility of a-. and c-axis samples of Tb versus temperature as published by Hegland et al.f o . In the insert the c-axis data near the N6el point are shown on an enlarged scale.0' 200 Z40 ZSO 3ZOToi300400 440 480 520 Fig. I i I °~=}0p=259. The general decrease of the 5d band electron population across the rare earths has been described by Duthie and Pettifor (1977) and also by Lindg~rd (1977) who has pursued the theory of rare earth alloys.2 4G 3~ 3G 2. There are thus two paramagnetic Curie temperatures for Tb. i _ 0. The high temperature (llx vs. Along the c-axis 0p = 195 K and in the basal plane the susceptibility is the same along the b-axis as along the a-axis and 0p = 239 K. The physical basis for two ordering temperatures has been discussed by Kasuya (1966) who proposed the crystal fields are responsible. 28 which shows the 1/X vs. ~. b-. This is contrasted with the isotropic character of the susceptibility of Gd single crystals above the Curie point. I.K I I . . Single ion anisotropy has been discussed by Rhyne (1972). .'tO00E ./" 0 0 20 60 I00 140 "r(K) Fig. Magnetization calculations for Dy by Niira (1960) involved such an energy gap. I I I I I I I I I 180 P. the theoretical S = R ln(2J + 1) is 21. As shown in the figure the ratio of the Debye temperature for Tb to that of Lu used to obtain the good fit to theory was 0.) The resistivity below 40 K displays some anomalies which have been discussed by Mackintosh (1963) who related this behavior to a spin wave energy gap in Tb. Pc-spin 5c . The dashed curves are the spin only resistivities. .20 260 300 340 earlier is the result of widely differing demagnetizing fields related to the different sample geometries. . Jennings et al. (1957) made measurements over a wide temperature range and their data are shown in fig.93. I# E 70 A H= ZERO / .5 to 16 K has been reported by Wells et al. There appears to be a shoulder on the curve just above 219. The specific heat of Tb from 1.5 K corresponding to 0c and a characteristic sharp peak at 228 K corresponding to the N6el temperature. LEGVOLD I L I I I I I I ! I I_ ~XIS.2 K in the lower branch for q = 0 at F.) The peak in the c-axis resistivity associated with the onset of magnetically induced energy gaps is very much like that in Eu near its N~el point.c H= 6. the center of the Brillouin zone. 30 for Tb.Y" "-. (1976).9 meV. . 31. some of this is surely present above the N~el point in Tb also. (The broad c-axis peak near Tc in Gd is generally attributed to short range order-disorder fluctuations. The entropy computed from the dashed curve comes out to be 21. (1969) and by Nellis and Legvold (1969) confirm the q = 0 spin wave energy gap and give a gap width of 1. .. The electrical resistivityof a.0 J/mole K. Inelastic neutron scattering data have been reviewed by Mackintosh and MOiler (1972) and they show the magnon dispersion curves of fig. More recent resistivity measurements on higher purity single crystals by Sze et al.222 13C _IIC~ I I II I 'A~ I S. ..3 I/mole K which does not include an allowance for conduction electron polarization. .and c-axis crystals of I"o versus temperature as reported by Hegland et al."/. 29. The energy gap of 2 meV is seen at 4. We have subtracted off the phonon and electron parts and show the magnetic part of the heat capacity as the dashed curve of the figure. (1963). 30. 30. Magnon dispersion curves for Tb along symmetry lines in the zone at 4.) d5 I" T K TM I I.~ I ~i" 60 80 I00 120 140 160 180 200 220 240 260 280 T(K) Fig. MK P 12.2 K (ferromagnetic curve gives the magnetic contribution. I X 20 J.///i t mole I I \'.5 r'A AA I' I I.OQ5 0 0 0.:o d5 ~_.13-r z~ J-t I i il 22o 2 ~ 2z4 t / ~ t #~ \ T(K) / ./'11 20 40 I i I i I i I // I .O 0 5 0 0.2 K (ferromagnetic phase).5 to w~l~ IA") Fig.~ Q5 I.O 70-TERBIUM Tb 80 . ~ f.RARE EARTH METALS A N D ALLOYS S H S A R LU 223 P. After Mackintosh and M¢ller (1972).Si. . I I I I I I I I' I I I I I IV I ii i / o-qi.. It 4 3 2 .oo 4. Magnon dispersion curves for Rb along symmetry lines in the zone at 4. The rapid rise of the moment below 100 K in the 2 kOe field marks the transition from the helical phase to the ferromagnetic phase. His a-axis isothermal magnetization data. The angle decreases with decreasing temperature down to 89 K at which it reaches 26. As the applied field increases the moment rises linearly until a critical field for that temperature is reached. as reported by Darnell (1963a. After Jew (1963).2~ S. taken in the temperature range where the helical structure is found. Below 89K Dy is ferromagnetic and the easy axis of magnetization is along an a-axis or (1120). Magnetization isotherms for the a-axis of ~ . Dysprosium The 4f shell of the element Dy. (1961) showed that the magnetic moments of Dy take on the helical structure below the 179 K Nrel point as described previously in fig. contains 9 electrons. atomic number 66. This makes J = L + S = ~ and the spectroscopic designation is 6H~5/2. LEGVOLD 2. Isofield data for the a-axis crystal from 90 K to 290 K are shown in fig. b). Magnetic measurements on single crystals of Dy have been made by Jew (1963). are displayed in fig. and the interlayer turn angle just below the ordering temperature is 43. 32.4. In applied magnetic fields below 10 kOe the sharp peaks in the magnetic moment versus temperature curves shown in the insert of the figure fix the Nrel point at 179 K. The helix axis is along c with the moments in the basal plane.5°. 33. i- I J J I I ~ I I I [ I I I i I I Z 4 6 O IO 12 14 H (KILO-OERSTEO) 16 19 20 Fig. Neutron diffraction results of Wilkinson et al. An applied field greater than 12 kOe clearly suppresses the helical structure. and then the moment rises sharply and ferromagnetic alignment is accomplished. 32. respectively. 20. and at low temperatures in the ferromagnetic state there is a small departure from this to orthorhombic. . We note the field required for this is considerably higher for Dy than for Tb where I I I I I I ! I I I I 0 I I I i I I I 70/ i ~ bo KX) TAI.2 °. there are 5 electrons with unpaired spins so S = ~ and 2 electrons with z projection orbital angular momentum quantum numbers m~ = 3 and 2. making L = 5. The room temperature crystal structure is hcp. .~ _ " t . 12-kOe IN 200 T (K) . The data for the a-axis crystal are rather prosaic when compared with the c-axis data which demonstrate the dramatic superzone effects at the ferro to helical transition at 89 K as well as in the vicinity of the N6el point. 33.2 equal 80 to get the saturation magnetic moment of 358 emu per gram.\ r T(K) .4$rB/atom higher than the gJ value of 10#a. the highest for any element and almost 1. . .4#a comes from 5d band polarization. . . Along the c-axis the data gave a paramagnetic Curie temperature of 121 K thus demonstrating large anisotropy.-Ax. The slopes of the Curie-Weiss lines gave a paramagnetic moment of 10.6 times that for iron (which has about the same density). ".o. The electrical resistivity of Dy as determined by Boys and Legvold (1968) on single crystals with resistivity ratios 24 along the a-axis and 13 along the c-axis is shown in fig. In the insert of the figure the data near the N6el point are shown and the manner in which the cusp for different fields may be extrapolated to zero field to get the N6el point. compared with the theoretical 10. 34. this result correlates well with the wider temperature span over which Dy has the helical structure as compared to the ten degree interval for Tb. . ~ . The c-axis resistivity calculated by Elliott and Wedgwood (1963) in the manner described earlier is shown as the dot--dash curve.s su ~ • . ... . The spin disorder resistivity as found by subtracting the phonon resistivities appears in the figure as 'the . Queen (1979) has used Dy of R3oo/R4.. Again the 0. Isofieid magnetization data for the easy a-axis of Dy as reported by Jew (1963). As in the case of Tb the susceptibility in the paramagnetic range along the b-axis was the same as that along the a-axis and the paramagnetic Curie temperature for both was 169 K. . . the critical field was less than 1 kOe. the general features are present but exaggerated in the theory. • 300 Fig.RARE EARTH METALS AND ALLOYS 1 225 I I 300 ~ \ Dy _ .64~B. this moment corresponds to 10. F I00 ' ~ ~ .83#.oo 1 I..---'''-~ 150 250 .4#Jatom which is 0. "'° - ~/. "~° 4° 30 iL / .. / / / / co-~!s . the curve at 98 K has a maximum at Q/qmax(see arrow) equal to about 0. .o . Spin wave dispersion in Dy has been investigated by inelastic neutron diffraction by Nicklow et al. . There is again a tail in the magnetic specific heat which extends above 179 K corresponding to short range ordering effects. . (1956) with results as shown in fig. ff"~'~L-o I10 j ~ ~ -AXIS " !~ ~ b o-. 120 160 200 TEMPERATURET (°K) . The large peak occurs at the 179 K N6el point with a smaller hump in evidence at the ferro-order to antiferro-order transition near 89 K. 36. . The effect of this gap shows up in the electrical resistivity at low temperatures as in the case of "lb. This demonstrates the significance of the generalized susceptibility X(q) and its relationship to the magnetic structure as discussed in the theory section. dashed curves..-. Hence. The spin only part in this case was obtained by assuming that Dy has the same Debye temperature as Lu.s . it is shown as the dashed curve. In fig. . .o 0 40 80 . . 240 0 . The dashed curves are the spin only resistivity and the dot-dash curve is the Elliott and Wedgewood (1963) theoretical curve. 35.. (1971a.17. 80! ~ a . The dashed curve yields a magnetic entropy of 22. b) and their results are shown in fig. which corresponds to a turn angle per layer in reasonably good agreement with the experimental finding. LEGVOLD foe D Y S P R ( ~ ' I U M 90. .. Quite the opposite is apparent in the c-axis direction. The specific heat of Dy was measured by Griffel et al. Electrical resistivity versus temperature for single crystals of Dy as reported by Boys and Legvold (1968).. a remarkable effect. / "t-. _ / ... 34. By comparing the resistivity jump at 89 K to the total magnetic resistivity we estimate that nearly 30% of the Fermi surface projected in the c direction is wiped out by the helical structure. 280 . . The sharp bend or knee in the a-axis resistivity marks the 179 K N6el point whereas there is only a barely detectable shift of the points at the 89 K ferromagnetic to antiferromagnetic transition. . Fig. 35b the Fourier transform of the exchange they obtained is shown. the Fermi surface area projections in the basal plane (a or b) directions are nearly unaffected by the onset of the superzones..... ..3 meV. .6 J/mole K . . . The data at 78 K in part (a) of the figure show an energy gap at q = 0 of 1.2~ S.x.// . . 0~ o 4.J O td o E-.- ~ ".. W O ~. 0 ~ ~ ~.RARE EARTH METALS A N D ALLOYS 227 o_. (^*"9 (o)r-Tb)r O < A E ~ I..IE T o O I s O o ~1" (Ae") eO Ag~I3N3 ~J -- 0 .:. o 9 ? 9 °! o 0 v e. ~ io e. The easy direction for Ho is along the b-axis and at 4.7ftB ferromagnetic component along the c-axis and with a basal plane component of 9.6 J/mole K I 140 i 160 II \ ~. The dashed curve is the magnetic contribution. 36. Particularly interesting are the three bends or knees seen in the curves at 49. 1967) showed that below the 132 K N~el point the magnetic moments lay in the basal plane and formed a spiral structure. S = ~ and to the spectroscopic state 5Is. 2. (1956). _ I 5O ~20D / ///~/ I 40 I 60 I 80 I I00 I 120 T.)0 240 ~/~1" " 20 I 180 Fig. (1966. Below 20 K the moments tilted out of the basal plane and formed a conical structure with a 1.2 K an external field will induce the full expected 10/~B in this direction. J = L + S = 8 = 6. 37. The angular dependence of the 4f wave function of fig.. Neutron diffraction work by Koehler et al.5/. according to Koehler et al. Specific heat of Dy as published by Griffel et ai. (1967).6 K and at 54.~8 70-I I I I S. This turns out to be the case. ~ ~--F-----I'--" 200 2. In the presence of an external field the magnetic phase diagram of Ho is extremely complex. (1962) are shown in fig. Results of isothermal magnetization measurements on a b-axis single crystal of Ho by Strandburg et al. which should be compared with the expected S = R ln(2J + 1) = R In 16 = 23.. Just below the N6el point the interlayer turn angle was 50°.~B in a distorted spiral so the half-cone angle was about 80°.5. H o l m i u m The element Ho has atomic number 67 and has 10 electrons in the 4f shell leading to L = ~ m t = 3 + 2 + l 7 .~3= 2 ... LEGVOLD I I I I I I I I DYSPROSIUM 60 Dy O.0 J/mole K.(K) //// Smog= 22. These come . As the temperature was lowered the turn angle decreased and at 20 K hit a low of 30°.8 K. 7 suggests that the three electrons beyond the half filled shell will begin to approach spherical symmetry and should show magnetic properties at least somewhat different from those of Dy and Tb. (1962).5"'1'~o.1e =19.. 6. then. 229 I 250 ~' 200 '150 IOC 50I~" I I ¢ 4. .8" 60.6#B expected. .o" Izr~ ° 1 50. This is six percent higher than the theoretical 10. The c-axis data in the insert show a relatively sharp rise in moment at the onset of the conical ferromagnetic phase which sets in at temperatures higher than 20 K when a field is applied along c.870. Magnetic susceptibility measurements on Ho at high temperatures have been reported by St. i. Isofield data for b. In the case of Ho.and a-axis crystals and with 0p equal to 73 K for the c-axis crystal.RARE EARTH METALS AND ALLOYS 35c ~ . (The fan structures involved are like those shown in fig. we have a saturation moment 0. the sample remains magnetized in the basal plane. 38. The small cusps in the b-axis data near 132 K identify the N6el point.3e ~5.2 K along the a-axis was 8.) The dashed curve of fig. The paramagnetic moment was 11.2 K shows hysteresis and remanence when the field is decreased. M a g n e t i z a t i o n isotherms f o r single crystal H o along the b-axis as published b y Strandburg et al. particularly for the 16 kOe b-axis data. The fan structure effect is observable in this figure also. For the c-axis the initial magnetization below 20 K was about 1.e. indicating that some conduction electron polarization persists into the paramagnetic regime. which is exactly cos 30° times the saturation moment of 10. -.34#B found along the b-axis.1" I 2~2"1 J -re.2#s/atom for all three crystals.34#8 larger than the expected gJ of 10#B and the surplus represents the polarization of the 5d conduction band electrons. about because the magnetic moments jump from one set of easy b-axis directions or fan structure in the presence of the field to the next set of easy directions or fan structure closer to the field direction.7#B which is in good agreement with the neutron diffraction finding. In the paramagnetic range the l/x versus T plots showed anisotropy with 0p equal to 88 K for the b. 37. The saturation magnetic moment at 4. 37 at 4.K_ 5 H(KILO-OERSTEDS) IO H ALONG b-AXIS 15 Fig.95#a.and c-axis crystals are shown in fig. 54. This means that the moments stay along the b-axis even in the presence of a field along the a-axis and demonstrates anisotropy in the basal plane. I 50__1.230 1 ! I I S.22.S cRY. We note there is no energy gap at q = 0 for the helical phase and there is a maximum in ~ ( q ) . and their findings are shown in fig.'~\\\\'. . I0 i I0 i 30 50 70 90 . 39.~. confirming the helical ordering.A X i S CRYSTAL .. The electrical resistivity of Ho single crystals has been reported by Strandberg et al. Of particular interest here is the substantial difference between the a-axis and c-axis spin wave only resistivity above 132 K. (1962) and by Nellis and Legvold (1969).-o. Isofielddata for singlecrystalHo along b. The a-axis resistivity typically changes slope at the N6el point and the c-axis resistivity has a broad hump below the N6el point. The results of the two sets of measurements are in substantial agreement. The dashed curves are the spin wave only resistivity curves and the dot-dash curve is the result of the Elliott and • Wedgewood (1963) theory for the c-axis resistivity.[[ C-AX.0¢(0) at q/qm~of about 0.ooo . 38. only a small disturbance was noticeable along the c-axis at 20 K where the conical phase forms. 40.__1 ) b . which gives the projection along an a-axis. . Quinton (1973).2 K for Ho with 10% Tb added to preserve the planar ferromagnetic structure has been reported by Mackintosh and M~ller (1972). by Kirchmayer and Schindl (1966). the trunk part. in this case the fit is rather good. We show the results of the former in fig. has diminished in size and this decrease continues to be the case across the rest of the heavy rare earths.and c-axis as reported by Strandburget al.-I-t ~ 150 I00 i10 ' 0 20 40 L 60 80 I00 T(I~ 120 140 160 _ 180 Fig. J - - __I- I L~ \ ~-sol-~\\\\\ 5 81" I'~ ~ ~ 5ol. Coupling of spin waves to giga-Hertz radiation has been studied by Akhavan and Blackstead (1976). (1962). and by Arajs and Miller (1960). It is a manifestation of a sizeable change from Tb and Dy in the Fermi surface geometry. so the behavior is much like that for Dy. LEGVOLD I I I I I I I I I I I I-- = fHo 300 250 '~'200 ~. It is seen that at q = 0 there is a spin wave energy gap of the type found in Tb and Dy. by Chechernikov (1962). Dispersion and o~(q)o~(0) curves for Ho in the helical phase are shown in fig. Spin wave dispersion at 4. 41. . versus temperature for Ho single crystals as measured by Strandburg et al. residual subtracted.REs =3.. Magnon dispersion curve at 4..s. o-Ax.. .2 0 60 I00 140 180 2ZO Z 6 0 300 T°K Fig. . 5-- o Q -- ~4 g g 0 RSOUCEO. 40.. .. A v ~ v s c ~ ~/o~=l G2 I (14 I (16 I O~ I LO Fig. 39.c .A ~ . .2 K for Ho-10% Tb as reported by Mackintosh and M¢ller (1972).~o. = . . .. ~:£x~ 2_2 . ...RARE EARTH METALS AND ALLOYS I10 I00 •. ° " - a. ~ ~ 8o Q~4G .. 9 0 ~ 7G 231 E HO i = . The dashed curves are the spin only contribution to the resistivity. ... 20 I0 L /f/'. The dot-dash curve is the resistivity calculated for the c-axis by Elliott and Wedgewood (1963). . . . . i i .-.. . (1962).. . i i i .o ./'~'------ q) . 30 g 6o ~ 50 ~-Ax~ :. Electrical resistivity. . 3 \\ ---/- i ~..99 5(: 2 o~ sc 20 40 60 80 100 120 T(K) . The entropy computed from the dashed curve gives a spin wave component of 23. -0. Gerstein et al.2 I 0.S I 1.---IId0 160 180 200 220 I 240 Fig.5 0 "~1/~ 0. (1957). LEGVOLD 0.4 I 0.~ll~ Ho 78K ~.6 I O. I 6C I I I I I I l | I I I I HOLMIUM He eo Lu 8o = 0.. with results as shown in fig.232 I i I I S..99 times that for Lu." f " ~ .4 -0.8 J/mole K. There is a very small peak at the 20 K conical ferro to helical transformation temperature and a very large peak at 130 K which is close to the N6el point. Magnon dispersion curves and o~(q).0 -0.6 J/mole K.. and was obtained by use of a Debye temperature for He of 0.8 I t I.. 42. (1971a).2 ~4 0.2 Ho 50K 'S ~' -0. .6 0 ' 0..1 ' I i i I I 0 / -0. (1957) measured the heat capacity of He. 41..T .I A 4 -o. The theoretical value of He is R In 17 equal to 23. The spin wave part is shown as the dashed curve of the figure.o Reduced wavevector(q/qmax) Reduced wavevector(qlqmax) Fig..I -.~(0) in the c direction for the helical phases of He as reported by Nicklow (1971) and by Nicklow et al.6 I 0. Specific heat of He as measured by Gerstein et al. 42. The dashed curve is the magnetic contribution to the specific heat. S = ~ and J = L + S = ~.6/zB and the basal plane c o m p o n e n t is 4. There is the usual shift of TN to lower temperatures at the higher fields as well as a shift of the ferromagnetic state to higher temperatures in the applied field. 43. It is a peculiar structure for which several atomic layers having c c o m p o n e n t s up (cones open upward) are followed by an equal number of atomic layers having c-axis c o m p o n e n t s down (cones open downward).6. .~ = : _200 E ~'20 i i~ 15o IOO 3 K-OI 9 7K. The c-axis c o m p o n e n t at 4. (1974). 20. 8 0 T K 90 50 o 0 I I0 I 20 30 40 50 60 70 80 90 I00 I10 T (K) Fig. (1965).2 K is 7. The crystal structure is hcp. Erbium The spectroscopic designation for Er. atomic n u m b e r 68.3/~B. and by Atoji (1974) it has been established that the magnetic structure of E r is quite complex. It is also found that the basal plane c o m p o n e n t remains random. The onset of antiferromagnetism is characterized by the usual cusp which is seen at 85 K in the low field curve. The quantum numbers are then L = 6. Magnetic measurements on a c-axis single crystal of Er by Green et al.RARE EARTH METALS AND ALLOYS 233 2. At 53 K a squaring off of the c-axis c o m p o n e n t wave modulation takes place and the basal plane c o m p o n e n t is found to order helically as shown in fig.0/zB. which is the e x p e c t e d full gJ value for Er. is 411512since it has four 4f electrons b e y o n d the half full shell of Gd. A plot of the critical field required to 300 / 9~. This structure changes f r o m an incommensurate to c o m m e n s u r a t e form at 35 K and then transforms to conical ferromagnetism below 20 K. an applied field favors the ferromagnetic state. (1961) yielded isofield data as shown in fig.e v I I I I I i i | ERBIUM C-AXIS CRYSTAL 250 . As the temperature of E r is lowered the c o m p o n e n t of the magnetic m o m e n t along the c-axis becomes ordered at 85 K in a sinusoidal manner with the q vector along the c-axis. 43. by Habenschuss et al. O. (1961). F r o m neutron diffraction studies by Cable et al. making the half cone angle about 30° and giving a total of 9. This may be described as a quasi anti-phase domain structure.Oe I0 . Isofieid magnetization data for a c-axis crystal of Er as reported by Green et al. this is called the c-axis modulated (CAM) structure. 60 t 20 / 40 / 80 IOO 120 140 160 T (K) Fig. . In the hard basal plane direction there was one jump to a fan structure at about 17 kOe followed by a less rapid change in moment with field until about 120 kOe was reached when another relatively sharp rise took place but the applied field was not high enough for saturation to occur.. if the c-axis data of Rhyne et al.... (1968) at 4... and this is reasonable. LEGVOLD bring about ferromagnetic ordering at different temperatures is extrapolated to zero field to get about 19 K for the spontaneous ferromagnetic ordering temperature. The onset of the modulated c-axis moment causes a sharp break in the curve at 85 K.. The c-axis data reflect the magnetic ordering phenomena beautifully. (1968) are extrapolated to H =o0 (1/H =0) a saturation moment of 9. The magnetic moment of Er single crystals was measured by Rhyne et al.2~ S.. which is a little higher than the theoretical 9. which marks the onset of the squared-up 60 50 Erbium ~ /~--:"~ _ _ /Pb-spin ~ ~'b-AXlS i ~4o ~30 C-AXIS Theory ~ _ l///. In general there is some thermal hysteresis in this order-order transition so it is difficult to pinpoint the transition temperature.° . It may be concluded that some conduction electron polarization is indeed manifested in Er just as in the other heavy rare earth metals...... Their results showed that in the easy c-axis direction there was an initial sharp rise at low applied field up to 8~B followed by a very gradual rise to almost 9/~B at an applied field of 130 kOe..2 K in a field ranging up to 150 kOe. (1961) also demonstrated anisotropy in the 1/X versus T plots which gave 0p of 32.. Other such calculations have been made by Southern and Sherrington (1974)... \Po .5 K along the a-axis and 61. Electrical resistivity results on single crystal Er by Boys and Legvold (1968) are shown in fig.. Then as the temperature decreases a rapid rise in the resistivity continues down to 35 K.......1/zn is found. Electrical resistivity of single crystal Er versus temperature as determined by Boys and Legvold (1968). These data demonstrate the strong anisotropy of Er which has foiled attempts to obtain the saturation moment..__: . 44..6/tB for Er..7 K along the c-axis while the paramagnetic moment was the same for both crystals at 9.9/~B. The high temperature measurements of Green et al..I '° 0 ... 44.. Jensen (1976) has made a five parameter molecular field calculation for Er to explain its magnetic behavior. The dashed curves are the spin only resistivity and the dot-dash curve is the c-axis resistivity calculated by Elliott and Wedgewood (|963).. However. . There is no spin wave energy gap at q = 0 and there are two branches. I" 1.q FIT WITH EXCHANGE PLUS CONSTANT AN ISOTROPY FIT WITH EXCHANGE PLUS WAVE-VECTOR 7/. The data for the latter show a maximum in energy at a reduced wave vector q/qm~. Their results for the conical phase are shown in fig.0 ! . 45.. (1971b).6 REDUCED WAVE VECTOR (2~r/c) fill 0. Spin wave dispersion in the c-axis direction for Er has been reported by Nicklow et al. another small peak at the 52 K helical ordering temperature and a large peak at the 86 K N~el point. a second small peak at 35 K where the moment squares up./ .75.q . Magnon dispersion curves in the c direction of the cone magnetic phase of Er reported by Nicidow et al.1 J/mole K. (1971b). A .--"i / t / 2"/ / " OATA . one for +q and one for . DATA F O R .0 Xx\ 5.0 A > /. 45. The rapid drop in resistivity at 20 K marks the onset of ferromagnetism and the disappearance of superzone effects on the Fermi surface.. Z Q. The magnon specific heat is shown as the dashed curve and the entropy computed from the curve yields a magnetic portion of 22J/mole K. it again exaggerates the effect of the magnetic moment structure change at 20 K on the resistivity.2 0.0 Fig. 46.f / Y E >w W 2. . The fit of Elliott and Wedgewood (1963) calculation for the c-axis is shown by the dot-dash curve.0 ". even though a Debye temperature for Er which 4. The specific heat of Er according to work of Skochdopole et al.8 1. of 0. There is a small peak at the 20 K order-order transition.OR .0 DEPENDENT ANISOTROPY 0.4 0. which is smaller than the R ln(2J + 1) of 23..RARE EARTH METALS AND ALLOYS 235 c-axis magnetic moment modulation and the helical basal plane structure. (1955) is found in fig. 2 b oY/'. 47. 20.05 Lue. (1970). (1955). Several neutron diffraction studies have been made on single crystals of Tm.2 K turns out .. Since the ionic moment is 7t~B this leaves a net of 1~8 in the c-axis direction for each seven layer period. was 5 percent higher than that for Lu was used. It did not seem realistic to go to a higher Debye temperature to get a better fit. LEGVOLD I I I I I I I I ERBIUM 5(: 4C Er 0o . The odd feature for Tm is its combined antiphase domain-ferrimagnetic structure below 32 K which consists of four moments pointing up along c followed by three moments pointing down.7. The dashed curve is the magnetic portion. Specific heat of Er as measured by Skochdopole et al. The pattern is shown in fig. the N6el point. with a sinusoidal variation of the magnitude just as in Er. Magnetic moment measurements in fields up to 95 kOe on Tm single crystals have been reported by Richards and Legvold (1969).' ~ / I0 I 20 I 30 I 40 " I 50 I 60 T(K) I 70 I 80 '. ~T--7---1---t-~ 90 I00 I10 t 120 Fig.= 1. (1962) was followed by investigations on more pure samples by Brun and Lander (1969) and by B r u n e t al. In fields above 30 kOe the sinusoidal modulation of the moments disappears and a ferromagnetic ordering only takes place./. 2. and the magnetic moment at 4. The characteristic cusps in the low field data mark the N6el point at 58 K. The spectroscopic designation for the ion is 3H6 sinceL=5.236 I I I I S. S=landJ=L+S=6. ~o 2C . 46. The q vector just below 58 K is incommensurate with the ionic lattice but becomes commensurate with a seven layer-period below 32 K.o . The c-axis component of the magnetic moment becomes ordered below 58 K. There is also a squaring up of the sinusoidal structure between 40 K and 32 K before the seven layer pattern sets in. Thulium There are 12 electrons (two holes) in the 4f shell of Tm so there are two electrons with unpaired spin.. Early work by Koehler et al. In low applied fields along the easy c-axis direction there is a rise in the magnetic moment for T below 32 K marking the onset of the ferrimagnetic phase. Their isofield data appear in fig. The inverse susceptibility versus temperature in the paramagnetic range for Tm single crystals as given by Richards and Legvold (1969)..O-OERSTEO u 40.1 7 K and a paramagnetic Curie point along the c-axis of 41 K showing anisotropy which. 2. 60 0 j 20 to be lftB. The usual knee in the basal plane resistivity.0 / / 0 ~ I I I~" I I I I I I I I I I 120 160 200 240 T (K) Fig.14/t. Dy.6/~B.RARE EARTH METALS AND ALLOYS I I I I I I I I 237 240 220 2O0 180 160 140 ~ A Tm c-AXIS -. The slopes were nearly identical and gave a paramagnetic moment of 7. 0 40 80 . 48 gave a paramagnetic Curie point along the b-axis of .EO FE' S 3tt\ \ \ ~t o 13.1 KLO-OERSTED ~ 120 "~100 SO 60 40 2O I00 140 IBO T (K) Fig.~o ~. and Ho..56/~B expected. 47. In high fields at 4.55KILO-OERSTED .2 K the saturation moment is 7. 49. is reversed from Tb. Their 1/X versus T plots as shown in fig. I I I I | I I I I I I i ~eff=2le3 ~ 4. to be compared with the 7. like Er. in excellent agreement with the neutron diffraction result. which proves to be about the most reliable method for finding the N6el point. The electrical resistivities of Tm single crystals reported by Edwards and Legvold (1968) are shown in fig. lsofield magnetization data for a c-axis crystal of Tm as reported by Richards and Legvold (1969). which is higher than the gJ value of 7ftB for Tm giving evidence again for conduction electron polarization. 48. .. The magnetic part of the specific heat is shown as the dashed curve. occurs at 58 K. ~b-AXI S :50 :L c-AXiS Theory / // %20 / . The shape is proper but the size is exaggerated. The Debye temperature used to determine the magnetic specific heat was 0.4J/mole K which comes close to the R ln(2J + 1) for Tm of 21. i I i Iz I~ I~'< --I "t I I 0 I0 20 30 40 50 60 70 T (K) 80 90 I00 I10 120 Fig. 50.238 I I I I S.. {/. 18 and discussed in the theory section. rb-Spin . Electrical resistivity versus temperature for single crystals of Tm as measured by Edwards and Legvoid (1968). there was a very noticeable spike at this temperature in Seebeck coefficient measurements of Edwards and Legvold (1968) on the c-axis sample. Their findings are shown in fig.. the N~el point. LEGVOLD I I I I I I ~ I 40 Thulium . 51) showing the surplus magnetic moment plotted against S(S + 1) and ..985 times the Debye temperature of Lu.. / / ! 1 i ./. It may be seen in the figure that any effect near 32 K is masked by the main magnetic specific heat peak near 58 K.j.cs. I0 .. This was the first evidence for the 32 K commensurate to incommensurate transition in Tm and is a nice illustration of the high sensitivity of such measurements relative to magnetic and Fermi surface phenomena. In neither resistivity curve is the 32 K onset of the ferrimagnetic commensurate c-axis modulation observable. 49.... This section on the high magnetic moment rare earths is concluded with a g r a p h (fig... Spin dispersion data for Tm have not been obtained. i ./ / ÷~-+7"÷ / / " . The dashed curve shows the result and gives an entropy of 21. (1961).3 J/mole K.. The specific heat of the metal has been reported by Jennings et al.. The c-axis resistivity reveals the very dramatic effect of the modulated magnetic moment along the c-axis. 0 ./. //I. The fit of the c-axis resistivity calculated from the theory of Elliott and Wedgewood (1963) is shown by the dot-dash curve of the figure. However.. / I \ I i .~ . It shows up as a pronounced bump just below the N~el point. This is the superzone effect on the Fermi surface of Tm shown in fig. the magnetic properties of the light elements differ from the h e a v y elements in several ways./////////////////////Srrlng : 2. 3. . . .4 J/mole K ' " . Magnetic moment in excess of the theoretical gJ value vs the spin factors ( g .5 "~ 0 .1 0 2 4 6 8 I0 12 S(S+I) or (g-I) z J(J+l) 14 16 Fig. ~A"~" I -I I I I I I I0 20 30 40 50 60 70 80 T(K) Fig. I I 2 I I I I I I 0. The crystal structures o f the light elements f a v o r the dhcp f o r m with fcc appearing when samples are quenched from higher tern- . against the de G e n n e s f a c t o r which one might e x p e c t the surplus m o m e n t as well as the highest magnetic ordering temperature to follow. 3 0 In b 0. 4 c 0 tO x (g-I) J(J+l) v S(S÷I) Gd xDY / x v ~//7 x v '~ 0 .RARE EARTH METALS AND ALLOYS I I I I I I I I I I I I 239 L 50 THULIUM Tm Oo Lu "'co = 0.l)'J(J + 1) and S(S + 1). (1961). W e see that the value for Tb is much too low so some other f a c t o r plays a role in this matter. . 50. The dashed curve is the magnetic part.2 <3 0. t / I -. .985 _° 2C /~// I IC //// ~. Pr. 51. Magnetic properties of Ce.. . Pm and Sm Briefly. Specific heat of Tm as measured by Jennings et al.6 _ 0. . .T'----'F'----T'-I 90 I00 I10 120 -'l . Nd. . which is radioactive. has been found to have the dhcp crystal structure and there is a slight hint some type of magnetic ordering may take place around 90 K. It is normally expected that one electron will be in the 4f state for which the spectroscopic designation is 2F~/2 with L = 3. The element Pm. that the presence of cubic sites and hexagonal sites in the dhcp and Sm structures can be quite significant in the magnetic ordering process. the dhcp (/3) form is also paramagnetic but shows two ordering temperatures of 13. The atomic number for Ce is 58 and the 4f level turns out to be very close to the Fermi level so that valence fluctuations can occur. It is therefore anticipated that low ordering temperatures and very complex magnetic structures will occur because all of the effects just listed are intermixed.8 and 12. one at 19. 3. paramagnetism. there is evidence for a N6el point at 106 K with an additional transition of the N6el type at 14 K. a valence variation from 4 down to 3. The condensed fee (a) form shows a nearly constant paramagnetic susceptibility. another very significant difference is found in the total quantum number J which is given by J = L .5 K. The fee allotrope of Nd is ferromagnetic with a Tc of 29 K.4 K.9 K and the other at 7. but specific heat measurements show that the complete story will likely be more complicated.S = 2. In the case of Sm there is the special nine layer structure which now bears the name of the dement.S for the light elements and this leads to very weak exchange interactions when compared with the heavies which have high moments and strong exchange effects. The physical properties of Ce have been reviewed by Gschneidner in the book edited by Parks (1977). for example. It is found.240 S. In the case of Sm. It is the only element which has both superconducting and magnetically ordered phases and the only solid known to have a critical point. As will be seen some features of the magnetic ordering in the light metals are just now emerging. Finally. A very brief description of the individual elements follows: The fcc (y) form of Ce is paramagnetic down to a N6el point of 14. In the latter case external fields can induce magnetic moments. It seems that one could spend a lifetime exploring cerium's ramifications.L .1. Cerium In a word the element Ce is phenomenal-it exhibits at least five crystal structures. and superconductivity. antiferromagnetism. the relative strengths of the crystal fields to the exchange fields are much greater for the light elements because of the L S coupling they display. When the 4f electron migrates to the conduction band (it is . Neutron diffraction measurements have shown that dhcp Nd has two antiferromagnetic ordering temperatures. and there is also a complication at very low temperatures because nuclear magnetic ordering occurs. which has the nine layer ABABCBCAC structure.5 K. LEGVOLD peratures.. In the case of Pr the fee allotrope is ferromagnetic with a Curie point of 8. diamagnetism. From the magnetic viewpoint.7 K while the stable dhcp form is the outstanding example of crystal field effects because it is now quite certain that pure samples of the metal take on the singlet configuration. S =-~ and Y . apparently no other solid has this feature. At high temperatures the stable structure is bcc (6 from) with fcc (3' form) the stable allotrope from 1000 down to 350 K. (2 I o. Returning to the behavior of Ce at 1 atm pressure it is found that for slowly decreasing temperatures. At pressures beyond 50 kbar Ce takes on the or' phase and the 4f level occupancy is near zero. hence to preserve the dhcp form the 15 to 60K regime must be traversed rapidly. . At low temperatures the collapsed fcc' (a form) is stable. Indeed. Quickly cooled samples will remain dhcp at 4. samples which are initially in the /3 form at room temperature collapse to the ot form at about 50 K.4 electron/atom.6oo C.2 K and upon slow warming will transform to ot at about 18 K. A very sluggish transformation to the dhcp (/3 form) is indicated by the dashed phase boundary lines. this phase is superconducting. The dhcp form is stable from 350 down to about 100 K. For the phase transitions which are sluggish the dashed lines are the average of several observations. Temperature-pressure phase diagram for Ce. Next it is seen that at 1 atm pressure several crystal structures are encountered.RARE EARTH METALS AND ALLOYS 241 believed about 0. PRESSURE. After Koskenmaki and Gschneidner (1978). The most remarkable feature in the diagram is the appearance of a critical point at 20 atm and about 580 K. use of rapid sample cooling to 4. GPo (lOkb) Fig.P ~ 500 400 300 200 I00 .67 electron/atom actually moves) the element must be treated as a tetravalent m e t a l .see the discussion of theory later on.2 K followed by rapid warming to room temperature and lengthy annealing at 350 K leads to t h e growing of the I100 I000 900 800 700 1 I I I I I I ~. 52. the volume is about 12% smaller for this phase and the 4f level occupancy is about 0. 52. Any discussion of Ce must begin with the phase diagram shown in fig. l ~ 20 2 DAY COOL. The data in the insert show the onset of antiferromagnetic ordering at the 12. . Electrical resistivity versus temperature of fl Ce and T Ce for samples cooled from 298 to 4. The addition of 5at. Warm up times were comparably short. L E G V O L D dhcp allotrope. The two ordering temperatures which appear at low La concentrations are associated with the dhcp form and are 12.% 50 I I I IO0 150 200 TEMPERATURE.~2 S. 56. I I IOO 150 2 0 0 2 5 0 T (K) Fig.2 K in five minutes.7 K. They conjectured that the moments on the hexagonal sites became 90 8O I I I I I . -co \ dhcp e. coo -oo I 300 ! otl /' I '/ I0 0 0 J-. 53 the data for slow cool down and warm up show that y has a lower resistivity at room temperature. If one starts at room temperature and follows the cool down-warm up cycle one sees the 3' to a back to y (plus a little/3) transitions and the /3 to mixed /3 and ot back to mixed /~ and y (mostly /3) at room temperature.1411 . 55.7 K. (1976) were able to obtain magnetic susceptibility data for/3 Ce which is shown in fig. (1976). b) and extensive studies of Ce-La alloys by Petersen et al. In fig. Electrical resistivity versus temperature of/3 Ce and y Ce for samples cooled down over a 2 day period and warmed up over 1. The data of Petersen et al. Fig. After Burgardt et al. (1976). K I 250 300 IOIy/~ 0 I 50 .J ~7 3 0 0 N u.. 54 the data obtained with rapid cool down and warm up reveal the stability of the dhcp allotrope and the manner in which y transforms upon cooling to a and then relaxes back to mixed fl and y upon warming up to room temperature. 54. (1978a) have shown that there is an additional ordering temperature at 13. (1978) are shown in fig. All of these observations are substantiated in figs. Specific heat measurements on /3 Ce by Tsang et al. _/. In fig. 54 has been explained in terms of the Kondo effect by Liu et al.5 days. 53 and 54 which show resistivity observations reported by Burgardt et al. (1976)..5 and 13. After the procedures for preserving/3 Ce had been established Burgardt et al.. At the higher La concentrations their samples contained some of the fcc phase which accounted for the third (upper) ordering temperature shown in the figure..5 K N6el point.% of La will preserve the dhcp allotrope once it has been formed. The remarkable resistivity of/3 Ce given in fig.DOWN 3°III // "~ . (1976a./" ~ 50 w a: 40 . (1976)./ _^1 E o 70 c~ ~ 60 p-Ce clhcp' ~ ~ . After Burgardt et al. 53. ~ .....54/.~" ~'^ I 50 ) I00 .SUSCEPTIBILITY Cub. 56.#. b). After Petersen et al.F" ~. COOLING 1 FARADAY o WARMING # RIG • COOLING t FONER i v WARMINGJ RIG ec SUSCEPTIBILITY t I I I 150 200 250 300 350 T(K) Fig.5 K by analogy with the magnetic ordering first reported for Nd. (1978a.7 K and that the moments on the cubic sites became ordered at 12. The fcc (y) phase of Ce has been investigated by Bates et al..o~. The insert shows the details near the N6ei temperature.4 0 K. If the linear portion of the 1IX versus T plot is extrapolated to the abscissa the paramagnetic Curie point found is . ordered at 13.~B....o ~--~. 55 yielded an effective Bohr magneton number /~eft of 2.RARE EARTH METALS AND ALLOYS 243 j - ~"o 2vn I0 O J~"" . O-0 Ce ' I i I i I J_ I i 20 40 60 80 LA CONCENTRATION (a/o) I O0 La Fig. ~6 i I i I ' I i I ' 14 ~ "" ~ • . This view is suspect because the most recent neutron diffraction findings on Nd by Bak and Lebech (1978) show small ordered moments appear on the cubic sites at the time that considerably larger moments become ordered on the hexagonal sites. (1976). c / " "~ \ ~."~. After Burgardt et al. The high temperature slope of the I/X versus T curve of fig. 55.. Magnetic ordering temperatures of Ce-La alloys. • HEAT CAPACITY RESISTIVITY • I2 . (1955) and their .61/~B to be compared with the expected 2.. The reciprocal of the magnetic susceptibility of fl Ce versus temperature. and the samples showed no evidence of/3 Ce contamination because the data show no anomaly at 12. the upper ordering temperatures (marked fcc) of fig. They conjectured that this was a case of exchange enhanced susceptibility. 80 I 90 K t I00 t UO I 120 t 130 t 140 150 TEMPERATURE. There is no evidence of magnetic ordering in the temperature range covered.6 0 I I0 I 20 I 30 I 40 I 50 I 60 I 70 . This suggests a high density of states at 4 . 57. mentioned earlier. The heat capacity results of Tsang et aL (1976a. It was their appraisal that their sample was single phase a Ce and that the rather rapid rise in the susceptibility below 15 K was not attributable to magnetic impurities.0 f ~ 3. 55. From a Cp/T versus T 2 plot it was found that the electronic specific heat constant was 12.2 o 4.4 K at zero La concentration so this gives a good estimate of the behavior of pure y Ce.8 (.7 K.8mJ/g atom K 2.9 X 3. one of the highest reported for a pure non-magnetic metal.4 2 K and reported a ~c. There is a sharp peak at the 12.4 m C- ~ 4.5 K ordering temperature and a shoulder which comes from the ordering process at 13. Direct measurements of the ordering temperature of cubic (T) Ce have not been made. A 12% decrease in sample volume accompanies the y Ce to a Ce transformation. As might be expected the collapsed cubic form is only weakly magnetic because the population of the 4f state is greatly diminished by the migration of electrons to the conduction band.6 iJ 4. In the case of Y Ce it would be difficult to obtain repeatable interpretable heat capacity data.3-20 K. The a phase (collapsed fcc) of Ce is the low temperature-high pressure form. = 2.58~tB which are both very close to the values reported for/3 Ce. b) for/3 Ce. LEGVOLD data for 1/X versus T are almost identical with the data for dhcp (/3) Ce shown in fig. of any type of magnetic ordering.After Koskimakiand Gschneidner (]975). but in the case of the collapsed cubic phase or (a Ce) the heat capacity has been measured by Koskimaki and Gschneidner (1975) with results which are shown by the lower curve in fig. .2~ S. Magneticsusceptibilityof a Ce(fcc')versus temperature. Fig. However. 56 extrapolates to a N~el point of about 14. The magnetic susceptibility of a Ce has been reported by Koskimaki and Gschneidner (1975) and their data are shown in fig. 58 for the temperature range from 1. are shown in fig. nor at higher temperatures. They found 0p = .5 K. 58. There is no evidence here. 8 x I 0 "s I I | I I I I I I I I I I I E 4. 57. Coqblin and Blandin (1968) used the Hartree-Fock approximation and Anderson's formalism for a treatment of virtual bound states (4f states).. (1976a) for the fl allotrope and after Koskimaki and Gschneidner (1975) for the a form. Kiwi and Ramirez (1972) and Aliscio et al.. (1976) • A I0 • 8 o / i / 9 _ Ce ' ~~. They found the 4f electron populations of 1. (1973) also used the electron promotion approach. 0.RARE EARTH METALS AND ALLOYS 245 14 I I I I I I I KOSKIMAKI ~ GSCHNEIDNER(1975)o 12 -Tsong et al.8 K. Ramirez and Falicov (1971). i. 0 ¢m t~•dl • l oo gO o m0 2 0 2 4 6 8 I0 T(K) 12 14 16 t8 20 Fig. the Fermi level leading one to believe a 4f band might be involved. This would be compatible with the observation of superconductivity in this allotrope by Wittig (1968) at a pressure of 50 kbar with Tc of 1. and 0. Specific heat versus temperature for /~ Ce (dhcp) and for a Ce (fce'). and a ' to be 0. They proposed that the change in occupation number n is caused by the short range part of the electron-electron interaction and assumed a linear relationship between n and the lattice constant. After Tsang et al.44.98. The basic phenomenon which must be explained is the phase transition f~om the room temperature y(fcc) phase to the collapsed a(fcc') phase with about 12% smaller volume.e.33. a.03 respectively. Two different approaches to the formidable problem of generating a theory for the electronic properties of Ce have been made. 3) extend close to the cell . They assumed that atomic like 4f electrons were promoted to the conduction band when the solid went from y to a. They used a free energy expression to calculate pressure and temperature effects and were able to get reasonable fits to experimental observations such as the critical temperature. As mentioned earlier the generally accepted number for a Ce is 0. the atomic state changed from 4f m(sd) 3 for y to 4f • (sd) 4-" for a. 58. Johansson (1974) proposed that the y to a phase change is a Mott transition. They discussed the y to a phase transition in Ce in terms of electron promotion from a sharp 4f state to the conduction band. The high pressure phase for Ce is denoted by a ' and it is this phase which is believed to be truly tetravalent. He assumes that the 4f radial functions (see fig. 1 = 4 and the spectroscopic designation is 3H4. 3. Indeed. More recently.2. McEwen (1978) induced a magnetic moment in Pr by straining a sample. Nevertheless it was possible for Bucher et al. is the second in the series of rare earth elements and has two electrons in the 4f shell. He avers that the 3' phase of Ce is on the high volume side of the Mott transition and that two conduction bands coexist in the condensed ot phase.S = 5 . atomic number 59. (1976) found the singlet state in a Pr sample cut from mother polycrystalline stock and in a single crystal grown from that stock. The normally expected high temperature phase (just below the melting poin0 is bcc just as is found for nearly all the rare earth metals. Johansson also says that the electron promotion model discussed above (i) does not provide the appropriate cohesive energy for Ce. Very high field (33 T) magnetization measurements at 4.8 eV found for this by Baer and Busch (1973). Johansson suggested his model was compatible with the experimental results. LEGVOLD boundary for Ce and that thermal contraction and/or an applied pressure will cause neighboring 4f functions to overlap enough to give rise to a 4f band. (1969). The singlet ground state was found for single crystal dhcp Pr by Johansson et al. Sakamoto et al. 59 where it is seen that the a-axis is the easy direction and the c-axis is the hard direction of magnetization. This state is characterized by the total quenching of magnetic moments by the crystal field effect.8/~s which is well below the theoretical 3. (iii) requires higher 5d--6s conduction electron numbers in the condensed a phase in conflict with positron annihilation data of Gustafson et al. It should be noted that the magnetization curves emanate from the origin in a paramagnetic fashion. In the c-axis direction a sudden rise in . It turns out that the balance between the crystal field and magnetic exchange energies is so delicate that sample purity. (1969) to obtain and retain the fcc allotrope by the rapid quenching process which arc melting over a cooled copper hearth provides. is very critical and many measurements on impure samples have given misleading results. In the basal plane easy direction the magnetization appears to grow toward a saturation value of about 2.2/~B value. by way of magnetization measurements up to 8 T. (1973). It is noted that the 4f band model has been invoked to explain superconductivity in La and that for the parallel actinide elements a 5f band model has been proposed by Veal et al. The results of Sakamoto et al.5 . The stable room temperature structure for Pr is dhcp. so J = L . both phase and chemical. (1973) who also observed the singlet state. Praseodymium The element Pr. (ii) assumes a 4f energy level close to EF in conflict with the 1. are in good agreement with those shown in the figure. (1970) using neutron diffraction. The most remarkable feature of Pr is its singlet ground state in the dhcp allotrope.2 K on a dhcp single crystal of Pr have been reported by McEwen et al. The spin quantum number is S = I and L = 3 + 2 . Their results are shown in fig.246 S. For this wave function configuration only induced paramagnetism occurs in modest applied fields.. High field m'agnetization data for single crystal Pr. 59. they discussed some of the crystal field states which might be involved in the two phases. The anomaly decreased with increasing temperature and vanished at 65 K.2T at 4.2K.RARE EARTH METALS AND ALLOYS 247 Pr I I i I0 20 B. obtained a sample of the fcc allotrope. After Bucher et al. Magnetization measurements on polycrystalline fcc and dhcp samples of Pr have been reported by Bucher et al. They attributed the magnetization jump to a first order transition on the hexagonal sites from a non-magnetic to a field induced magnetic phase (the term metamagnetic is now used to describe this type of magnetic material). The spontaneous moment they obtained was 0. The normally expected form for pure Pr is the dhcp allotrope but by arc melting a sample of the metal over a cold Cu hearth Bucher et al.5 c iI) o 0 2 4 6 8 HkOe I0 12 14 Fig.76/~B/atom which was about a fourth of the full value and was explained as a crystal field level effect. The results of their magnetic measurements are shown in fig.43 K for dhcp and fcc Pr. . After McEwen et aL (1973). the moment at 31.5T was found to have a hysteresis of 0. The upper curve in the figure is for fcc Pr and shows the typical ferromagnetic jump to high magnetic moment in a weak field followed by the slow approach to saturation. (1969). The lower curve of the odhcpPr *fcc Pr "0. (1969). 60.nt (tl'esla) 30 Fig. Magnetic moment versus field at 1. 60. -20 0 20 40 60 80 I00 T (K) Fig. There is a small difference in the slope of the high temperature linear part of the curve for the fee allotrope which does not appear significant. Bucher et al. The reciprocal of the magnetic susceptibility of a sample of dhcp Pr as a function of temperature found by Bucher et al..7 K Curie point. 62. (1972) are shown in fig.7 K Curie point. (1976) for single crystal dhcp Pr exhibited considerable anisotropy of the type found in the heavy rare earths..24 kOe is shown in the upper part of fig. After Sakamoto et al...~/. (19/6).// I I / / . / /I t // /i . oL 0971) Andres et. The temperature dependence of the initial magnetic susceptibilities found by Sakamoto et al. The paramagnetic Curie point for dhcp Pr is about .10 K while that for fee Pr is 8 K which is in good agreement with the observed 8. ./ /7 /-P .~8 S. al. The slope of the linear part of the dhcp curve yields an effective moment of 3.68/LB for Pr./ // / / eo / / //' // Ijp . (1971) and by Andres et al. LEGVOLD figure shows the nearly linear behavior with field of the polycrystalline Pr sample. (1972) ..2 0 K for the c-axis data and about 13 K for the a-axis data.. I I '°tf E ..65/xB which is very close to the theoretical 3.v . (1969) in a field of 14. o o Present work • • Johansson et. 61. In both phases it appears that the susceptibility is strongly affected by the crystal field levels of the 4f electrons and that all levels in both allotropes become occupied above about 100 K. Their data along with results of previously reported investigations by Johansson et al... Reciprocal of the magnetic susceptibility for a c-axis sample and for a basal plane sample of Pr. The fields here are relatively weak which makes it difficult to make a quantitative comparison of these results with the very high field results on single crystals described above. A very crude extrapolation to the abscissa of the nearly linear trend at 90 K yields paramagnetic ordering temperatures of about . 6]. . . . invoked crystal field properties to explain the absence of a specific heat anomaly for fee Pr at the 8. These data do not extend high enough in temperature for a determination of the paramagnetic moment. fcc 90 80 ~ ~o ~ 60 ~ 70 50 40 50 5 o 20 I0 80 T 160 (K) 240 5~'( Fig. These magnetic excitons play a strong role in the magnetic susceptibility and electrical resistivity results described previously.4 K on the dispersion relations for the hexagonal site magnetic excitons (these are the excitations of 4f electrons to higher energy crystal field states). T h e y identify the lower curve from F to M as being responsible for magnetic ordering when small amounts of Nd are added to Pr.RARE EARTH METALS AND ALLOYS 249 25 2O ~.~. results at 6. Their results are shown in fig. H o u m a n et al. Crystal field levels in a single crystal of P r have been investigated by Rainford and H o u m a n (1971) using inelastic neutron diffraction techniques along principal crystallographic directions. At the top is the reciprocal of the magnetic susceptibility versus temperature for dhcp Pr and for fcc Pr.~. After Bucher et al. The electrical resistivity of polycrystalline P r has been reported by Arajs and Dunmyre (1967) and their results are shown in the bottom part of fig. more detailed. At the bottom is the electrical resistivity versus temperature of polycrystalline Pr. One can conclude that the crystal field levels are within 100 K (about 8 m e V ) o f the Fermi level in the metal. (1975b) have obtained additional. T h e y found two types o f dispersion curves and identified a single v e r y fiat curve at 8 meV with the cubic sites of the dhcp lattice and a more dispersive group of curves in the 1 to 4 m e V range with the hexagonal sites. After Arajs and Dunmyre (1967). The curvature below 80 K is anomalous for a metal and is believed to represent the effect of the crystal field levels as they b e c o m e occupied thermally. F r o m their results Mackintosh (1971) has derived the magnetic part of the . (1969). This interpretation goes hand in glove with the behavior of the susceptibilities in the upper part of the figure. 62. Specific heat measurements on P r have been reported by Parkinson et al. 63. (1951). 62. 4 K.o ! . o / o ± [ i . and by Bleaney (1963).6 1..k--. Rainford for the different types of sites are also s h o w n . . . 3.o 35 - ~ ~ 3.8 r = 0. (1975) who found a A type of anomaly in the heat capacity between 25 and 30 mK. heat capacity as shown in fig. doublet. Crystal field levels and magnetic heat capacity of Pr calculated by Rainford and Houman (1971) and shown by Mackintosh (1971).' z o 0. .D. 64. The s. The extended zone representation is used in the FA direction. Crystal field levels suggested to Mackintosh by B. They invoke a nucleus-ion-nucleus magnetic coupling which has been described by Murao (1972) and by Triplett and White (1973). triplet states. ~.4 0.. 1 o~ T I I"5 . . i .8 T ~ T i .o 0. 6 8 I0 20 40 608010OT(•K) Fig. Dispersion relations for the magnetic excitons propagating on the hexagonal sites in Pr at 6. After Houman et al.2 0. ' .2 WAVE VECTOR (~-) Fig. T. .4 1..o j .5 o. .o-°°.2 1.o 0.5 1..b o t h sites have singlet ground states as required in the absence of magnetic ordering in observations down to 1 K.3 0. t represent singlet.6 0.g 250 2OO 1. T h e o r y of the singlet ground state system has been treated by Cooper (1967).o. Below this temperature nuclear magnetic ordering at the hexagonal sites in single crystal Pr has been reported by Lindelof et al.0 d m d- 150 (*K) I00 50 0 0. 63.2 0.0 $ ~.0.1 0. . °o~'" o~ o. c/. o . . LEGVOLD K I" A " .11 2 4.4 d-$ .0 -F 35 ~ ' X ~ .0 0.2 0 0 8 0 6 0.0 ~ I ~ ku~ I i i b-o. / t "o "~ _ ! t ". 0 .5 I "° F °°:'°" . o ~+ u i . 0.4 0.~ . ~ S X d ~ o" ~~ "1" / 0. (1975b). 64.- O2 i a a • .6 0. "°. . .4 0.250 I" M S. d. .o~i'~o°"o. t ---- • . i . .: ii t i . ~ /io. "sh° o / . (1970) obtained similar results and showed that along the a-axis two additional moment jumps occur.125 at 7. S = ~ and J = L .RARE EARTH METALS AND ALLOYS 251 3. C) sites and with the c direction components on the cubic sites about this same order of magnitude. The beautiful magnetic moment pattern of the A layers and of the accompanying lattice distortion proposed by Bak and Lebech is shown in fig. This is reminiscent of the magnetization of Ho. It is expected that other interesting effects will be seen on the basis of electrical resistivity and specific heat results described below. but this result has not been corroborated by other investigators. Just as in the case of Pr the crystal field interaction should be expected to influence and complicate the magnetic properties of Nd. The normal crystal structure for the pure metal is dhcp with ABAC stacking although Bucher et al. atomic number 60. In measurements up to 60 kOe at 4. The 4f electron quantum numbers are L = 6. The insert in the figure shows the low field data at 4. (1964) that antiferromagnetic ordering sets in at T~ = 19.5 K was not explored. It is seen that the magnetization rises linearly with field at low field in line with antiferromagnetic requirements.S = ~ and the spectroscopic designation is 419/2. (iii) that there is a lattice distortion which accompanies the onset and growth in magnitude of the ordered magnetic moments. one at 20 kOe and the other at 30 kOe.2 K of Behrendt et al. Very high field magnetization data on single crystal Nd obtained at 4. (1957) on what is believed to be the first macroscopic rare earth single crystal grown. Neodymium Since the element Nd. (1969) were able to obtain an fcc sample by the same arc melting process they used to obtain an fcc Pr sample as described in the previous section. The most recent neutron diffraction results of Bak and Lebech (1978) have confirmed earlier work of Moon et al. The magnetic moment at 30 T along the easy axis is about . The behavior of the moments and lattice below 7. They found that the magnitude of the magnetic q vector varied from an incommensurate 0. has three electrons in the 4f shell it is a Kramers ion and cannot have the singlet ground state. and (iv) that the metal has the "triple-q" magnetic structure.3.5 K which is the temperature at which Moon et al.9 K and have found (i) that the transition at TN is second order.2 K on single crystal Nd Johansson et al. (ii) that moments on all sites are involved in the magnetic ordering with the size of the moments on the cubic (A) sites about 15% of the moments on the hexagonal (B. had reported the onset of ordering on the cubic sites (they had interpreted their results at TN = 19. 65.2 K by McEwen et al. The in-plane magnetic moment components give the three leaf clover pattern in part (a) and the lattice distortion is the triangular pattern of part (b). 66.9 K as the onset of ordering at the hexagonal sites). There is a rapid rise in moment with field at about 10 kOe indicating that the external field has passed a critical level for some of the moments to jump into alignment with the field.144 at TN = 19.9 K to an apparently commensurate 0. The easy direction of magnetization is along an a-axis. (1973) are shown in fig. ~ • . ~ . T plots only settle down to linear form above 150 K one concludes that crystal field levels have an effect below this temperature. (a) The magnetic structure of N d below 19 K as proposed for the A sitesof N d by Bak and Lebech 0978). ~ . " . '. . ' . (b) The accompanying latticedistortionthey proposed. Some basal plane anisotropy at 4. The two paramagnetic Curie points are 0plI 17 K and 0p~ = . . / . T. %~ . . 2. . the atoms are shifted to the dot end of the line. . The paramagnetic moment yielded was 3.11 K so there is some two fold anisotropy in Nd. l . 65. " .% "~-\.19x 10-2)/(T + 17) and X l = (1.7/za well below the theoretical saturation value of 3. .' "". Since the l / x vs.. .~.62/~B from theory.71/~B to be compared with the expected 3.2 K may be seen in the low field = - . ~ .27/~B which it appears to be approaching asymptotically..e~ . ". . . . LEGVOLD •. t ... . ~. / / .~.252 S. Above 20 K Behrendt et al. / . (1957) was linear with temperature above 150 K with XM-(1. . In the paramagnetic range the reciprocal of the magnetic susceptibility found by Behrendt et al.~ . ~ [ ~ I / . observed no basal plane anisotropy..' (a) 0 ~. \ . Fig...20x 10-2)/(T+ 11) in cgs units. ~.* *~I~$~LI[~. I . I 7 . / . RARE EARTH METALS AND ALLOYS I 253 I00 90 80 70 60 E b 40 30 20 [. (1957). The electrical resistivity of Nd single crystals has been measured by Petersen et al.8 kOe as shown in the lower part of the figure. The peak at 6. Results of specific heat measurements on electrotransport purified Nd by Forgan et al. (1979) are shown in fig. After Behrendt et al.2 K for a-axis. The peaks are modified in the presence of an applied field of 2. The low temperature data shown in the insert shows sharp changes in slope at 6 K and 8 K which correspond to the two double specific heat anomalies. Some o f the peaks are more pronounced and the peak just below 8 K has apparently increased at the expense of the peak just above 8 K. In the insert the low field magnetization data at 4.~ ~ ~. There are five distinct specific heat anomalies or peaks in the 5 K to 8. b-axis and c-axis crystals are shown. Apparently low temperature data are dependent on thermal and magnetic history so the magnetic ordering is fraught with complexity and very precise neutron diffraction measurements will be needed if an understanding of the structures is to be found.5 K regime. 67. After McEwen et ai.7 K seems to have shifted to a slightly lower temperature.2K a-AXIS 2~s c-AXIS 50 o-AXiS.2 K for a-axis and c-axis crystals of Nd. magnetization data in fig. . (1973). 20- 15- /' I-'° 7/ *OERSTEDS i I I0- 5 IO i I O I 5 I I0 0 I0 20 INTERNAL FIELD (TESLA) 30 Fig. The individual specific heat peaks are too close for a resolution by resistivity methods. It thus appears that additional elastic. High field magnetization data at 4. (1978) and their results are shown in fig./r Neodymium 4. 66 where the critical field for the magnetization jump at about 9 kOe is smaller along the a-axis than along the b-axis. neutron diffraction and Seebeck coefiieient measurements are essential if the low temperature magnetic properties of Nd are to be resolved. as well as inelastic. 66. 68. It is known that the stable crystal structure is dhcp which is in keeping with the light rare earths.200 Fig. After Forgan et al. (1973).300 0.900 i I 4 I I 6 Y (K) I I 8 i 10 1.t' ~ .4. L = 5.800 6.100 8 o ° /" # ~ • .200 .400 9. S = 2 and J = L .0 * ~..200 I I 3. u 3. is 2. Promethium The information available on Pm is necessarily sparse because all known isotopes of the element are radioactive. Samarium There are five electrons in the 4f shell of Sm so it has the spectroscopic designation 6H~/2 with S = ~. 1.254 10. LEGVOLD I I I I I I Neodymium Happ.500 E 5. This gives a succession of atomic site symmetries of chhchhchh. 67.. Since Pm has an even number of 4f electrons it is not a Kramers ion and so might have magnetic properties like those of Pr.800 6. They carried out a variety of neutron diffraction experiments and established (i) that the crystal structure was dhcp./ t I= J°°°/ I 2 I H°pp'=2"6k°e 5.6001 1. They noted that the latter would not be consistent with crystal field levels anticipated for the ground state of the metal. Heat capacity of high purity Nd versus temperature. and this sequence plays a very strong role in the magnetic properties of the element.5. The crystal structure is rhombohedral but is generally treated as a nine layered hexagonal structure with stacking ABABCBCAC as shown on the right of fig. The atomic number of Pm is 61 and it has four electrons in the 4f shell.S = 4 so the spectroscopic designation is ~I.S =-~.5 to 320 K had to be less than 0.'~" 7.100 7. O . About the only information regarding the magnetic properties of Pm comes from a neutron diffraction study at Oak Ridge by Koehler et al.400 9. 3.4/~B. gY. =0 ~ % of oo t 10. . and Y = L . 3.4/~n and (iii) that a very small ferromagnetic moment might be present below an ordering temperature of 98 K.500 2.900 0 I I I I S. The expected saturation moment per atom. (ii) that any ordered moment in the temperature range 7. The quantum numbers for this configuration are L = 6. (1979). (1978a.50 4 e 4O • c-oxis • • O-oxis ::t. T h e y found that the moments on the hexagonal sites become ordered antfferromagnetically below a N6el point of 106K. where 0 means that no order moment exists on this cubic site layer and .RARE EARTH METALS AND ALLOYS I00 I I 255 300 I 200 I 70 ee 60 a- OxiS . 0. . This gives a magnetic moment sequence on the consecutive layers of + + 0 . • " tO o oxis 3O oe ° D • ¢ - 20 00 10000 • I0 e• mf 0 I 5O I0 I00 I 15 MSO T(K) I ii0 ZOO I ~15 250 I 120 ~00 Fig. . The low magnetic moment of gJ = ~#B per atom and the high neutron capture cross section of ordinary Sm prompted them to use a sample enriched in a low capture cross section isotope. After Petersen et al. b).. For this magnetic structure the exchange field is zero on the cubic . Electrical resistivity of single crystal Nd versus temperature.. The moments pointed along the c-axis with two adjoining hexagonal site layers pointing in the plus c direction and then alternating to point along the minus c direction on the next pair of hexagonal layers and so on.means the moment is pointed along the minus c-axis so it takes eighteen layers to make a magnetic cell.0 + + . 68. Neutron diffraction measurements on a single crystal grown from metal enriched in ~54Sm have been made by Koehler and M o o n (1972). . It is seen that Sm is extremely hard magnetically. This gives ferromagnetic layers in (1011) planes (here the c-axis parameter spans 9 atom layers or three cubic site layers) with two adjacent planes having plus c direction moments followed by the next two adjacent planes with minus c direction moments and so on. (1974) show peaks at 14 and 109 K.14 Sm I o[I I0] o[oo~ OJO 0. Fig. The magnetic scattering amplitudes found yielded about 0. (1973). indicating that the moments originally aligned opposed to-the field have flipped and ferromagnetic alignment has been achieved. After McEwen et al. . They propose that the spin part of the ionic moment plus the induced conduction electron spin polarization nearly cancels the orbital contribution to the total magnetic moment since here J=L-S.8 K. LEGVOLD sites. 69. Their work is shown in fig.12/x.71/zB expected. 70. . The very low magnetic moment found by neutron diffraction is in good agreement with results of magnetization measurements on single crystal Sm reported by McEwen et al.02 I0 20 30 40INTERNAL FIELD (TESLA) 0 40 120 200 T(K) 280 Fig. with the. It is not surprising then that the magnetic moments on the cubic sites do not become ordered until the temperature has been lowered to 13. The direction of the moments on these sites is also parallel to the c-axis. Electrical resistivity versus temperature for polycrystalline Sin. High field magnetization data at 4. 69. However. applied field along the c-axis the magnetic moment makes a sizable jump near 30 T. After Arajs and Dunmyre (1966).256 S. (1973). The moment at 32T is about 0. per atim which is in good agreement with neutron scattering results as mentioned above. two rows of atoms perpendicular to the b-axis in a cubic site layer have plus c direction moments followed by two rows with minus c direction spins. I00 ~I ] I I 1 I I I 90~ 80 70- 0.2K for single crystal Sm. Magnetic susceptibility data along the c-axis of McEwen et al. In fields below 25 T (250 kOe) the moment rises nearly linearly with field and the a-axis is the easy direction of magnetization.1/za per atom as compared to the 0.06 o I ! "~ 6o ~ 5o Q.08 0.r o / 1 I /o 40 317 20 I0 I I I I I I I I - ~ao4 0 ~= 0. RARE EARTH METALS AND ALLOYS | I I I I I I I I I I I 257 SAMARIUM 50 - v 20 . Specific heat of Sm versus temperature. The high resistivity characteristic of the rare earths in general is also in evidence with the room temperature resistivity nearly 90/z ohm era. La and Yb The elements Sc. (1959). This concludes the discussion of the elements which exhibit ionic magnetic moments. The electrical resistivity of polycrystalline Sm has been published by Arajs and Dunmyre (1966) and their results are shown in fig. Y. T (K) 140 r---l----~ . This yielded the magnetic entropy of 15. 4. The weakly magnetic rare earth related elements are described next. The dashed curve is the magnetic part of the specific heat obtained by the subtraction of the specificheat of Lu with a Debye temperature ratio O D for Sm to 0Dfor Lu of 0. Y. particularly the heavy rare earths which have the same crystal structure. Magnetic properties of Sc. The dashed curve at the bottom of the figure shows the magnetic part of the heat capacity found by subtracting the heat capacity of Lu adjusted by use of the ratio of 0S for Sm to that for Lu of 0. 180 r---¢---~ 220 Fig. La is the trivalent forerunner of the rare earths while Yb . Lu. The results shown in fig.88. 71. 71 are a composite of both sets of data and show a small specific heat peak at 14 K with a much higher and broader peak at 106 K... The knee at 14 K marks the low temperature ordering temperature associated with the cubic sites and the upper temperature knee at 106 K faithfully marks the hexagonal site ordering process. The specific heat of Sm has been measured by Roberts (1957) and by Jennings et al. and Lu are hcp trivalent metals and have a close relationship with the rare earth metals..o jj//ij /I" 20 I I Smog-15.0 J/mole K as compared with the R ln(2J + 1) value of 14. This difference reflects the ~ to ~ ratio which would be expected because of the corresponding ratio of ~ to ] cubic site to hexagonal site magnetic sublattice occupancy. 70..88. After Roberts (1957) and Jennings et al.9 J/mole K.0 J/moleK 60 I I I00 I "h"... (1959). 258 S. ..0 A XlS "I ! / x z. Y. The results obtained by Spedding and Croat (1973) on single crystal Sc arc shown at the top of the susceptibility versus temperature graph of fig. The susceptibility increases almost linearly with decreasing temperature down to about 25 K. below which the behavior is more complex. La.8" I 40 I I ~ L a (Poly) I I I I I 120 200 260 T (K) Fig. When purer samples became available the data were not quite as confusing.. Magnetic susceptibility versus temperature for Sc. 4. ¥ 1. These conduction electron bands are much like those of the hcp rare earths with which it generally will form solid solutions..1. Scandium The clement Sc has atomic number 21. Lu.. it is the third element of the fourth period in the periodic table and so has a valence of three. This low temperature behavior is impurity sensitive and since the single crystals used contained 19 atomic ppm (parts per million) Fe and several atomic ppm magnetic rare earths it 8'4 ~ ' ~ ~ 8. has the hcp crystal structure and its three conduction electrons are found in 3d and 4s bands.c-AXlS 0..2 ~ at. and so departs from the main rare earths in its magnetic properties. Dy. It is an early element in the 3d transition (iron) group of elements. After Spedding and Croat (1973) for Sc. after Queen (1979) for Yb.. The early magnetic susceptibility measurements on Sc gave results which were very much sample dependent.4 ~ . It is seen that the a-axis has the higher susceptibility and so Sc is reminiscent of Tb. La. Lu. in fact some of the samples even appeared to have a magnetically ordered phase. and Ho in this respect.-o-Ax. Y. and Yb.. 72.s . 72. LEGVOLD turns out to be divalent with a full 4f shell.6 1. I 1. The electrical resistivity of electrotransported Sc single crystals has been determined by Queen (1979).. after Queen (1979) for Sc.76 2. which appears to show enhancement at low temperatures much like Pd.. One outcome of the susceptibility results for Sc has been a series of theoretical papers about the metal. 73. Thus one concludes that small quantities of magnetic impurities lead to sizable effects on the low temperature magnetic susceptibility of Sc. y o. ~ ~ i ~ z ~ o 40 80 120 160 200 T (K) 240 260 320 360 Fig. Lu. Electricalresistivityversus temperaturefor polycrystallineYb and for singlecrystalsof Sc. There is no evidence of any low temperature anomaly for either sample. (1976a. . after Hall et al. IO o i . and 350 for the a-axis sample. b) on electrotransported samples of Sc show no low temperature peak of the type which a sample containing 30 atomic ppm Fe exhibits. La... The well behaved heat capacity results found for Sc by Tsang et al.J. 73.. (1959) for Y. after Boys and Legvold(1968) for Lu.65 /// / / / c::] 30 2O I0 o /// /// 40 30A 20 o. (1960) for the related elements Lu.© a AXIS - 70 6O 50 40 I~ c-Axis . (1969) and Capellman (1970).c . After Kayser (1970) for Yb. Among these is a publication by Rath and Freeman (1975) who calculated the generalized susceptibility and the Fermi surface and one by Das (1976) who computed the magnetic susceptibility. The samples showed resistivity ratios R3oo/R4.6 2. and Y if the data are adjusted according to Debye i i i i i ! | i Lu b-AXIS /I Y b-AXIS ResiduoI Resistivifles / / / = / ~ . These papers followed earlier calculations by Koelling et al. heat capacity measurements of Tsang et al.2(=-AXlS) /// ////// _ Lu 0.3 of 270 for the c-axis sample. His results are shown in fig. The resistivity for the a-axis sample at room temperature is over twice as high as that for the c-axis sample reflecting the Fermi surface area effect.5 cm) b-am O. b) may be compared to the heat capacities obtained by Jennings et al. (1976a. Y.RARE EARTH METALS AND ALLOYS 259 is very likely the low temperature anomaly will disappear in high purity electrotransported Sc. Indeed. This close relationship makes solid solutions of Y with the rare earths possible.2~ S. 26 if it is scaled according to the Debye temperatures of 214 K for Y and 166 K for Lu. It has the hcp crystal structure and is the trivalent element near the left end of the 4d electron transition elements of the fifth period of the periodic chart. In the case of Lu the three conduction electrons are in the characteristic rare earth 6s and 5d bands and Pauli paramagnetism of these conduction electrons accounts pretty much for the susceptibility. It appears that Pauli paramagnetism would account for the observed susceptibility of Y. The three conduction electrons of Y are in 5s and 4d bands and. 131. Lutetium The element Lu. 214. atomic number 71. (1959). Lu. It has a full complement of 14 electrons in the 4f shell. Magnetic measurements on single crystals of Lu have been made by Spedding and Croat (1973). (1960) is essentially the same as that for Lu as shown in fig. has the hcp structure and is the end point of the rare earth or lanthanide series. They reported 8 ppm Fe and about 10 ppm magnetic rare earth impurities. respectively. these bands are much like the 6s and 5d conduction electron bands of the heavy hcp rare earth metals. The difference in magnitude compared with Y is partially accounted for by the diamagnetism of the larger number of filled shells in Lu although a difference in the density of states at the Fermi level may also be a contributing factor. 4. The susceptibility drops only slightly with decreasing temperature in contrast with the behavior of Sc which is shown at the top of the figure and the magnitude is about a fourth of that for Sc.3. Yttrium The element Y has atomic number 39. As in the case of Sc the a-axis susceptibility is higher than the c-axis susceptibility. The magnetic susceptibility of single crystals of Y has been measured by Spedding and Croat (1973) with results as shown in the center section of fig. 4. 166. LEGVOLD temperatures (see fig. as in the case of Sc. 26). It also makes the purification problem difficult. 72. It appears that Debye temperatures appropriate to specific heat data for Sc. La and Yb are 347. The electrical resistivity of single crystal Y has been reported by Hall et al. Their magnetic susceptibility results are shown towards the bottom of fig. 72. 73 where it may be seen that Y has higher resistivities than Sc although the anisotropy is about the same as that for Sc. Y. and 107 K. The data look very much like those for Y with almost no temperature dependence and with a magnitude almost exactly half that for Y for both the a-axis and c-axis results.2. The slight upward turn of the susceptibility at very low . The relatively sharp rise in the susceptibility below 15 K is very likely the effect of impurities in the samples. The heat capacity of Y reported by Jennings et al. Their results are shown in fig. Again it is believed the rise in the susceptibility below 30 K is an impurity effect since the sample contained 6 ppm Fe and about 18 ppm magnetic rare earth elements. Results of electrical resistivity measurements on Lu single crystals as reported by Boys and Legvold (1968) are shown in fig. The similarity of the Lu resistivities to those for Sc and Y is apparent in the figure and one may conclude that the Fermi surface projections must be nearly Mike for all three elements. 72. (1960) is shown in fig. The heat capacity of Lu as found by Jennings et al. Electrical resistivity versus temperature for dhcp La and fcc La alloyed with 0. .2at. 26.2at. 73. (1977b).RARE EARTH METALS AND ALLOYS 261 temperatures is again a likely consequence of the iron content of 17 ppm and the magnetic rare earth content of 5 ppm. Use of electrotransport methods to eliminate the Fe would be advantageous. Lanthanum The forerunner to the rare earth elements is La.% Gd to stabilize that 70 60 5O ~ ~. The electrical resistivity of polycrystalline La as reported by Legvold et al. 74. It is normally considered to have an empty 4f shell. The susceptibility increases with decreasing temperature and crosses the curves for Lu at about 60 K.4. although some conjecture exists about the possibility of a 4f band just slightly above the Fermi level in the 6s and 5d conduction bands which are occupied by three conduction electrons. After Legvold et al. 3O LQ"O'2% Gd 20 I0 / O0 40 80 120 160 200 240 280 320 T IKI Fig. The results of magnetic susceptibility measurements on high quality polycrystalline La as published by Spedding and Croat (1973) are shown near the bottom in fig.17 K for the fcc form and 5. and single crystal magnetic data have not been published.15 K for the dhcp form. The resistivity of the dhcp allotrope is higher than that of the fcc form which contained 0. 4. atomic number 57. The latter structure is the stable one at room temperature and is the form which is characteristic of the light rare earths.% Gd. The most interesting property of La is its superconductivity with Tc of 6. (1977b) is shown in fig. Considerable difficulty is encountered in the growing of La single crystals. 74. and Th correlated with the c/a ratio of the samples and (ii) that the ordering . The specific heat of La has been published by Parkinson et al. Magnetic susceptibility measurements on a polycrystalline sample of Yb have been made by Queen (1979) and his results are shown as the dashed curve at the bottom of fig. The main difficulty encountered occurs when light elements which favor the dhcp crystal structure are alloyed with the heavy elements which favor the hcp structure. 5. La. Binary rare earth alloys The fact that the trivalent rare earth metals (this excludes Eu and Yb) form solid solutions has made the study of a wide variety of rare earth alloys possible. The problem of impurities was not serious even though analysis showed the sample contained about 30 ppm Fe and 15 ppm of magnetic rare earth impurities. The low temperature (a) form was found and reported by Kayser (1970) and by Bucher et al.. Lu. The crystal structure of Yb below 270 K is hcp (a) while the fcc (/3) form is stable between 300 and 1100 K. This configuration would yield L = 3. The small drop in resistivity at 6. Lu. The factors governing the ordering temperature of alloys must include electron mean free path effects according to the work of Legvold et al. However. Heat capacity data for Yb have not been published. 4.262 S. This concludes the discussion of the magnetic properties of the pure rare earth and rare earth related elements. Ytterbium The rare earth element Yb has atomic number 70 and would normally have 13 electrons in the 4f shell. It is generally observed that for such mixtures of elements the samarium structure turns up in the middle concentration range. No effect of a possible crystal structure change from fcc to hcp was seen. The insert of the figure shows the low temperature part o f the dhcp sample resistivity. 73 where it is seen that considerable thermal hysteresis goes with the a . Hence Yb is a divalent metal with calcium-like properties. (1951) and discussed by Jennings et al. (1970). The resistivity results of Kayser are shown in fig. Mg. and La in this respect.5. (1977a). Y. Y. LEGVOLD allotrope.15 K gives the superconducting transition temperature of the dhcp allotrope. The latter found that the specific heat of La would scale to that of Lu if Debye temperatures of 131 K for La and 166 K for Lu were used./ i . They found that (i) the saturation moments of Gd alloyed with Sc.17 K occurs at the superconducting transition of a small fraction of fcc crystallites in the sample while the large drop to zero at 5. this trivalent configuration is not found in the metal because a lower energy configuration is accessible to the metal if one conduction (valence) electron migrates into the 4f shell to fill it. (1960).a transition. Yb. It is not highly magnetic and belongs in the class of Sc. S = ½ and J = L + S = 7 for a spectroscopic designation of 2F7/2. 72. and to a smaller extent by Sc as attested by the increased surplus moment of fig. or 17. (1964) are also shown in the figure. conduction electron scattering by solute atoms (see fig.8 P_ "u (.8 for Lu makes it the most incompatible solute 0. 76 for the decrease in ordering temperature. (b) Excess magnetic moment per Gd atom in units of ~tB versus the unit-cell volume for Gd (polycrystal mother) and the Gd alloys. (1958). Their results are shown in fig. Gd-Y. ~ 3 ) Fig.7 V + O. (1977). or Gd-Sc by Nigh et al.9 0 I I I o Gd + Sc 0. The symbols indicate the solute atom. The small atomic volume 15..o co LU x A 0.RARE EARTH METALS A N D ALLOYS 263 temperatures did not correlate with c]a. the other effect. (1977a).4 1.590 I 1. The departure of the data for Gd-Sc.595 I 62 I 64 I 66 0. . 75.0 ×0.(S1 + 1)+ C2S2($2 + 1). (a) Excess magnetic moment per Gd atom in units of/zB versus the unit-cell axis ratio c/a for Gd (polycrystal mother) and the Gd alloys. t-Z W z~yb xTh 0. rather.81 v~l (.580 I 1. for Tb.6 o . tended to lower the ordering temperature. Tb-Sc.9 V Ay • Lo v Lu o Mg 0.5 W x~ (b) 0 0 0 Q • r. It is seen that the ordering temperatures of intra-heavy rare earths followed the straight line established by the pure elements as described earlier in fig. Lu.5 X W x 0. One of the effects tended to raise the ordering temperature via enhanced 5d band polarization by Y. After Legvold et al.4 68 c/a RATIO CELL VOLUME ( ..03 cm3/mole for Sc as compared to 19. Their data and data of Koehler (1972) were used by Legvold (1978a) for fig. the drop in Tc (ATc) was found to vary nearly linearly with sample residual resistivity. The ordering temperatures they obtained are shown in table 3. 77 which shows a plot of the ordering temperature (filled circles) versus average spin factor given by C~S. Dy. 19. (1965).88 for Gd. and Er-Y by Child et al. 75. 75 for the excess saturation magnetic moment and in fig.585 I 1. 76). for Tb-Sc by Child and Koehler (1966). and Tb-Y from the line for the elements was attributed to a combination of the two opposed effects discussed at the start of this section. Intra-heavy rare earth alloys should be relatively compatible and not suffer much from this phenomenon. A large number of such alloys has been investigated by Fujiwara et al. The symbols indicate the solute atom. Ho.. 4.86 for Y. Results on ordering temperatures for Gd-Y by Thoburn et al. Magnetic ordering temperatures for heavy rare earth alloys versus the spin factor S ( S + 1). 9 MO. 76. S. After Legvold (1979). . (1979a) to reexamine the effect of spin disorder on the residual resistivity of dilute alloys. 77. . (b) Depression of the Curie temperature ATc of Gd alloys vs. . The observation of Heisenberg exchange for heavy rare earth alloys prompted Legvold et al. .g SOLUTE CONGENTRAT.(s. the residual resistivity. and Sc give evidence for conduction electron scattering by these solute atoms.1 for all samples as indicated by M0./#~//E+r* . In the insert of fig. . ION (o~%) s . . . ~ ~ ' + PUREELEMENTS ~ • INTR~RARE EARTHS A Tb-Y o Gd-Y v Tb-Sc o C-d-Sc o Oy-Y =.46p0 in K. Results showed that the atomic volume difference between the host and the solute was a large contributor to the 300 280 260 240 22(3 200 . . cm) Fig.g. They measured the residual resistivity of one atomic percent of heavy rare earths in thorium. 77 the residual resistivities of Gd and Tb alloyed with Y.9 MO. 4O. The metal solute concentration is 0. LEGVOLD .t. 50' ~z120 IO0 80 20 ~ | | 2 6 g .~ .60 ~.2~ .592 -Izo (b) I 50 I0 .594 / ] 150 c / a RATIO po (p.t) Fig.2 .o . b-L. 90 80 70 60 50 Mg ~b Gdo. I M 60 • Sc p Lu ~e <:1 40 50 2O Th ~.4. (a) Depression of the Curie temperature ATe of Gd alloys versus the hexagonal-lattice c/a ratio./.590 Gd I 1.o0.%s/s 2. The equation for the straight line shown is A T e = 15 + 0. and so it should lower the ordering temperature the most.6 qs.b . the dashed curve is from theory. Lo Sc /- J40 3 0 '~ '-~ (a) Y I 1. . After Legvold et ai. Lu./ // o • ~ / "~. Tb-SC / . Gd-Lu G d ~' 'Gd " / ' ~140 /~:rb-~. ."Y llo I I00 ! 1. (1977a). .I Gdo. I ~3 . I I ~ I q I @ ~.. [.1 • ~ ~ I I I I I I I I I ~ I I ~ I I I ~ I I I i I I I I I I I I I I I I i I I t I I I I i I I i I I . I ..Z ¢'4 ¢xl L'~ C q ~'4 ¢'4 + t~ ~~ 265 ~ ZZ~ ~ ~ .. ~..[.t. ~.-- c~ I II I I I I I I I ] .T. . ~. / Gd/ -- 250 "o Gd. This led them to reexamine the data of Mackintosh and Smidt (1962) for heavy rare earths dissolved in Lu.~ ~" L~y p/'/'O / ~<2°m J - 150 ~.. 78.. when these results were adjusted for the volume effect the spin only residual resistivity was found to be proportional to S ( S + 1).. In table 4 the parameters found to be appropriate by 350 I i x ELEMENTS o Gd-Dy o-Gd-Er ~ Gd - 300 HO ~ ~ ~ ~ ? ~ ~. ~ \ .) His results are shown in fig. Magnetic ordering temperature of intra-ra~e earth alloys versus the t w o thirds p o w e r of the average de Gennes factor.~/ r.~'~ / I ~ /~" II.. This outcome was explained classically by calculations which showed that the transit time of a conduction electron across a 4f function range ( . i. 78 where it is seen again that the alloys of Gd with Sc and Tb with Sc depart from the universal G 2/3 factor dependence.~) was .e. t "" 1 t i ' ' 1 T 46G 213 N= "-. LEGVOLD observed residual resistivity. . In an earlier study of a large number of hcp binary alloys Bozorth (1967) found that the magnetic ordering temperatures were proportional to the twothirds power of the average de Gennes factor of the alloys.. a value too short compared to the 10-t4 s 4f spin precision time around J (the total 4f angular momentum) for the conduction electron to sample just the component of S along J. / o//"~ 7 7" ~_ o] . The theoretical basis for the unexpected de Gennes factor dependence and the departure of the Sc alloys from the universal curve has been discussed by LindgArd (. After Bo zo rth (]967). .266 S.i .Lu -o T b ' L u JO Dy'Ho ? Dy:Er Gd-Tm / ~ . .Lu 0 Tm-Lu H0-o~// ¢ yo. ~ Er.1 0 -16 s.1 . (g .1)J. ! ~2t~= < ( g _ l ) 2 J ( j + l ) > 21~ Fig.(.. (He did not show a plot versus the average spin factor. ~?" .3 4 5 s . who attributes the observed results to concentration dependent exchange interactions and to variations in the conduction electron density of states at the Fermi level as one goes across the series of elements.1977)..c~ o-.Tm o Er.2 ..Lu _ .7 /~i J "~ T~xb~ / / - -200 & Ho-Er <~ Ho-Tm '~ Ho. .~>" ~ × X 267 .~. I I 0 I o. 0 ~'~1. ~ ~ ~ {".< 0 I 0 eq. U • . I I I ! I I I I I I I I J .. I q •~ .1 O0 0 OC.o " 63 U I ! 0 ~' ~ 0 .. 80.268 S. One study by Legvold et al. (1978). (1978) found the dependence of the superconducting transition temperature of La was not a linear function of the de Gennes factor of the solute. Y. It should be noted that the ordering temperatures for the pure elements fall close to the universal curve in fig. LEGVOLD LindgArd for the heavy rare earths are listed. (1977b) showed that the interatomic electron 4f wave function overlap with the 5d wave functions would explain why one atomic percent trivalent Gd in La would depress Tc twice as much as an equal amount of divalent Eu even though both solutes had seven 4f electrons. Their double butterfly diagram of the superconducting transition temperature of fcc and dhcp La containing one atomic percent rare earth solutes is shown in fig. The ht of the table is the h~ch of eq. A wide ranging series of alloys of La containing small concentrations of rare earths has been investigated in studies of their effect on the superconducting transition temperature of La. and Sc. 79 and their plot of 7'= versus the de Gennes factor and versus S(S+ 1) is shown in fig. There is a considerable spread in the calculated and experimental conduction electron density of states at the Fermi level for Lu. • I I I ~ I I I I I I J I I • 5. ° \. In another study Legvold et al. 79. Double butterfly plot of the superconducting transition temperature Tc versus rare earth element in the sequence of nominal number of 4f electrons./~ : ~zI -• + LEGVOLD LEGVOLD • LEGVOLD I I I I I 7 5 _ 8 ! I/d el al (1976) el ol (1977) el ol (19780) I ] W 6 I I I I I I I I - Lo Ce Pr Nd R'n Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Fig. 78. After Legvold et al. the localized exchange interaction for each element will probably have to be calculated carefully to bring about agreement between experiment and theory.. . . (5) and it is of high interest to note it is nearly constant across the series of hop elements shown. Since the conduction band is essentially fixed here. 83.1)2j(] + 1) for lat. (1978). The magnetic properties of Eu alloyed with Yb have been investigated by Legvold and Beaver (1979). At lower Eu concentrations the magnetization curves gave indications of ferromagnetism in the samples in the low temperature regime. The slope of the I/X versus T plot shown gave a paramagnetic moment of 8. and does not alloy readily with the other rare earths save for Yb which is also divalent. Also it is divalent.% Eu and had the fee form which is the room temperature form for Yb (Eu has the bee structure). Eu base alloys Since Eu oxidizes rapidly it is not an easy element with which to work. There is a peak in the magnetic moment which is interpreted as a N6el point marking the onset of a low temperature antiferromagnetic structure. The isofield data they obtained for the 40 atomic percent Eu sample are shown in fig.1. Superconducting transition temperature versus the spin factors S(S + 1) and (g . The alloys contained 10 to 40at. 5. The dot-dash curve for 0p extending out from 40% Eu is an estimate of the behavior leading down to the 0p of .94/x~ and the paramagnetic Curie temperature was 14 K.2Yb0. 80. A plot of their Curie temperatures and N6el (isofield peak) temperatures is shown in fig. A survey of much of the binary alloy work on the individual elements is given next. belongs in the calcium family.RARE EARTH METALS AND ALLOYS I I 6 -"--C"Tc PURE fcc Lo I I 269 ! I • • I ot % SOLUTES S(S+l) (g-I)2 d (d+l) •Tm• ~ • Er Ho 5 • Dy • ---L 4 Tb " Gd 3 "• I 2 I 4.% of heavy rare earth metals in fcc La. A dashed curve is shown extending from the N6el points of the samples studied up to the N6el point of Eu.9/~B per Eu atom as compared to the expected 7.8 sample. 81. 2 K . After Legvold et al. An example is shown in fig. From plots of cr2 versus H/or it was possible for them to obtain Curie temperatures for several of the samples.3 . I 6 (g-I)2j I 8 (d+l) I i0 or S ( 8 + I 12 I) I 14 I 16 Fig. 82 which shows the isothermal magnetization data for the Eu0. . 82. 0 °K 0 I 2 3 I 4 5 6 7 X (KOE) • 8 9 I0 II Fig. i i 200 i I 240 ' : : 280 : l Fig. Magnetization isotherms for 20at. I ." IO'O°K 3025 / ~ • . After Legvold and Beaver (1979)."-'I50°K o b~ . ~ 2 7 . After Lcgvold and Beaver (1979).32OK ~4'2°K " . 81.2 IO 6 4 2 4 .. I 35 ~ I I I ~ ~ I I ~ ~ I I I I I ~ ~1.% Eu in Yb. Isofield magnetization data for 40at. 40 I ~ 80 120 T...% Eu in Yb.2 0 .~-~l).0 8~_1~1 ~< .270 18 ' l 1 I I S.~60.. L E G V O L D l I I I I 16 . . J / I I I I l II OE 8KOE I 1. ss'sl // 2o / I 0k \ Ferro \ I I "o. apparently in this system the net magnetic interaction is ferromagnetic at high temperatures.E u alloys. A f t e r L e g v o l d and Beaver (1979). as the temperature is . Lu. Data on Gd-Sc were reported by Nigh et al. by Lind~ard (1977) and by Redner and Stanley (1977).e~l -*"-.~ ep ./t / .J.. 83. by Bak and Mukamel (1976). Figure 85 shows the results of a detailed study by Legvold et al. (1977a) described at the start of this alloys section. b). (1964) and similar work on a few samples of G d . Theoretical work on the magnetic properties expected for samples in the vicinity of such points has been reviewed by Hornreich (1979). 5. The magnetic properties of Gd-Y and G d . Then.. In the detailed magnetic phase diagrams a variety of critical points will be seen. This difficulty holds for alloys of Gd with the light rare earths so these are not the simple solid solution type. Magnetic phase diagram f o r Y b .L a alloys were reported by Thoburn et al. Alloys of Gd with So. 84. (1958).L u were employed in the study by Legvold et al. It is seen that the highest ordering temperature has a 5 K gap or drop at the changeover from ferromagnetic to helical ordering. (1961).% La... The results of these studies are shown in fig.. The data for La are quite different with a good part of the difference accounted for by the onset of the samarium crystal structure at a concentration of about 16at. and Y give ordering temperatures which are much alike. The point of intersection of the curve for the ferromagnetic ordering temperature with the curve for the N6el points gives a potential Lifshitz point because the generalized susceptibility here has a true maximum at Q = 0 (ferromagnetism). (1979b) of the Gd-Y system near 31 at. There is some work reported by Mukamel and Krinsky (1976a.2. Gd base alloys A large number of binary alloy investigations involving Gd have been completed. I "~"1"-°.RARE EARTH METALS AND ALLOYS 271 I I I I i i i PARAMAGNETIC CURIE POINT FERROMAGNETIC CURIE POINT NEEL POINT I00 81= o 8c A ON • ° 80 16O 40 1__o.~llf \.i I I 0 0 Yb I0 20 50 40 50 60 PERCENT Eu 70 80 90 I00 Eu Fig. found for Eu from the susceptibility data between 300 and 400 K of Colvin et al. The precipitous drop in the Curie temperature above the Lifshitz point concentration is a consequence of the generalized susceptibility dependence on the q vector.% Y. \ (A. and Er have been given in table 3. (1977a) for G d . Paramagnetism exists above the Tc curve out to 94% Tb and 230 K. Lu. omic %) Sc~29 t'. \\_ I T. "~. The phase diagram for Gd alloyed with Tb is at the top of the figure. \' 2ooi\:i I / I I I Sc ~6oFl~ I N . Dy. 280 Tc\'\3 ~'-. and La. the Lifshitz point.. 4 0 1 - ': \e. TC~\ \ D \~P I ' ~--Estimated N " N \ \\ \ "~.272 520 I'-.. Magnetic data of Fujiwara et al. Ha. It appears that this alloy system shuns the Lifshitz requirements.Y and G d . After Thoburn et al. \ \\ ~ Lu ~\ I~'\ F.L a . ." \ ~ ' .L u . (1958) for G d . ~ ' r S. after Legvold et al. 28/0~'~ Gadolinium Alloys p\ k ~ "~0p ~ . The diagram consists of the ferromagnetic phase below the Tc (Curie temperature) curve extending from 293. L E G V O L D ~ ~ J ~ J .5 K for pure Tb. (1977) for Gd alloyed with Tb.. . The latter have been useful in the preparation of phase diagrams for heavy rare earth alloys of Gd as shown in fig. 20 I TN 40 50 60 . after Nigh et al. . 86. lowered the antiferromagnetic interaction (possibly the next nearest neighbor part) overtakes the ferromagnetic interaction (possibly the nearest neighbor part) and this automatically suppresses the highest ordering temperature. Data came from table 3 and from Burgardt and Legvold (1978).N r ' ..-. (1964) for Gd-Sc. The dashed curve also marks the upper boundary of the triangular shaped helix structure region associated with pure Tb from 230 K . "-. Sc.4 K for pure Gd across to 219.\ \\ \ ~ -.. Magnetic phase diagrams for Gd alloyed with Y. 84. N 30 I / "'. This suggests that all systems should be explored near the critical concentration.-'~'" ""~ - 320 T 280 I-N \ 240 I L\.0 otomic % Solute I "~-I I I "4 / 80 I 0 ~ Gd IlO 90 I / 100 Fig. where the pressure dependence of the ordering temperatures as well as the ordering temperatures themselves are shown. and then above the dashed TN curve which extends from this point to 23 K at 100% Tb.~ \ o I \\ I'. The Tc curve extends from the 293.0 30. (1979b). For Er concentrations from 60% to 100% a c-axis modulated (CAM) plus helix structure exists over a fairly large region and the CAM only phase of pure Er extends over a small triangular region back to 13% Gd (or 87% Er). 85. (1977) given in table 3 were used in the drawing. Enlarged magnetic phase diagram for Gd alloyed with Y showing the temperature gap o f 5 K near 31at. (1976) as well as from Fujiwara et al.05%) I 30.RARE EARTH METALS AND ALLOYS 220 273 ~ . (1976) show the line extended along the dotted portion to the cone region but Fujiwara et al. The phase diagram for Gd-Er as given by Fuji et al.5 32. 86. Fuji et al. Data for the figure come from Fuji et al.5K 210 Gadolinium . After Legvold et al.% Y. The TN dashed line from the 225 K.0 . Below 40 K a rather large . For Gd-Ho the phase diagram is the third from the top in the figure and begins to show some complications at the Ha rich end. 206 K Lifshitz point. show no T~ for 75% Ha. The ferromagnetic cone structure region extends from about 85% Ha up to pure Ha.5 K. Next from the top in fig. Below the dashed TN line the helix magnetic structure exists down to the questionable region below about 80 K. 25% Ha Lifshitz point out to the 132 K N6el point of pure Ha.4 K Tc point for pure Gd out to about 70% Ha where confusion sets in.0 I I I 31. (1977) as shown in table 3. (1976) shows much greater complexity to the right of the 36% Er. Even so. A displaced (downward) temperature scale has been used to avoid confusion for the other phase diagrams of fig. down to 219. 86 is the Gd-Dy phase diagram which is just like that for Gd-Tb.aTOMIC % YTTRIUM Fig. TN is observable all the way from the 245 K. Apparently the single ion anisotropy of Er makes it magnetically incompatible with the elements Gd and Tb. 50% Lifshitz point to 179 K marks the upper boundary of the triangular helix region.Yttrium Ferro Helix 200 (31. The diagram shows ferromagnetism below the T~ curve which extends from 293.5 31. It can be seen that the Lifshitz point marks the start o f a region of unknown magnetic structure designated by the question mark. It must be concluded that samples show inhomogeneous magnetic behavior from 70% to 90% Ha.4 K for pure Gd across and down to 85 K for pure Dy.-. The data of Fujiwara et al. .274 320 280- S. .. \ \ _206K "<L.~ 240 re\ Ferro '~ \.I-~. 86 is a tentative educated guess formulated in the absence of published data by extrapolation from the Gd-Er diagram and by incorporation of the changes suggested by the Tb-Er and Tb-Tm diagrams which have been published and which appear later here.160 2oo.4 K for pure Gd and terminates near 45% Tm at the region (marked A) of inhomogeneous magnetic structure (perhaps amorphous l i k e . . ~ \ ~- Iz 0 "" Helix ~"2oo _ . The structure there is not ferromagnetic because Fujiwara et al. There is likely a small cone plus helix region at low temperatures which extends from about 45% Tm out to 80% Tm where the magnetically inhomogeneous area B exists. ~ 280 .""~'~t ~~ 80 A CAM. ~ C~. Dy.~~*E~r \~. region of conical ferromagnetism extends from 50% Er out to 100% Er.~. Er and Tm.. ~ ~ .5% Ho ~ Helix -" . . LEGVOLD i i I ~ ~ . Ho. The phase diagram for Gd-Tm at the bottom of fig.. 86. J ALLOYS 250Kv i 320 280 GADOLINIUM Fe r r o ~ .. : j 4 0 I 90 +HelIx/~ F~. ... The T~ curve extends out and downward from the T~ of 293. ~ 80 -. (1977) did not report a T~ for the 75% Er sample.+Helix \ " ~ 8 0 " .. x'x~. B""'_~. A small CAM plus helix region is shown from 60 to .. (1977) and Fuji et al. \ ".I 80 40 0 I I0 I 20 Cone Gd +He... 280 ~ Er "'-.-----x~ ""-: I I I I I "I 30 40 50 60 70 80 ATOMIC % SOLUTE " + Helix "".. (1976) with some data for Gd-Tb after Burgardt and Legvold (1978)..o r spin glass like) like that observed in Tb-Tm..M-I . After Fujiwara et al. I I I00 Fig..x . At 75% Er a region of inhomogeneous magnetic structure (apparently an unstructured system) extends from 40K up to about 80K. 240 . "> T~_~ 2 3 0 K ~ -"----~: 240 .....~: -If 20 Hol -t so ... Magnetic phase diagrams for Od alloyed with Tb.. CAMI31'~. ~ ~ 240 - _ I-erro "c-~. . 3at. 84) with small changes in the concentration and temperature at the Lifshitz point.2K. Tb base alloys Since Tb has a N6el point at 230 K and then becomes ferromagnetic at 219. about half this for 35% Pr or 50% Nd.4 kOe he found about 10 emu moment/gram for Gd with 30% Ce at 4. (1974) on hcp Gd-Nd and Gd-Sm alloys showed that these alloys were very much alike and that the ferromagnetic Curie temperature dropped steadily from 293. At the top of fig. They obtained a saturation moment of 6.55/~B. (ii) that the magnetic moment of Pr has 3. 87 the behavior of Tb alloyed with Pr. for samples with more than 50at.2/~B per atom.% Pr.% Sm. His slowly cooled samples had the Sm structure and in an applied field of 8. Magnetic measurements were not definitive at the higher concentration. On the basis of susceptibility measurements of Speight (1970) on Tb-Pr and Tb-Ce alloys it is possible to conclude that the phase diagram for Tb-Ce would be like that for Tb-Pr in fig.4 K for pure Gd down to about 200 K at 25at. The La and Th data were obtained by Burgardt (1976). 87.% Pr there was no magnetic ordering down to 2 K. The . Tissot and Blaise (1970) found that 7.2 K. The Nd and Pr alloy data were published by Curry and Taylor (1976). Ce. In all four cases the helical structure is eliminated when the concentration is high enough to reach the Lifshitz point. This result compared favorably with the 6. 5.5 K the magnetic phase diagrams for Tb have a different appearance from those for Gd. In general the magnetic phase diagram for these alloys is like the diagram for Gd-La (fig. and (iii) that the spins coupled parallel to each other so that the magnetic moments were opposed to each other. (1977c).% solute range of Gd alloyed with La. Samples in the 30 to 50at. and La and with the tetravalent metal thorium is shown. Pr and Nd were rapidly quenched from the molten state by Speight (1970) who found they had the hcp structure with magnetic properties about like those one might extrapolate from the dilute hcp regions. Magnetic measurements by Fujimori et al. The concentration of solute at which the crystal structure changes from hcp to the Sm form also varies in about the same manner. The latter two had broad peaks suggestive of N6el like behavior at about 12 K. It is most interesting that such a small percent of Th should have such a strong effect.% Pr alloyed with Gd was measured by Legvold et al.63/~B at 4.60/~B obtained under the assumptions (i) that the saturation moment of the mother Gd stock was 7.3. Several papers on Gd alloyed with the light rare earth elements have appeared. They observed further that at 4. The magnetic moment of a hcp single crystal of 9at.RARE EARTH METALS AND ALLOYS 275 80% Tm. Also the CAM and ferrimagnetic phases of pure Tm must extend into the dilute Gd in Tm regime as shown.6at.2 K the easy direction of magnetization was along the b-axis and that there was a jump in the magnetization of the c-axis sample at an applied field value of 16 kOe which gave a measure of the anisotropy.% of Pr in Gd had the hcp structure and was ferromagnetic with a Curie temperature of 254 K and that the Sm structure occurred for concentrations greater than 19. Pr. The magnetic phase diagrams for Tb alloyed with heavy rare earths are shown in fig.~. In a neutron diffraction study at higher Pr concentration Curry et al. and Sc are shown in fig. For this figure most of the data were obtained through use of neutron diffraction by Child et al..97 K 220 22( 200 0 . As in the case of Gd the successive diagrams get more complicated. L E G V O L D 24O 22O -- TN I TERBIUM ALLOYS I I .~rPr45 had the Sm crystal structure. Speight (1970) obtained hcp for such alloys by quenching from the molten state. after Burgardt (1976) for Tb-La. The magnetic ordering temperatures of Tb alloyed with the non-magnetic trivalent elements Y. (1977) found that Tb. La.~k~ 217K " ~ _ ~ I 5 Th ~ Lo I 15 I I0 ATOMIC % SOLUTE Fig. some low concentration solute data of Burgardt (1976) have also been used in the diagram. For all three solutes the helical structure is stabilized relative to the ferromagnetic structure. and Th.. 87. After Curry and Taylor (1976) for Tb--Nd and Tb-Pr. alternate pairs of hex site planes had antiparallel moments. 89. In fact some twenty to twenty five atomic percent of these solutes is sufficient to wipe out the ferromagnetic phase. after Burgardt and Legvold (1975) for Tb-Th. The data of Fujiwara et al. Partial magnetic phase diagrams for Tb alloyedwith Nd.2 K and that the turn angle was 60°. Lu. 88. In samples of 20% Pr in Tb and 25% Nd in Tb Achiwa and Kawano (1973) found that a martensitic transformation from the Sm structure to hcp took place at very low temperatures and that ordering was ferromagnetic in the hcp phase. They also found that Dy and Ho alloyed with Pr and with Nd had zero magnetic moments on cubic site layers (recall the Sm magnetic structure) while moments on adjacent hexagonal site layers were parallel and in the basal plane. (1977) for Tb with 50% Dy established the plots of TN and Tc for Tb-Dy which form a textbook example phase diagram with a linear change with alloying across the whole concentration range from one element to . that the magnetic moment structure was helical at 4. They interpreted the latter results in terms of two contrarotating helices with 60° turn angles on each helix.2% S. At higher concentrations of the light elements with Tb there is a change to the Sm type crystal structure which brings about large changes in the magnetic properties. (1965) for Y and Lu solutes and by Child and Koehler (1966) for Sc solutes. nesting feature of the Fermi surface for Tb is highly sensitive to an increased number of conduction electrons and explains this result. In a recent study of a Tb-50% Ho study Isci and Palmer (1977) found ordering temperatures in excellent agreement with those shown in the figure.y I iy O I0 I 40 50 60 70 80 90 IOO ATOMIC% SOLUTE Fig. -. Sherrington (1973) has suggested that the Er rich alloys may favor a tilted helix or tilted cone magnetic structure.~"~ LU I . Lu.. The data of Koehler (1972) for Tb-Ho and Tb-Er are shown in the middle of fig. (1975). "~'. The ordering temperatures found by Spedding et al... The magnetic phase diagram for Tb-Er is more complicated than that for Tb-Ho because of the difference in 4f charge densities and consequent single ion anisotropies of the constituent metals. ~Sc I -. "~'-. The TN curve extends out to 75% Tm (to the vicinity of area marked B) where difficulties relating to finding magnetic order are encountered. The diagram shows a CAM plus helix region between 80 and 100% Er and a small region where the Er CAM structure alone is found. "-. 89. 20 I 30 I I i I the other.% involves Tb moments on a cone with an angle from the c-axis of the order of 80-85 ° and the Er moments on a cone with an angle from the c-axis of about 30°.. 89..% Er where complications arise.~. _ C 40 \ L u "..""-. according to an interpretation of NMR data of Sano et al. (1970) for several Tb-Ho samples are in good agreement with the results given here.5 K for pure Tb so that planar ferromagnetism disappears . In a similar fashion the curve for Tc extends rapidly downward from 219.. ". The TN data fall on a relatively smooth curve across the system out to about 90at. The planar helix structure of Tb has to compete with the c-axis modulated (CAM) structure of Er.RARE EARTH METALS AND ALLOYS 240 277 I I x I I I I I TERBIUM ALLOYS I i 200 I. The magnetic phase diagram for Tb-Tm published by Hansen and Lebech (1976) is shown at the bottom of fig. ~.. Magnetic phase diagrams for Tb alloyed with Y. (1965) and Child and Kdehler (1966). and Sc. At low temperatures the conical structure shown for Er content above 50at. In the case of Tb-Ho the N6el points T~ go linearly from one element to the other but the curve for Tc has to reflect the fact that the planar ferromagnetic phase of Tb has to suffer a marked change to arrive at the low temperature conical ferromagnetic structure of Ho. The out of plane ferromagnetic phase observed at high Ho content at low temperatures seems to be in order.120 80 erro \\\ \\\ Helix "-~ ".. After Child et al. . 88. *-... O . 160 ~ Cone • ~.. 120 CAIw 8 0 . --~T_~ ..__ I i' _ TERBIUM ALLOYS .~__~ +Helix CAe... 0 Tc\ Ferro Helix ~ . Dy base alloys As in the case of Tb the element Dy has helical and planar ferromagnetic phases..~.~ . 40 . 40 0 +H. 5.40 g 160 _ ~-120 80 \Tc ... Er and Tm. ~ Helix I I I I I I I 200 -160 IDU " " . . the N6el point TN and Curie temperature To are more widely separated and this affects the appearance of the magnetic phase diagrams in . 200 \ 160 120 80 ~TN ~ \ " / +SAM~/.. Er. X~x \ \ -"-~ "~'~ ~r - I /r "~/ 0 ~..~ _Ferro ~'---~T.. After Hansen and Lebech (1976)for Tb-Tm alloys.% Tm with a very small adjacent area in which the CAM plus helix magnetic structure is found.. However. - _ p B O o S n ~ B la s a l 240 c ~ Helix ~ --" 120 Ha .. Magnetic phase diagrams for Tb alloyedwith Dy... which is close to the magnetically inhomogeneous area marked A.. ~ Helix .. 89.4.... Tm . LEGVOLD [-. 200J= ~ 240- 2401.~ A "~'~ ~" "-~'"'1 B Fdl'ri I I I I I0 20 50 40 50 60 70 80 90 I00 ATOMIC % SOLUTE Fig. ~ Basal Plane Ferro 200 \ o. There are also small regions at the Tm rich end in which the CAM and ferrimagnetic phases of Tm are found... for concentrations of Tm higher than 20%. ~ ° n ' . After Koehler(1972) for Tb alloyedwith Dy...80 ! .278 S..~.. At low temperatures a double cone plus helix phase (Tm varies from 9° to 13° from the c-axis and Tb varies from 86° and up) is found which extends from about 35 to 70at. Ho. Ho.CA& 120 80 240. . ._. ..... . 80 401 :_..... ..% Dy in Ho. . and Y. "---. ... (1977). .... 80 ~x.. The data are again from the work of Koehler (1972) modified to accommodate the results of Fujiwara et al.. .... 90 the magnetic phase diagram for Dy alloyed with Ho is shown as determined from the data of Fujiwara ct al.. oJ-. ..o go 7'o 8o ' Atomic% Solute go I00 Fig.0 Planar ~/-'--Ferro Dy lO 20 3'o 4....... .. Helix I I I I i I I I 120 / Dy Ho 40 f" Ferro 0 ~-~ '-. Y 4. .... .... . 90. Helix"IN .._. " . (1965) for Dy-Y........ Magnetic phase diagrams for Dy alloyed with Ha.Er C/~F....RARE EARTH METALS AND ALLOYS 279 which the helix is dominant. Tc \ Planar 4. (1977) for Dy alloyed with Ha.. . . + Helix f . .. Er and after Child et al.. CAM ~\ J CAM ~ . ... ..j I Plnnnr ~ \ ' // //~Helix + CAM 160[. At the top of fig. .Dy ~ Helix ~. Er. Dysprosium Alloys TN ... . A small region on the lower left shows the planar ferromagnetic phase of Dy and a small area on the lower right shows the conical ferromagnetic phase of Ho which extends out to the left to about 10at. . Tc 120 .. . . . Helix TN . Next on the figure is the diagram for Dy alloyed with Er..° ' . The Ts data fall on a line extending from 179 K for Dy toward the 85 K N~el point of Er with a departure from the line at 90at. After Koehler (1972) and Fujiwara et al... Tm...0 -f/~/Ferr° 0 16o :" Tm ~ J] (Estimated)' Cone +H e ~ .. .. The N6el point data fall on a line from 179 K for Dy down to the 132 K point for Ho.. ... (1977) and of Koehler (1972). " TC Corn 160 120J -Dy J~.Tc ... T.% Er 160[ k ------4__ ..20 [ D_ y " " .. A smaller region of planar ferromagnetism at the lower left is compatible with the trend from Er to Tm to Y in the Tb phase diagrams. 91. The estimated phase diagram shows TN going nearly linearly from the Dy N6el point to the 58 K N6el point of Tm with a slight change at the Tm rich end where the CAM phase of Tm takes over. 90 is the Dy-Y magnetic phase diagram based on data of Child et al. On the lower right of the diagram there is a region where the helix plus CAM coexist and a region at low temperatures where the stable magnetic structure is the conical ferromagnetic phase (a double cone phase with Er moments on one and Dy moments on the other).5. Even so the helix form favored by Ho dominates the diagram. Metallurgy difficulties with Tm leaves the Ho-Tm phase diagram to the best estimate approach which is found in the middle of fig. The Er rich end at high temperatures has the c-axis modulated phase starting at about 80% Er. Then there is the mixed region of the helix plus the CAM form. At the lower left of the diagram the planar ferromagnetic phase of Dy is again found. 91. The planar ferro region is estimated but is probably close. There is little doubt about the position of the TN line on the basis of the other diagrams but the cone and ferri phases at low temperature are probably in error. The CAM and CAM plus helix phases on the lower right of the diagram seem reasonable when Ho-Er and Ho-Tm are compared. there was a sample at 5at. LEGVOLD where the c-axis modulated moment phase of Er takes precedence over the helix favored by Dy. The compatibility of Ho and Er suggests that Ho and Tm might give the cone range shown. 5. Since both Ho and Er have conical phases at low temperatures this feature was not unexpected. is shown at the top o f fig. At the bottom of fig. published by Koehler (1972). . and these have different ordering temperatures. (1965). It is interesting that the Tc for the conical ferro phase reaches a value almost twice as high as for either one of the pure elements at the concentration midpoint.% Y in Dy for which the Tc point was not seen. This set the right hand limit for the planar ferro phase which certainly exists for small Y concentrations. Then on the lower right the CAM and ferri phases of pure Tm should be expected to carry over to about 10% of Dy in Tm. The N6el point curve is slightly concave downward and heads toward zero for Y. Ho base alloys The phase diagram for Ho alloyed with Er. A small CAM plus helix region at low temperatures is postulated at the middle concentrations because this phase is found in the Tb-Tm diagram. All across the bottom of the phase diagram it is seen that the cone structure exists. The N6el point curve extends from 132 K for pure Ho and is slightly concave upward as it approaches the 85 K ordering temperature at the Er end of the diagram.2~ S. Data on Dy-Tm alloys are unavailable so an attempt has been made to show what might be expected on the basis of the Tb-Tm phase diagram and the general patterns for these systems which seem to emerge. 91.. 40 20 0 I0 NLE °l I I I I I 20 30 40 50 60 70 ATOMIG % SOLUTE 80 I 9O I I00 Fig. according to K a w a n o and Achiwa (1974).. (1965) for Ho-Y. .Y alloys are s h o w n at the b o t t o m of fig. .-La Helix "'-. Outside the b r o a d helix region only a small p o c k e t of a conical ferromagnetic structure at the lower left of the diagram is p r o p o s e d in the a b s e n c e of data there.I 120 I00 I I I I I I I I gSO ~ 60 40 2O 0 120 I00 HO He... and after Kawano and Achiwa (1975) for Ho-La.. T h e c u r v e f o r TN drops m o r e precipitously for the L a alloys than f o r the Y alloys.. after Child et al. Helix // Er /" / Helix +CAM ~ / "-.q. 91..L a alloys up to 16at."'Y y •-• ".. Also shown in the lower part of the figure are data of K a w a n o and Achiwa (1975) f o r Ho--La alloys. GONE 0 .% Ce. After Koehler (1972) for Ho-Er. //+Helix I I ~.. T h e TN and Tc points for Ho--Ce alloys arc nearly coincident with those for H o . Tm and Y.RARE EARTH METALS AND ALLOYS 140 120 I I I I I I I I I J B 281 100 -Ho 80 p- 60[ 4O 20 "" . (1965) data for H o ./~AM . Tm (Estlmoted) Tc II I I I ~1"~ I ... Magnetic phase diagrams for Ho alloyed with Er. T h e Child et al...~ = ~TN 80 P" 60 HO "..x ""'~-. . . LEGVOLD 5. C-AXIS Modulated .o 80 60 ~ Er I~-. .. .. . At the bottom of fig.. . l t l Y . Upper part: magnetic phase diagrams for Er alloyed with Tm and Y. .2 L i F . Just below TN is the c-axis modulated phase of pure Er which borders the CAM plus helix of the basal plane components. i i I i i i i i i 80 1 . A small cone phase characteristic of pure Er is shown at the lower left. . C-AXIS I l Modulated l -'"-" . . Lower part: magnetic phase diagrams for Tm alloyed with Y. I I0 20 30 Atomic % Yttrium 40 50 60 70 80 90 I00 Fig. .. C_AXIS-.. .20 k. T-.dl . "-. " " ... N.... 80 I 90 I I00 Atomic % Solute Tm-Y Alloys 60 . . 92. .282 S. .. "'-... .. The N6el temperature will most likely follow a nearly linear curve from the 85 K point of Er to the 58 K point of Tm as shown... "''--. 92.. The conical phase has to merge with the ferrimagnetic phase characteristic of Tm at the Tm rich end. . .. After Child et al. (1965). I .. .. 20 0 Paramognet '--r'~ Tc 1 I . . .[ . . " TN - Erbium Alloys i..'X~ ern i I . ~ 4 0 1 . .... The regular TN curve which extends from the 85 K point for Er extends downward and heads toward zero for pure Y as should be expected. (1965) for Er-Y._ I I I i ~--Cone I ~I I I I0 I 20 i 30 I 40 I 50 i 60 i 70 I. .m : I ~ I i T I ... only Er-Tm in that category remains. ... ..Component Helix 0 -~"-----. 01. . . ..x (Est. Paromagnet 60F t~ r Y -'--. . .. .... . T.CAM He. A CAM plus helix region characteristic of Er at the lower left along with an extended cone region are conceivable. .6. . .' T. After Child et al. (1965).."'" -I I I 40 c A # " . Er base alloys Since all of the earlier heavy elements have been discussed.mat. T m . An estimate of the phase diagram for this system is shown at the top of fig. . 92 the magnetic phase diagram for Er alloyed with Y is given as determined from the data of Child et al. . 5. (1975) for Nd-Pr. Light rare earth alloys Some light-heavy rare earth alloy studies have been covered in the discussion of the heavy elements. (1975) investigated several single crystals of Nd-Pr and found the results shown by the top curve of fig. The N6el points follow a linear pattern and tend toward zero for pure Y.'2. b) for Nd-La and after Lebech et al. ~ v \ 4 0 / 0 NO i I 20 f I 40 I I 60 i I 80 i I00 CONCENTRATION ('/o) Fig.Z Tm base alloys The only Tm base alloy left for display is the T I n Y diagram shown at the bottom of fig. Then for Pr concentrations above 75at.8. 92. (1965) on 45% Y in Tm and 85% Y in Tm. Magnetic phase diagrams for Nd alloyed with La and with Pr. . Lebech et al. as mentioned in the discussion of Pr earlier.RARE EARTH METALS AND ALLOYS 283 5. 93. From magnetic and electrical resistivity measurements on several poly- 20 ' l ' I • • ' I ' RESISTIVITY SUSCEPTIBILITY I ' I.% the N6el point drops precipitously toward the 0 K point actually found in pure unstrained Pr. Shown at the lower left is a smaller pocket of the ferrimagnetic phase of pure Tm which is expected to exist for Y concentrations up to about 10%. Two intra-light rare earth investigations which have been reported give the ordering temperatures of Nd alloyed with Pr on the one hand and Nd alloyed with La on the other. It is based on data of Child et al.6 K ordering temperature for Nd the N6el temperature drops nearly linearly with Pr concentration as though Pr had a N6el point of 10 K. After Petersen et al. All other Tm alloy information is covered in the preceding phase diagrams. 93.. (1978a. Starting at the 19.- z 8 ° ~ l ~ oo° "-. %.%. d~) + K°Y°(O.% La in Nd only one transition was observable. .2~ S. d#) + K~[Y~(O. The coefficients KS have a complicated temperature dependence which has been described by Callen and Callen (1966). K°(T)= K°(0)tr ~° and K°(T)= K°(0)tr 21 so the temperature dependence arises indirectly through the basic Brillouin function temperature variation of the reduced magnetization. The magnetic anisotropy energy consists of the crystal field energy expressed in the appropriate macroscopic form. The experimental values of the anisotropy constants are shown in table 5. Magnetic anisotropy energy and magnetostriction The large magnetic anisotropy of the hcp heavy rare earths has its origins in the asymmetrical charge distribution of the 4f electrons as shown in fig. There is a considerable spread in some of the coefficients reported. LEGVOLD crystalline alloys of Nd with La. If the coefficients K ° and K ] are positive the magnetic moments lie in the basal plane as in the case of Tb and Dy. for hexagonal lattices the equation generally used is H. ~) are normalized spherical harmonics and 0.~-I(cr) is the inverse of the Langevin function and ~r is the reduced magnetization M(T)IM(O). (36) Here the YT'(O.and a-axes of the hexagonal lattice.~-l(cr)] (37) where ft+n/2 is the reduced modified Bessel function of odd half integer order. 6. ~b are the polar coordinate angles of the magnetization relative to the c. If K ° and K ° are of opposite sign and about equal in magnitude the easy direction is on a cone around the c-axis. 4~) + K°Y°(O. Tm) the magnetic moments are aligned along or near the c-axis. Petersen et al. If these coefficients are negative (Er. 7. (1977) found two ordering temperatures for La concentrations less than 50at. As noted in the table the only data on Tm comes from dilute alloys and are likely lower than the Tm metal would show. If there is a basal plane component of the magnetic moments then the sixth order terms determine the easy sixfold direction. The system appeared to be inhomogeneous magnetically for La concentrations above 50at. They give the expression KT'(T) = KT'(0°)]~+l/2[. The temperature dependence of the magnetic anisotropy constants of Gd has been investigated by Mihai and Franse (1976). 92 and show that above 50at.&)]. At low temperatures the dependence on cr expected is K°(T) = K°(O)tr 3. ~b) + Y~-6(O.t = K~Y°(O. They used a torque method along with a magnetic anisotropy energy expression in the form . Their data are at the bottom of fig. 07 . . 0.27 0. . (1968) McEwen (1978) Feron et al.~.~ ~ + ½A~'2[(aJ3x + ay/3y) 2 .1.~z 2. . (1975) Graham (1967) ~4 .1 ~)](t3~2 + t ~ ) + [.~ ~.4 . - Holmium Erbium Thulium Gadolinium 1. For a more detailed discussion of magnetic anisotropy energy see McEwen (1978).1.a x e s . T h e o b s e r v a t i o n o f g i a n t m a g n e t o s t r i c t i o n in r a r e e a r t h s is d i r e c t l y r e l a t e d t o their magnetic structure and the magnetic anisotropy energy. cr3 . (1968) Cock (1976) Jensen (1976) Touborg and I-I~g (1974) Feron et al.19 0. . EA = K0 + K2 s i n e 0 + K4 sin 4 0 + K6 sin 6 0 c o s 6~b + . T h e i r r e s u l t s f o r C l a n d C2 a r e s h o w n in fig.08 0.30 .0 1] / L 2 = [A?'°+A?'2(ot 2 . (1970) Houman et al.1 a" ~15 - Reference Feron et al.4 -2. -3.1 3.( K 2 + / ( 4 ) a n d 2(?2 = / ( 4 . (1970) Rhyne et al. (1970) Mishima et al. .14 o'" K° 5.4 .23 .(aJ3y .6 5. 33. y a l o n g b.o+ .7 2. An analysis of s i n g l e i o n e f f e c t s f o r h e x a g o n a l c r y s t a l s h a s b e e n m a d e b y C l a r k e t al. .5* 0. 94.1 -3* 0.1 -6* -0. .21 -0. The coefficients determined from paramagnetic susceptibility anisotropy data are also considerably lower than results of the more direct measurements.. (1968) Rhyne et al.7 -30* -0. (40) H e r e fli a r e t h e d i r e c t i o n c o s i n e s o f t h e l i n e o f t h e s t r a i n m e a s u r e m e n t and the . .4 2. K° . (1975) Rhyne and Clark (1967) Roeland et al. .7 -4. a n d z a l o n g c ) f o r t h e m a g n e t o s t r i c t i o n c o r r e c t t o s e c o n d o r d e r in t h e c o s i n e s ai o f t h e m a g n e t i z a t i o n is AL/L . .~.a J 3 x ) 2] + 2A "2(otd3~ + ay~y)a.0 6.0006 26 - * The data for thulium are from dilute alloy measurements. (1970) Rhyne et al.1. In the cases of Th and Dy the constants found this way were about one third the values found for the pure metals. (38) w h e r e 0 a n d tk a r e t h e p o l a r a n g l e s o f t h e m a g n e t i z a t i o n r e l a t i v e t o t h e c r y s t a l c a n d a . The temperature dependence via tr" is also given where available Element Terbium K~ 90 87 76 Dysprosium 87 78 87 66 32 -9.RARE EARTH METALS AND ALLOYS 285 TABLE 5 The zero Kelvin magnetic anisotropy energy constants of eq. All values are in units of 107 ergs/cm 3 (106 J/m3). 2.7 3.1 . (1963) a n d t h e i r e x p r e s s i o n in c a r t e s i a n c o o r d i n a t e s ( x is a l o n g a. (1975) Shepherd (1976) Feron et al.2(.014 . F o r t h e t o r q u e d a t a t h e y f o u n d it c o n v e n i e n t t o u s e L A = C1 sin 2 0 + C2 sin40 (39) w h e r e LA is t h e t o r q u e a n d C1 = . - K~ 0. 3 7. Clark who gives the expression for AL/L out to sixth order in the direction cosines.. L E G V O L D ! u u E 0.6 c) ~'2 ~t.4 2. A?° and A~"° are related to anomalous thermal expansion and exchange magnetostriction. In table 6 the available magnetostriction coefficients are given.4 -0. a n d C2 o f e q .2 A2 . b) A f t e r R h y n e (1972). A~'2 represents shear in going along the c-axis.3.5 °) .5.E.. A?2 represents dilatation along the c-axis.3 4.i o n t h e o r y .3 7.2 . It is noted that in some cases the coefficients can only be determined in combinations and are reported in this fashion.2. c) E x t r a p o l a t e d f r o m p a r a m a g n e t i c r a n g e u s i n g s i n g l e .0 1ffi.0 1 ~ a. The temperature dependence of magnetostriction coefficients is like that for the magnetic anisotropy constants so has the form A(T) = A(0)~+i/2[A°-l(cr)].1 =) 0.286 S.0 *) 5.8 -2." must be determined experimentally.2 . A~2 represents a distortion of the hexagonal symmetry into orthorhombic (circles go to ellipses). (41) Since the magnetic moments of Tb and Dy are essentially constrained to lie in the basal plane at low temperatures it has been necessary to go to higher order terms in AL/L. coefficients Am. (39) f o r G d v e r s u s t e m p e r a t u r e .14 . (1976).0.. 0 c) - 0.0 . 94.11 8.13 9 .2. TABLE 6 M a g n e t o s t r i c t i o n c o e f f i c i e n t s a t z e r o K e l v i n in u n i t s o f 10 -3 Element G a d o l i n i u m a~ T e r b i u m b~ D y s p r o s i u m b) H o l m i u m b) E r b i u m b) A?2 0.9 + 0.1 1.3 A 2 j[7. M a g n e t i c a n i s o t r o p y e n e r g y c o n s t a n t s C . For details see the chapter of the present volume on the magnetostrictive rare earth-Fe2 compounds by A.2 A*. It has also been necessary in these cases to use theoretical considerations to make extrapolations of paramagnetic data down to low temperatures to obtain some of the magnetostriction coefficients. .. The coefficient A?2 represents dilatations in the basal plane.02 15. A f t e r M i h a i a n d F r a n s e (1976).5 ! I 0 I00 200 -.1 6.7 9.5 - ") A f t e r M i s h i m a e t al.2 AI --3AI ~ .---~T(K) 300 Fig.5 - . 95.--r"I i i I I I I I I I I I " 160 200 24.~-I(tr)] and those for A ~. 0 4.4f512[~-~(cr)] and those for A v." . (1976). This is expected because Gd has the half full 4f shell and is spherically symmetric. After Mishima et al. The strain modes are shown in fig. The data for A*'2 gave a reasonably good fit to 9. 0 Ioo aoo .6 6 n. T h e data for A ~a gave a good fit to 8.4 \ \6 o ×.RARE EARTH METALS AND ALLOYS 287 In fig. 96. (a) Magnetostriction coefficients for Od versus temperature.14i9/2[~-i(cr)]. 96.I./3 ×'~" - o 1. o I-- [ 2.' s o ~ ~ I. After Rhyne and Legvold (1965a)..~-. Magnetostriction coefficients of Tb extrapolated to zero applied field versus temperature.I00 1 l ." ~ .50 . 97.~. (1976) is shown.w' el.150 x~ a ' 1 b Fig..o I-- 0. 95b. 95a the temperature dependence of the coefficients for Gd found by Mishima et al.4 were close to 1.4 to -2.715/2[.0 280 T(K) Fig. (b) Strain modes associated with the hexagonal magnetostriction coefficients.4II3/2[Le-l(~r)]. I.- ~.. In the case of Dy the results of Rhyne (1965) c a m e out as shown in fig.0 80 120 .8 7 -0~ . Here and in the table the magnitude of the coefficients is clearly an order of magnitude lower than for Tb or Dy.." ~o 15o 0 ~" I00 U 5O Z 0 V-0 Gd 1 . The data of Rhyne and Legvold (1965a) for Tb is displayed in fig.6 ~ t~. 2." _--7-5. Thermal contraction is indicated as T decreases from room temperature and then magnetically induced strains appear as T goes below the 132 K N6el point.O av2 w o o E 3 z 2 9 F-. / I F ~.O I 200 a2 3 Xi ' l 240 T(K) Fig. Principal strains for Ho versus temperature. 98. ~ Dy H=30 k O c _ a.--~ L ~ ~ S./" "~"X=2OkOellb I I I I I I -" I 0 40 80 120 160 2 0 0 2 4 0 2 8 0 T(K) Fig.2 -4.Xllb \ • Gllc \ ii/ /~ " ¢= ~. (1967).I ee" Fz -I -2 0 I 4.__L..o /\ . Z "' 6 5 4 ~ .. (1967) for Ho are shown in fig.0 -0.2 "4. Data for the strain gauge G along the a-axis are read on the right hand ordinate and data for G along the b.b .¢~-A i IG.o.2 . For 5.b ///..and c-axes are read on the left hand ordinate. L E G V O L D I I I i I-.0 .I..HIIb / 4-3.7" L.° i ." .b.0 t 80 I 120 I 160 a.. 98. After Rhyne (1965).8 "1..o . A ~..4 Glib H-o " z < " -3.. Magnetostriction data of Rhyne et al..8 1--..8 / \.0.6 41 z n.0 --// % 1 l.\ O_ 2.4 \ 4.6 -2.8 o.J_G.T.// A V G. After Rhyne et al.6 -6...4 "'.288 7 _--..GIIo.o.4 <~ . .~ .--u') 0.l-'-H.6 4. Magnetostriction c o e f f i c i e n t s of D y at 30 kOe versus temperature.8Hllo/I \ I -4. G.. 97.._ q 0. . . 99... -'.I -= Z n. The c. o-Ax.and a-axis strains of Er versus temperature..=~o~ . -0.8 .RARE EARTH METALS AND ALLOYS 289 Er the magnetostriction data along a. .. i .4 - -3. O0 -0.0 0 40 I 80 i 120 160 TEMPERATURE I I 200 (*K) I 240 I 280 I I Fig. I (3. .2 = o = ~ J -1 % 0. Their data with the strain gauge along the b-axis were like those along the a-axis./ n ~ n / H=30 KOe II c-AXIS -3. .') x -2. Again thermal contraction is indicated down to the 85 K N~el point. .8 .-. H=30 KOe II c-AXIS 1-.6 .6 J / TT. 99.8 .s / I ° -2. After Rhyne and Legvold (1965b).1~ i 'J') ~. -I.and c-axes of Rhyne and Legvold (1965b) are shown in fig.~ ° H=oER -~ o ~ .2 - -4. .4 .0 ER o H=O n H=50 KOe II b-AXIS t. . Phys. Kevin R. J. Acknowledgements The author is grateful to John Queen. for her forebearance throughout the project.. J. Partington. 800. 5086. Baer. S. Blackstead. Sailsburgy for their help in the preparation of the figures. Shanks. J. This work was supported by the U. to Roy L. . Bagguley. 1973.S. 1976. 1209.A. 1973. Rev. Arajs. 1967. F 5. This concludes the d i s c u s s i o n of magnetostriction. 1968. Phys. E. L39. Phys.L. Miller. and Dennis W.'5 (K) ~o as TEMPERATURE Fig. 1976. J. 325S. B 13. 167. S. Phys. Materials Sciences Division. Atoii. 1966. 1324.. Phys. Aliscio. Arais. 303. After Ott (1975). 40. Burce Harmon of the Physics Department for help on the manuscript.R. Dunmyre. B 13. S. B. Kawano. J. to Janet Hartman for typing the manuscript. 1975. Rev. Phys. Phys. Z. and D. 1978. 1047. Busch. Naturforsch. The magnitude of the magnetostriction is seen to b e about two orders of magnitude lower than for Tb.. Andersen. 313.F. and S. K. Lett. B 6. Department of Energy. Rev. Loucks. and T. Solid State Commun. Ohmedo.b . 162. and H.12 u E b ~4 C. N. . Suppl. Lopez and C. and P. References Achiwa. D. In fig. P. Anderson. Phys.P. 14. Dunmyre. 1856. to Karl Gschneidner. Bak. LEGVOLD ~a 0 I-- 16 z _o i.S. Flukiger. and G. Rev. Japan 3S. 1974. Lavona.. 1973. 551. and B. Arajs. and Berni Evans of the Rare Earth Information Center for their help in the literature searches. 1960. M. Akhavan. Lebech. 31. and finally to his wife. Bak.E. Rev. Magnetostriction of Pr at 10 kOe (1 T) versus temperature. Bucher.K. A. J. Y.M. Rev. F 3. 1972.AXIS o . Mukamel. Phys. L. 31.2~ m S. Jr. and Prof. Malta. Phys. and D. Paul Burgardt. M. and G.R. Longinotti and R. Soc. P. Less Common Metals 12. and G. 21.D. 100. Office of Basic Energy Sciences. Thomas Petersen. Appl. O. Andres. Lett. 35. 100 the magnetostriction data of Ott (1975) for Pr indicate that the 10kOe (1 T) applied field induced a magnetic moment in this normally nonmagnetic singlet state metal.S. Phys. Lett. M.E. 1977. J. 1967. R.W. Wollan. Phys. Bieany and W. 104.. F. H. J. 156. Sinha. Prec. 1896. 1970. Phys.. J. 1039. 189.. Arajs and J.W.J. 1979. J. Lander. Burgardt. Soc. Naseau and P. 1961. Malta.M. 1957.A. Darnell. part A (Academic Press. 1977. Rev. Dernier. Lander.) Cable. 20.A. 118. Callen. Legvold. Bates.. de Gennes. to be published. 138..G.. R. 165. F.C. 2995. Dimmock. L. Rev.A. Phys.R. 564. Bucher.W. K. 1968. B.. 1963. L. and S. P. J. 1964. Pauthenet. J. R. Curry. D.J. Suits. J. B. Culbert.. 57. P. S.H. Duthie. P. Rev...C. D. in Solid state physics. 3978. Tanner. Phys. Phys. A.. J. 1975. Phys.O.. Brun. Phys. and W. Rev. Van Vleck. Loasby. Phys. Rev. New York) pp.. Burgardt. Loucks. London B 68.R. and F. 859. 24. J. H. Spedding. Hug and R.J. Child. 971. R. C 9. Brun. C. 14. B 14. Dimmock. Phys.N. Jones and K. Forgan.R. Phys.M. 163. 1967. 122.. A. Rev. Leach and R. 1976. Freeman. 750. Legvold. 34. 23. 30. Koehler. J. Jr. J. S.J. Wollan and J. G. 13. Beaudry and Gschneidner 1978 Bleaney. S... Roy. .. Chechernikov. Low Temp. 61.W. B. Ehrenreich. C. Rev. Met. 1971. Solids 27. 1976. 627.. 1353. Phys.J. Ames. and E. University of Amsterdam. Koskenmaki. 3911. Corner. Angew. Lett. 1969.C. Phys. 130.H. 1976. 1970. Phys. Phys. and J. Elliott.. 1. E. 141. Finnemore. A. Wedgewood. 753. Andres. Peck. Phys.M.G. Prec. Magnetic properties of the rare earth metals (Plenum Press. 1958. Fleming. 1524. Z. Callen. 1968. 1970. Koehler and M. B2. Phys.G.D.O. Legvold and F. Jayaraman. J. E. Koehler. H. H. Legvold and F.. G. Blandin. SJ. 1976. and S. 1966. Phys..S. W.F. 1295. Cooper. 1965.P.D.N.J. Andres. Hayes.W.O.I. 1955.. Vyrostek. 1968.-W. Phys. Amsterdam). 1978 Burgardt. 247. Buehler and K.L. Beaudry and B. Rev. Phys. Legvold. T. D. Bozorth. Fiz. Phys. 37. Spedding. Curry. Rev. J.V. M. Rev. 50011. 1968. (eds. 140. Appl. 1972. G. H.H. 1972.R..D. Cable. Cracknell. 444. Cooper. 26. Phys. Legvold. Iowa. Cable.O. Burgardt.M. and Metallored 13. thesis. 1971. 38. Prec.M. Lett.) Chen. 1979.. Das. 1024. 176. 100. S. Darnell. 3. Jr. Phys. Phys. 13. chapter 2 of Magnetic properties of rare earth metals (editor R. 1976.P. B 14. Phys. C. Rev. 339-341. thesis. Adv. Phys. B 1. Lett.W. Bozorth. Behrendt. Schmidt.R.. P.R. E. 1963.H. Appl. Bozorth and B. and K. Moorman. (London) A 247.M. 1970. and S. 1963a.H. Coqblin. 134.M.. K. 1251. 1968. Legvold.H.W. Phys. S. H. Feron. 1974. 418. Liu and T. Phys. D. T. 1964. Elliott. S. 17. Callaway. 1969. Physica 86-88B.. 1966. 1965.. C. W. V. B. 1963. R. Appl. N. Harmon. Rev. Rev.. 1836. 701. 1825.O. Cock. Lctt. London). New York. Soc. 132.C. Child. Stassis and T. P.. J. Adv. B. R. B 13.R.K. Rev. K. Phys.N. Stringfellow and K. Chem. 106. L. |366. J. Edwards. ed. 723. K. 174.O. Legvold. 21. and S. J. Pettifor.G. and J. Rev. P. S. E. S.A. A. and Metallogr.. 1962. J. 1963b.R. 1098. B.RARE EARTH METALS AND ALLOYS Baker. Muirbead. Rev.. Phys.H.O. Clark.C. Burgardt. (London) 81.B.J. and G.K. Rev.. Phys. (Lifshitz point of Gd Tb. C. 377. Magnetism and metallurgy 291 of soft magnetic materials (North-Holland. 1977.K. Maita.O. Wakabayashi. AIP Conf. Iowa State University. Colvin. and D.S. 458. R. 38. B. 1966. E. Rev. Phys.. Edwards and F. Capellman.R. DeSavage. (Phys. R. Lctt. unpublished Ph. Rev. 1960. Phys. W. Acad. 117. R. Rev. 1493. Phys. 1967.V. P. Curry. 846. Boys. E.R. A1655.L. and B. Nassau. 1260. 1976. 281. Cooper. to be published.. 22. New York and London). 4219. Rev. Quantum theory of the solid state. Gschneidner.P. Phys. 5. Wollan. Spedding. Phys. Rev. Bucber.J. and A. 733. Sci. Prec.A. Seitz and D. 1960. Appl. Turnbull) eel. Rev.G. 35. Eiliott) (Plenum Press. R. Rev. Met. Gschneidner. G.L.. D. Taylor.H.. J.C. and E. Taylor. F. USA.. Phys. Chu. Wilkinson.G. 1271. Soc. and A. Bozorth. 292 S. LEGVOLD Harmon, B.N. and A.J. Freeman, 1974b, Phys. Rev. B 10, 4849. Hed6n, P.O., H. L6fgren and S.B.M. Hagstr6m, 1972, Phys. Stat. Sol. (b) 49, 721. Hegland, D.E., S. Legvold and F.H. Spedding, 1963, Phys. Rev. 131, 158. H~g, J. and P. Touborg, 1974, Phys. Rev. B 9, 2952. Hornreich, R.M., 1979, J. Magnetism and Magnetic Mat., Proc. of ICM 1979(paper 7AII, to be published). Houman, J.C.G. and R.M. Nicklow, 1970, Phys. Rev. B 1, 3943. Houman, J.G., J. Jensen and P. Touborg, 1975a, Phys. Rev. B 12, 332. Houman, J.G., M. Chapellier, A.R. Mackintosh, P. Bak, O.D. McMasters and K.A. Gschneidner, Jr., 1975h, Phys. Rev. Lett. 34, 587. Hsieh, Y.Y. and D.A. Pink, 1972, Solid State Commun. 11, 783. Hntchings, M.T., 1964, Solid State Physics 16, 227. Isci, C. and S.B. Palmer, 1977, J. Phys. Chem. Solids 38, 1253. Jennings, LD., E.D. Hill and F.H. Spedding, 1959, J. Chem. Phys. 31, 1240. Jennings, L.D., E.D. Hill and F.H. Spedding, 1961, J. Chem. Phys. 34, 2082. Jennings, LD., R:E. Miller and F.H. Spedding, 1960, J. Chem. Phys. 33, 1849. Jennings, L.D., R.M. Stanton and F.H. Spedding, 1957, J. Chem. Phys. 27, 909. Jensen, J., 1976, J. Phys. F 6, 1145. Jepsen, O. and O.K. Andersen, 1971, Solid State Commun. 7, 731. Jew, T.T., 1963, unpublished M.S. thesis, Iowa State University Library, Ames, Iowa, 50011, USA. Johansson, B., 1974, Phil. Mag. 30, 469. Johansson, T., B. Lebech, M. Nielsen, H. Bjerrum Moiler and A.R. Mackintosh, 1970, Phys. Rev. Lett. 25, 524. Johansson, T., K.A. McEwen and P. Touborg, 1971, J. de Phys. (Paris) Suppl. 32, CI-372-4, 372. Kasuya, T., 1966, Magnetism, vol. IIB (eds. G.T. Rado and H. Suhl) (Academic Press, New York) p. 215. Kawano, S. and N. Achiwa, 1974, J. Phys. Soc. Japan 37, 569. Kawano, S. and N. Aehiwa, 1975, J. Phys. Soc. Japan 38, 285. Kayser, F.X., 1970, Phys. Rev. Lett. 25,662. Franse, J.J.M. and V. Mihai, 1977, Physica 86-88B, 49. Freeman, A.J., 1972, ch. 6 of Magnetic properties of rare earth metals (ed. R.J. Elliott) (Plenum Press, New York, London). Freeman, A.J. and J.O. Dimmock, 1966, Bull. Am. Phys. Soc. 11, 216. Freeman, A.J., J.O. Dimmock and R.E. Watson, 1966, Phys. Rev. Lett. 16, 94. Fuji, H., Y. Hashimoto, A. Mishima, N. Shohata and T. Okamato, 1976, J. Phys. Soc. Japan 41, 1179. Fujimori, H., K. Goto and D.E,G. Williams, 1974, J. Phys. F 4, 2152. Fujiwara, H., H. Fujii, Y. Hidaka, T. Ito, Y. Hashimoto and T. Okamoto, 1977, J. Phys. Soc. Japan 42, 1194. Gerstein, B.C., M. Griffel, L.D. Jennings, R.E. Miller, R.E. Skochdopole and F.S. Spedding, 1957, J. Chem. Phys. 27, 394. Gerstein, B.C., F.J. Jelinek, J.R. Mullaly, W,D. Shickell and F.H. Spedding, 1967, J. Chem. Phys. 47, 5194. Graham, C.D., 1962, J. Phys. Soc. Japan 16, 1310. Graham, C.D., 1967, J. Appl. Phys. 38, 1375. Green, R.W., S. Legvold and F.H. Spedding, 1961, Phys. Rev. 122, 827. Griffei, M., R.E. Skochdopole and F.H. Spedding, 1954, Phys. Rev. 93, 657. Griffel, M., R.E. Skochdopole and F.H. Spedding, 1956, J. Chem. Phys. 25, 75. Gshneidner, Jr., K.A., and L. Eyring, eds., 1978, Handbook of the physics and chemistry of rare earths, (North-Holland, Amsterdam). See ch. 2, B.J. Beaudry and K.A. Gschneidner, Jr.; ch. 3, S.H. Liu; and ch. 6, K.A. McEwen. Gschneidner, Jr., K.A., T.-W.E. Tsang, J.H. Queen, S. Legvold and F.A. Schmidt, 1978, Proc. Conf. on Rare Earths and Actinides, University of Durham (England) July 4-6, 1977. Gustafson, D,R., J.D. McNutt and L.O. Roellig, 1969, Phys. Rev. 183, 435. Habenschuss, M., C. Stassis, S.K. Sinha, H.W. Deckman and F.H. Spedding, 1974, Phys. Rev. B 10, 1020. Hall, P.M., S. Legvold and F.H. Spedding, 1959, Phys. Rev. 116, 1446. Hansen, P. and B. Lebech, 1976, J. Phys. F 6, 2179. Harmon, B.N. and A.J. Freeman, 1974a, Phys. Rev. B 10, 1979. RARE EARTH METALS AND ALLOYS Keeton, S.C. and T.L. Loucks, 1968, Phys. Rev. 168, 672. Kirchmayr, H.R. and K.H. Schindl, 1966, Acta Phys. Austriaca 22, 267. Kiwi, M. and R. Ramirez, 1972, Phys. Rev. B 6, 3700. Kobayasi, S.-I., Fukuchi and S. Nagai, 1976, Solid State Commun. 20, 589. Koehler, W.C., 1972, ch. 3 of Magnetic properties of rare earth metals, (ed. R.J. Elliott) (Plenum Press, New York, London). Koehler, W.C. and R.M. Moon, 1972, Phys. Rev. Lett. 29, 1468. Koehler, W.C., J.W. Cable, E.O. Wollan and M.K. Wilkinson, 1962, Phys. Rev. 126, 162. Koehler, W.C., H.R. Child, E.O. Wollan and J.W. Cable, 1963, J. Appl. Phys. 34, 1335. Koehler, W.C., J.W. Cable, M.K. Wilkinson and E.O. Wollan, 1966, Phys. Rev. 151, 414. Koehler, W.C., J.W. Cable, M.K. Wilkinson and E.O. WoUan, 1967, Phys. Rev. 158, 450. Koehler, W.C., R.M. Moon and H.R. Child, 1973, AIP Conf. Proc. 10, 1319. Koelling, D.D., A.J. Freeman and F.M. Mueller, 1969, Bull. Am. Phys. Soc. 14, 360. Koskimaki, D.C. and K'A. Gschneidner, Jr., 1975, Phys. Rev. B 11, 4463. Koskenmaki, D.C. and K . A . Gschneidner, Jr., 1978, oh. 4 of Handbook on the physics and chemistry of rare earths, vol. 1, (North-Holland, Amsterdam). Lea, K.R., M.J.M. Leask and W,P. Wolf, 1962, J. Phys. Chem. Solids 23, 1381. Lebech, B., K.A. McEwen and P.-A. Lindgard, 1975, J. Phys. C 8, 1684. Legvold, S., 1979, Phys. Rev. B 19, 446. Legvold, S. and J.P. Beaver, 1979, Solid State Commun., tobe published. Legvold, S., B.N. Harmon, B.J. Beaudry, P. Burgardt, D.R. Younkin and H.W. White, 1977a, Phys, Rev. B 16, 4986. Legvold, S., B.J. Beaudry, J.E. Ostenson and B.N. Harmon, 1977b, Solid State Commun. 21, 1061. Legvold, S., P. Burgardt and B.J. Beaudry, 1977e, in Crystal field effects in metals and alloys (ed. A. Furrer) (Plenum, New York, London) p. 340. Legvold, S., P. Burgardt, B.J. Beaudry and K.A. Gschneidner, Jr., 1977d, Phys. Rev. B 16, 2479. Legvoid, S., R.W. Green, J.E. Ostenson and B.J. Beandry, 1978, Phys. Rev. B 18, Legvold, S., J. Queen, B.J. Beaudry and B.N. 293 Harmon, 1979a, J. Magn. Magnetic Mat., Proc. Int. Conf. on Magnetism (to be published). Legvold, S., P. Burgardt and B.J. Beaudry, 1979b, J. Magn. Magnetic Mat., Proc. Int. Conf. on Magnetism (to be published). Lewis, E.A.S., 1970, Phys. Rev. B 1, 4368. Lindelof, P.E., I.E. Miller and G.R. Pickett, 1975, Phys. Rev. Lett. 35, 1297. Lindg~rd, P.-A., 1976, in Magnetism in metals and metallic compounds (eds. J.T. Lopuszansky, A. Pekalski and J. Przystawa) (Plenum Press, New York) p. 203. Lindgard, P.-A., 1977, Phys. Rev. B 16, 2168. Lindg~rd, P.-A., B.N. Harmon and A.J. Freeman, 1975, Phys. Rev. Lett. 35, 383. Liu, S.H., 1978, ch. 3 of Handbook of the physics and chemistry of rare earths (eds. K.A. Gschneidner and L. Eyring) (NorthHolland, Amsterdam). Liu, S.H., R.P. Gupta and S.K. Sinha, 1971, Phys. Rev. B 4, 1100. Liu, S.H., P. Burgardt, K.A. Gschneidner, Jr. and S. Legvold, 1976, J. Phys. F 6, L55. Loucks, T.L., 1967, Augmented plane wave method (Benjamin, New York). Lounasma, O.V., 1964, Phys. Rev. 133, A219. Mackintosh, A.R., 1963, Phys. Lett. 4, 140. Mackintosh, A.R., 1971, J. de Phys. (Paris) Suppl. 32 C 1,482. Mackintosh, A.R., 1977, Physics Today 30, 23. Mackintosh, A.R. and H. Bjerrum M¢ller, 1972, in ch. 5 of Magnetic properties of the rare earth metals (ed. R.J. Elliott) (Plenum Press, New York, London). Mackintosh, A.R. and F.A. Smidt, 1962, Phys. Lett. 2, 107. Maezawa,K., K. Moil, K. Sato, Y. Saito and S. Wakabayashi, 1977, J. Phys. Soc. Japan (Letters) 43, 1815. Mannari, I., 1959, Prog. Theoret. Phys. (Kyoto) 22, 335. Mattheiss, L.F., J.H. Wood and A.C. Switendeck, 1968, Methods in Computation Physics 8,64. Mattocks, P.G. and R.C. Young, 1977, J. Phys. F 7, LI9. McEwen, K.A., 1978, ch. 6 or Handbook of the physics and chemistry of rare earths (exis. K.A. Gschneidner and L. Eyring) (NorthHolland, Amsterdam). McEwen, K.A., G.J. Cock, L.W. Roeland and A.R. Mackintosh, 1973, Phys. Rev. Lett. 30, 287. 2~ S. LEGVOLD Jr., T.-W.E. Tsang and J.O. Moorman, 1978a, J. Appl. Phys. 49, 2115. Petersen, T.S., S. Legvold, K.A. Gschneidner, D.W. Jones, D. Fort and B.J. Beaudry, 1978b, to be published. Queen, J.H., 1979, private communication. Rainford, B.D. and J.G. Houman, 1971, Phys. Rev. Lett. 26, 1254. Ramirez, R. and L.M. Falicov, 1971, Phys. Rev. B 3, 2425. Rath, J. and A.J. Freeman, 1975, Phys. Rev. B 11, 2109. Rathmann, O. and P. Touborg, 1977, Phys. Rev. B 16, 1212. Redner, S. and H.E. Stanley, 1977, Phys. Rev. B 16, 4901. Rhyne, J.J., 1965, Ph.D thesis, Iowa State University Library, Ames, Iowa, 50011, USA. Rhyne, J.J., 1972, ch. 4 of Magnetic properties of the rare earth metals (ed. R.J. Elliott) (Plenum Press, New York, London). Rhyne, J.J. and A.E. Clark, 1967, J. Appl. Phys. 38, 1379. Rhyne, J.J. and S. Legvold, 1965a, Phys. Rev. 138, A507. Rhyne, J.J. and S. Legvoid, 1965b, Phys. Rev. 140, A2143. Rhyne, J.J., S. Legvold and E.T. Rodine, 1967, Phys. Rev. 154, 266. Rhyne, J.J. and T.R. McGuire, 1972, IEEE Trans. Magnetics 8, 105. Rhyne, J.J., S. Foner, E.J. McNiff and R. Doclo, 1968, J. Appl. Phys. 39, 892. Richards, D.B. and S. Legvold, 1969, Phys. Rev. 186, 508. Roberts, L.M., 1957, J. Phys. B; Proc. Phys. Soc. London 70, 343. Roeland, L.W., G.J. Cock, F.A. Mueller, A.C. Moleman, K.A. McEwen, R.G. Jordon and D.W. Jones, 1975a, J. Phys. F 5, L233. Roeland, L.W., G.J. Cock and P.-A. Lindgard, 1975b, J. Phys. C 8, 3427. Rosen, M., 1968, Phys. Rev. 174, 504. Sakamoto, S., J. Nakai and Y. Nakagawa, 1976, J. Phys, Soc. Japan 40, 686. Sano, N., K. Shimizu, Y. Aoki and J. Itoh, 1975, J. Phys. Soc. Japan 39, 93. Schirber, J.E., F.A. Schmidt, B.N. Harmon and D.D. Koelling, 1976, Phys. Rev. Lett. 36, 448. Schirber, J.E., F.A. Schmidt, B.N. Harmon and D.D. KoeUing, 1977, Phys. Rev. B 16, 3230. McEwen, K.A., P.F. Touborg, G.J. Cock and L.W. Roeland, 1974, J. Phys. F 4, 2264. McFeely, F.R., S.P. Kowalczyk, L. Ley and D.A. Shirley, 1973, Phys. Lett. 45A, 227. Meaden, G.T., 1965, Electrical resistance of metals (Plenum Press, New York). Meaden, G.T., 1971, Contemp. Phys. 12, 331. Mihai, V. and J.J.M. Franse, 1976, Rev. Roum. Phys. 21, 1041. Millhouse, A.H. and K.A. McEwen, 1973, Solid State Comm. 13, 339. Milstein, F. and L.B. Robinson, 1967, Phys. Rev. 159, 466. Mishima, A., H. Fujii and T. Okamoto, 1975, J. Phys. Soc. Jap. 38, 284; 39, 873. Mishima, A., H. Fujii and T. Okamoto, 1976, J. Phys. Soc. Jap. 40, 962. Miwa, H., 1963, Prog. Theoret. Phys. (Japan) 29, 477. Moon, R.M., J.W. Cable and W.C. Koehler, 1964, J. Appl. Phys. 35, 1041. Moon, R.M., W.C. Koehler, J.W. Cable and H.R. Child, 1972, Phys. Rev. B 5, 997. Mukamel, D. and S. Krinsky, 1976a, Phys. Rev. B 13, 5065. Mukamel, D. and S. Krinsky, 1976b, Phys. Rev. B 13, 5078. Murao, T., 1972, J. Phys. Soc. Japan 33, 33. Nellis, W.J. and S. Legvold, 1969, Phys. Rev. 180, 581. Nereson, N.G., C.E. Olsen and G.P. Arnold, 1964, Phys. Rev. 135, A176. Nicldow, R.M., 1971, J. Appl. Phys. 42, 1672. Nicklow, R.M., H.A. Mook, H.G. Smith, R.E. Reed and M.K. Wilkinson, 1969, J. Appl. Phys. 40, 1452. Nicklow, R.M., N. Wakabayashi, M.K. Wilkinson and R.E. Reed, 1971a, Phys. Rev. Lett. 26, 140. Nicklow, R.M., N. Wakabayashi, M.K. Wilkinson and R.E. Reed, 1971b, Phys. Rev. Lett. 27, 334. Nigh, H.E., S. Legvold and F.H. Spedding, 1963, Phys. Rev. 132, 1092. Nigh, H.E., S. Legvold, F.H. Spedding and B.J. Beaudry, 1964, J. Chem. Phys. 41, 3799. Nilra, K., 1960, Phys. Rev. 117, 129. Ott, H.R., 1975, Solid State Commun. 16, 1355. Parkinson, D.A., F.E. Simon and F.H. Spedding, 1951, Proc. Roy. Soc. A207, 137. Parks, R.D., 1977, ed., Valence instabilities and related narrow-band phenomena (Plenum, New York) p. 89. Petersen, T.S., S. Legvold, K.A. Oschneidner, RARE EARTH METALS AND ALLOYS Shepherd, C.H., 1976, thesis, University of Salbord. Sherrington, D., 1973, J. Phys. C 6, 1037. Simons, D.S. and M.B. Salamon, 1974, Phys. Rev. B 10, 4680. Skochdopole, R.E., M. Griffei and F.H. Spedding, 1955, J. Chem. Phys. 23, 2258. Slater, J.C., 1937, Phys. Rev. 51, 846. Southern, B.W. and D. Sherrington, 1974, J. Phys. F 4, 1755. Spedding, F.H. and J.J. Croat, 1973, J. Chem. Phys. 58, 5514. Spedding, F.H., Y. Ito and R.G. Jordan, 1970, J. Chem. Phys. 53, 1455. Speight, J.D., 1970, J. Less-Common Metals 20, 251. Stevens, K.W.H., 1952, Proc. Phys. Soc. (London) A 65, 209. St. Quinton, J.M.P., 1973, J. Phys. F 3, 597. Strandburg, D.L., S. Legvold and F.H. Spedding, 1962, Phys. Rev. 127, 2046. Sze, H.H., K.V. Rao and G.T./deaden, 1969, J. Low Temp. Phys. 1, 563. Taylor, K.N.R. and M.I. Darby, 1972, Physics of rare earth solids (Chapman and Hall, London). Thoburn, W.C., S. Legvold and F.H. Spedding, 1958, Phys. Rev. 110, 1298. Tissot, L. and A. Blaise, 1970, J. Appl. Phys. 41, 1180. Touborg, P., 1977, Phys. Rev. B 16, 1201. Touborg, P. and J. HOg, 1974, Phys. Rev. Lett. 33, 775. Triplett, B.B. and R.M. White, 1973, Phys. Rev. B 7, 4938. 295 Tsang, T.-W.E., K.A. Gschneidner, Jr., D.C. Koskenmaki and LO. Moorman, 1976a, Phys. Rev, B 14, 4447. Tsang, T.-W.E., K.A. Gschneidner, Jr. and F.A. Schmidt, 1976b, Solid State Comm. 20, 737. Van Vleck, J.H., 1932, Electric and magnetic susceptibilities (Oxford University Press, London). Veal, B.W., D.D. Koelling and A.J. Freeman, 1973, Phys. Rev. Lett. 30, 1961. Voronel, A.V., S.R. Garber, A.P. Simkina and I.A. Charkina, 1966, translation Sov. Phys. JEPT 22, 301. Wells, P., P.C. Lanchester, D.W. Jones and R.G. Jordan, 1974, J. Phys. F 4, 1729. Wells, P., P.C. Lanchester, D.W. Jones and R.G. Jordan, 1976, J. Phys. F 6, 11. White, H.W., BJ. Beandry, P. Burgardt, S. Legvold and B.N. Harmon, 1975,/kiP Conf. Proc. 29, 329. Wilkinson, M.K., W.C. Koehler, E.O. Woilan and J.W. Cable, 1961, J. Appl. Phys. 32, 48S. Will, G., R. Nathans and H.A. Elperin, 1964, J. Appl. Phys. 35, 1045. Wittig, J., 1968, Phys. Rev. Lett. 21, 1250. Yan8, T.-T and L.B. Robinson, 1969, Phys. Rev. 185, 743. Yosida, K., 1964, Progress in low temperature physics, vol. 4 (ed. C.J. Gorter) (North-Holland, Amsterdam) p. 265, Young, R.C., R.G, Jordan and D.W. Jones, 1973, Phys. Rev. Lett. 31, 1473. Zumsteg, EC., F.J. Cadieu, S. Marcelja and R.D. Parks, 1970, Phys. Rev. Lett. 25, 1204. chapter 4 RARE EARTH COMPOUNDS K.H.J. BUSCHOW Philips Research Laboratories Eindhoven Netherlands Ferromagnetic Materials, Vol. 1 Edited by E.P. Wohlfarth © North-Holland Publishing Company, 1980 297 CONTENTS 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Compounds with non-magnetic elements . . . . . . . . . . . . . . . . . 2.1. Interaction between the localized 4f moments . . . . . . . . . . . . . . . 2.2. Crystal field effects . . . . . . . . . . . . . . . . . . . . . . . 2.3. Magnetic properties . . . . . . . . . . . . . . . . . . ~ . . . . . 2.3.1. C o m p o u n d s with group III elements . . . . . . . . . . . . . . . 2.3.2. C o m p o u n d s with group IV elements . . . . . . . . . . . . . . . 2.3.3. Compounds with group Ia elements . . . . . . . . . . . . . . . 2.3.4. Compounds with Be, Mg and group IIa elements . . . . . . . . . . . 2.3.5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . 3. Compounds with d transition metals . . . . . . . . . . . . . . . . . . . 3.1. Exchange interaction in metal systems containing d electrons . . . . . . . . 3.2. Magnetic properties . . . . . . . . . . . . , . . . . . . . . . . . 3.2.1. C o m p o u n d s with 3d transition elements . . . . . . . . . . . . . . 3.2.2. C o m p o u n d s with 4d and 5d transition elements . . . . . . . . . . . 3.3. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Ternary compounds or hydrides . . . . . . . . . . . . . . . . . . . . Appendix. Tables A . I - A . 4 . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 303 303 307 312 312 319 323 326 331 334 334 338 338 349 351 356 361 400 298 I. Introduction The number of stable binary intermetallic compounds in which one of the components is a rare earth element is of the order of a thousand, In the first place this large number is a result of the fact that the rare earths group comprises 15 elements, or even 16 if one includes the element yttrium. In the second place each of these 16 elements, when combined with a non-rare earth partner, can give rise to more than one compound, in general. Examples of binary systems are known which contain more than 10 different intermetallic compounds, each of these being characterized by a different composition and crystal structure. The reason for this is probably to be sought in the rather large metallic radii of the rare earths. Combination with elements of much smaller metallic radii then encompasses a much larger number of possible atomic arrangements of sufficiently high space filling than would be the case for two components of almost equal size. Furthermore, the stability of a given atomic arrangement will not be strongly influenced by symmetry requirements of the wavefunctions of the incomplete-shell electrons since the 4f electrons occur well to the interior of the rare earth atoms and their effect on the bonding can be taken as being relatively unimportant. Most important for the readiness with which the rare earths form compounds is the fact that their electronegativities (~b*) are rather low compared with those of other metallic elements. Miedema et al. (1975, 1976, 1977) have proposed a simple model in which the heat of formation is given by ZIH = f ( c ) [ - P e ( A c k * ) 2 + Qo(AnwO m 2 - R]. In this expression q~* and n lw/3represent the electronegativity and the electron density parameter of the composing elements, respectively. The quantities P, Q0 and R are approximate constants for large groups of alloy systems; e is the elementary charge. The function f ( c ) = c ( 1 - c ) [ 1 + ] c 2 ( c - 1)2] is symmetric in the molar fraction c of the rare earth component. The large electronegativity difference between rare earth elements and other metals is the main reason why in most cases A H is negative, i.e. a compound is likely to exist. Values of A H calculated by Miedema et al. (1975, 1976, 1977) for various binary compounds are listed in table 1 (a slight adjustment has been made recently in the R values of the rare earth elements (Miedema et al. 1977)). 299 300 K.H.J. BUSCHOW TABLE 1 Heat of formation of intermetallic compounds of Y (identical to Gd, calculated at three concentrations, 75at.% and 25at.% Y. In order to indicate the variation in A H for different (trivalent) rare earth metals, LaM and ScM have also been included. The heat of formation of other rare earths can be found by interpolation according to their molar volumes. AH is given in kcal/g-at, alloy. All data are from Miedema et al. (1977). M = transition metal Y3M +0 +2 +3 +2 -0 -0 -4 -5 +2 +5 +5 -5 -6 -10 - 16 + 1 +2 +5 +5 -5 -5 - 10 - 16 +0 +3 + 1 LaM +3 +9 +12 -10 +5 +7 -1 -4 +1 M = non-transition metal Y3M +1 +6 -4 -6 -13 +3 +4 +5 +0 -2 -7 -9 -11 -8 - 9 - 10 - 10 -10 -6 -10 -12 - 14 - 13 -21 -19 - 18 -16 LaM +1 +5 -7 -10 -22 +0 +2 +2 +5 -3 -12 -15 -18 -12 - 14 16 M Sc Ti V Cr Mn Fe Co Ni Y Zr Nb Mo Tc Ru Rh Pd La Hf Ta W Re Os Ir Pt Th U Pu YM +0 +4 +6 -4 -0 -0 -7 -10 - ScM +2 +3 -0 -3 -4 -10 -13 +0 YM3 +0 +3 +5 +3 -0 -0 -6 -9 - M Li Na Cu Ag Au Ca Sr Ba Be big Zn Cd Hg B AI Ga In Tl C Si Ge Sn Pb N As Sb Bi YM +3 +10 -9 -11 -26 +4 +6 +7 +1 -3 -13 -15 -18 -15 - 16 17 ScM +4 +12 -10 -12 -27 +6 +8 +9 -1 YM3 +2 +6 -7 -8 -16 +2 +3 +4 +1 +7 +17 +17 -2 -3 -12 - 23 +9 +17 +17 +0 -1 - 10 -22 +3 +11 +6 +3 +10 +8 -10 -12 -18 - 29 + 1 +3 +9 +8 -8 -9 - 18 -29 +0 +5 + 1 +1 +6 +4 -14 -15 -21 - 30 +3 +1 +6 +3 -13 -14 - 22 -31 -0 +2 - 0 +2 +7 +6 -8 -9 -15 - 22 + 1 +3 +7 +6 -6 -7 - 14 -21 +0 +3 +I -3 -13 -15 -16 -16 - 16 16 -2 -10 -I0 -12 -15 - 13 - 13 - 10 -10 -11 -12 -14 - 14 - 13 -27 -23 - 18 -15 - 17 -18 -8 -15 -20 - 22 -23 -36 -30 - 29 -26 - 16 -16 -12 -18 -21 - 22 -21 -39 -32 - 28 -24 - 14 -13 -14 -19 -20 - 20 - 18 -40 -31 - 26 -20 T h e p r e p a r a t i o n o f r a r e e a r t h i n t e r m e t a l l i c s is m o s t c o n v e n i e n t l y p e r f o r m e d b y fusing the stoichiometric proportions of the composing metals in an arc furnace o r in a l e v i t a t i o n f u r n a c e . C o m b i n a t i o n o f t h e m e t a l s b y h e a t i n g in a c r u c i b l e (A1203, M g O o r T h O 2 ) is l e s s s u i t a b l e o w i n g t o t h e r a p i d r e a c t i o n o f t h e r a r e earth component at elevated temperatures with the crucible material. In some cases one (or both) of the starting materials may possess a low heat of sublimation of evaporation (for example: Eu, Yb, Zn, Cd or Mg). Combination of the composing metals has then to be performed in a closed system consisting RARE EARTH COMPOUNDS 301 of metals such as Ta or Mo. These latter two metals not only have a high melting point but in addition (as more or less follows from the large positive values of AH in table 1) do not react with the molten rare earth alloy. A meaningful study of the physical properties of intermetallic compounds can only be made on single phase materials. Only a fraction of the compounds is in single phase condition after the melting together of the components. This is usually the case with congruently melting compounds such as for instance LaA12 in fig. 1. Incongruently melting compounds do not form directly from the melt. LaA1 in fig. 1 is an example of such a compound. It is formed at 873°C •by a so-called peritectic reaction between the primary LaAI2 crystallites and a more La-rich liquid (44 at.% A1). Slow diffusion of the metal atoms at low temperatures prevents this peritectic reaction from reaching completeness during a normal cooling process. Single phase condition can be reached here by vacuum annealing at temperatures close to but below the peritectic reaction temperature (873°C in the case of LaAD. Sometimes the situation is more complicated. It is o, o _J .J .J o~ o ..1 J I t 50~ I I Jll 1405 ° 100 o 0 )19 ° I- / I 64' )o 500 547° 550 ° 0 0 I I0 I 20 I 30 I I I 70 80 90 100 40 50 60 AT % A~ Fig. I. Phase diagram of the La-AI system. The stoichiometric composition of LaAI~ is approximately LagAIH. The compound LaAh is slightly Al-deficient. Its actual stoichiometry corresponds to La3Alm 302 K.H.J. BUSCHOW seen in fig. 1 that LagA12~ is also formed peritectically. In this case the vacuum annealing is strictly limited to the region between 1240° and 1090°C and subsequent quenching is required. The reason for this is the eutectoid decomposition of LagA121 into the adjacent phases LaA12 and LaAl3 at 1090°C. The compound LaAl4 is an example of a compound that needs heat treatment after melting, even though it melts congruently. At 915°C a structural phase transformation occurs. If the high temperature phase is desired, quenching from above this temperature is required. On the other hand, if one wishes to obtain the low temperature phase, one can remove residual amounts of the high temperature phase by annealing below the transformation temperature. The examples given above may demonstrate that the availability of phase diagrams is often a great help in the preparation of single phase samples. Information on phase diagrams can be obtained from the books by Elliot (1965), Gschneidner (1961), Hansen (1958), Savitsky and Terekhova (1975), and Shunk (1969). The most common crystal structures adopted by rare earth intermetallics have been collected together in table A.1 in the Appendix at the end of this review. The formulas of the compounds representing the structure type (column 1) have been written down in a manner that the sites of the first element correspond to the R sites in all cases. The last column of the table indicates with which non-rare earth component the rare earth partner can be combined in a particular structure type. For instance it can be derived from the table that RBe13, RC013 and RZn13 compounds exist, and that these have the cubic NaZn~3 structure with space group Fm3c. Very often the stability of a given crystal structure depends to a large extent on the relative size of the two components. In view of the lanthanide contraction of the rare earth it can happen that this particular structure does not persist through the whole lanthanide series. This is for instance the case with RCo~ which compound exists only for R = La. Alternatively one could say that, with the exception of LaCo~3, compounds of the type RCol3 are not stable with respect to R2Col7 and elementary cobalt. In the interpretation of magnetic data and, afortiori, in the evaluation of hyperfine field data it is desirable to know the number of crystallographically non-equivalent R and M sites in a given compound. This can be derived from the data given in the fourth and fifth columns of table A.1. Again using the NaZn~3 structure type as an example, there is only a single rare earth site (a) but two different non-rare earth sites (b and i). The numbers in front of the parentheses indicate the occupation numbers. From these one can also find the number of formula units per unit cell. This is eight in the case of NaZnt3 and four in the case of Th~Mn23. Some of the structure types listed are closely related. The crystal structures of Th2NilT, Th2ZnlT, Ce2NiT, Gd2C07, CeNi3, PuNi3 and MgCu2 can be derived in a simple manner from the CaCu5 type. For instance, the structure of Ce2Nit7 (Th2Nil7 type) is obtained from CeNi5 (CaCu5 type) by an ordered substitution of one third of the Ce sites by a pair of Ni atoms (3 CeNi5 ~ Ce2Ni2Ni15 = Ce2Ni17). Another example is the CaBs type, which can be visualized as CsCI type with Ca RARE EARTH COMPOUNDS 303 at the Cs sites and an octahedron of B atoms at the CI sites. It falls outside the scope of this review to go into more detail regarding the various relationships of the structures given in table A.1. For this the reader is referred to excellent text books on this subject (Schubert 1964, Pearson 1958, 1972). For the rare earth intermetallics the various representatives of the crystal structures of table A.1 are listed in tables A.2 and A.3 in the Appendix at the end of this review. The list is not complete in so far as it does not comprise those (few) groups of intermetallics for which no magnetic data are available in the literature. In most of the compounds listed in tables A.2 or A.3 it is possible to replace the M component, or part of it, by a third component M' without changing the crystal structure. One speaks of pseudobinary compounds R(M1-xM')n if there exists a statistical distribution of M and M' atoms over the crystallographic site(s) available for the non-rare earth component. In some cases the substitution of M ' atoms at M sites is not a random process but shows a preference for particular site(s) or for a particular coordination. If the preference is very pronounced these compounds can no longer be regarded as pseudobinaries but must be classified as ternary compounds. Apart from the ternary compounds that can be thought to arise from atomic ordering within pseudobinary compounds, compounds of a completely different composition and crystal structure exist which are in no way related to binary compounds. No systematic studies have as yet been made of the magnetic properties of ternary compounds. The only exceptions are compounds of the type RM2M~ and RM4M~. The compounds RM2M~ (M = Cr, Mn, Fe, Co, Ni, Cu, Ag and Au; M~ = Si, Ge) have the ThCr2Si2 structure derived from the BaA14 type (Rieger and Parth6 1969), in which the M atoms are restricted to the 4(d) sites and the M ' atoms to the 4(e) sites (see table A.1). The compounds RM4M~ have the CeMn4Als structure derived from the ThMnn type (Zarechnyuk and Krypiakevich, 1963). Here the M atoms (Cr, Mn, Fe and Cu) occupy the 8(f) sites while the M ' atoms (A1) are accommodated at the 8(i) and 8(j) sites of the ThMnn structure (see table A.1, line 2). Representatives of both ternary series, together with a few other ternary compounds derived from the Fe2P type (Dwight et al. 1968) are given in table A.4. 2. Compounds with non,magnetic elements 2.1. Interaction between the localized 4f moments The spatial extent of the 4f electrons is very small in comparison to the interatomic spacings. There is no substantial overlap of the wave functions of 4f electrons centered on different atoms. This precludes a direct interaction between the localized moments. Two mechanisms have been proposed in which the 4f moment can interact in an indirect way. In the first of these, called the RKKY interaction, the magnetic coupling proceeds by means of spin polariza- 304 K.H.J. B U S C H O W t/on of the s-conduction electrons. In the second mechanism the spin polarization of the appreciably less localized rare earth 5d electrons plays an important role. These two mechanisms and their implications for the magnetic properties of the various intermetallic compounds, listed in tables A.2, A.3 and A.4 are briefly discussed below. In its simplest form the R K K Y theory was originally proposed by Ruderman and Kittel (1954) to describe the interaction between nuclear magnetic moments. Extensions to the model were made later on by Yosida (1957), Kasuya (1956) and DeGennes (1962a). In metal systems involving rare earth elements the localized rare earth spins S are engulfed by a sea of conduction electrons. These latter are spin polarized by the former through the exchange interaction = -2J(q)s • S (1) where s represents the spin of the Fermi surface conduction electrons and where the exchange integral J ( q ) - J ( k ' - k ) depends on the wave vectors k and k' of the conduction electrons before and after scattering by the localized spin, respectively. This exchange interaction between localized spins and conduction electrons is treated as a perturbation on free conduction electron states. The conduction electron polarization is obtained by applying a first order perturbation to the free electron wave functions. The spatial spin up and spin down densities IO±(r)l: of the conduction electrons are then given by IO±(r)l2 = ½N +-(3n/16E~) ~, J (q)f(q) ~, Si(e i~(r-R,)+ e-iq.(r-R~)) q i (2) The sum over i counts the number of localized spins in the crystal. The other symbols in eq. (2) have the following meanings: N: n: EF: total number of conduction electrons present in a volume V, average conduction electron to atom ratio, Fermi level energy, position vector of the i'th localized spin S~. Ri: The q'th Fourier component of the static free electron susceptibility f ( q ) in this expression is given by f ( q ) = 1 + 4 k ~ - q2 [2kr + q[ 4kFq In [2k-~'q-q[ (3) kF being the Fermi wave vector. Ap analytical expression for the conduction electron spin polarization P ( r ) o: I O + ( r ) l 2 - IO-(r)l 2 is obtained if J(q) in eq. (2) is assumed to be a constant, J(0) P(r) = 9n2~rJ(0) 2EF I<Sz>l F(2kF. [r-R,[). (4) Due to the oscillating character of the function F ( x ) = (x cos x - sin x)/x 4 this spin polarization is spatially non-uniform. The spatial variation of F ( x ) is shown graphically in fig. 2. In the bottom part of the figure the positions of several we see that this interaction will vary from one neighbour site to the other: the neighbour atom will orient its spin moment according to the local spin polarization.sin x)/x 4. 2.) 2EFgnlxn (7) . If we consider. Spatial variation of the RKKY function F(x)= (x cos x . The sign of this sum determines whether the 4f spin moments will ultimately order ferromagnetically or antiferromagnetically. distance ~ ® ® ® ® Fig. second. for instance. An expression for the paramagnetic Curie temperature 0p can be obtained from a combination of the molecular field model (DeGennes 1962a. characterized by the Hamiltonian = A(q)s. I (6) one finds in a similar manner an expression for the hyperfine field HN (Yosida 1957) HN =- 9~rn2AJ(O) I(S~)I ~ F (2kFR. an interaction of the central 4f moment with only one of the neighbouring 4f moments.RARE EARTH COMPOUNDS 305 ~ xcosx-sJnx x l. ksEv i (5) If one includes in the total energy expression the hyperfine interaction between the s-conduction electrons and the nuclear magnetic moments (I). For each localized moment. the total interaction with the other moments present in the crystal is obtained by summing the contributions originating from the conduction electron spin polarization produced by all the other moments at this particular site. b) with the expression of the second order perturbed energy associated with the s-f exchange interaction (Yosida 1957) Op = 3"trn2j(0)2 S ( S + 1) ~ F ( 2 k F R i ) . third and fourth neighbour shells of the central 4f atom. These may be visualized as representing 4f atoms residing in the first. The position of several localized momentsat a distanceR~from the central ion (r = 0) is indicatedby arrows. localized moments have been indicated. and the magnitude of the interaction is proportional to P (r). (5). through kF appearing in eq. t~B the Bohr magneton and K0 the Knight shift due to Pauli paramagnetism only. i. but that this cancellation depends strongly on the radius of the neighbour atom shell and the number of 4f atoms present in it. For a given structure. For larger or smaller kF values. A represents the effective hyperfine structure coupling constant. 1960) K = K0[1 + Jst(S" J)xf/2gflx~J(J + 1)] where Jsf = . 2 that the contributions due to the moments residing in the various neighbour shells largely cancel. R. The expression for the EPR g-shift due to the s-f interaction is given in the RKKY model by (Yosida 1957) Ag = 3nJ(0)/2Ev. The effect of changes of kF are most conveniently illustrated again by means of fig. In the second place it is seen that. N and V k3F= 3~r2nN/V. nN. and where the summation runs over all the other lattice sites. are reduced or increased.306 K. as it were. via the sum function Y. The quantity Xf is the 4f electron magnetic susceptibility.J. for fixed neighbour atom distances. the distances. (12) It follows from the above discussion that the RKKY model lends itself fairly well to a comparison with experimental data derived from magnetization measurements. (5) the value of 0p is also dependent on the number of conduction electrons. this leads to an altered contribution for each of the neighbour shells. and gn and/~n are the nuclear g-value and the nuclear magneton.e. respectively. In the magnetically non-ordered regime it is more appropriate to consider the Knight shift (K) rather than HN. In the first place it is to be noted that the paramagnetic Curie temperature.i F(2kFRi) in eq. compressed or expanded in the R direction. present per unit cell volume V [see eq.1)Jl~a/2EF. The appearance of a wave number (kv) rather . which can seriously affect the value of 0p. (11) In the free electron model one has furthermore the following relation between kF (or EF) and n. i (8) (9) Here gf is the rare earth ion Land6 g-value. respectively. is structure dependent: It can be inferred from fig. This quantity is given by (Jaccarino et al. The extent of this cancellation therefore differs from structure to structure and can lead to order of magnitude differences in the value for 0p. (12)]. where the function F(2kFR) passes through zero. 2. (10) The excess bulk magnetic moment due to the spin polarized conduction electrons can be expressed as (DeGennes 1962a) A M = 3nJ (O)(gf .12¢rnJ(0) ~ F(2kFRi).H. The oscillations are. BUSCHOW where the origin is chosen at the nuclear site that is considered. Campbell argues that since the d-d interaction is positive and since the f--d interaction occurs twice in the total coupling term between two R-moments. According to these calculations all electron states on or very near the Fermi surface have 80-95% I = 2 character. one ends up with a net positive indirect 4f-4f interaction. Furthermore.2.RARE EARTH COMPOUNDS 307 than just the number of conduction electrons is inherent in the long-range nature of the interaction expressed in eq. (7). Part of the electrons at the Fermi level should exhibit therefore a pronounced d-character. the Mtssbauer effect and EPR. If a given intermetallic compound orders ferromagnetically at low temperatures one can compare the excess magnetization measured on top of the free ion value (gJlxB) with the theoretical result given by eq. By means of ordinary f-d exchange the 4f moment induces a positive local d moment. partial filling of the narrow 5d bands implies a high density of states at the Fermi surface. The following requirements should be satisfied: If the above d--d coupling scheme is effective the 5d bands in the corresponding intermetallics should be partially filled. 2. Although the contact of the d-d coupling scheme with the experimental situation is much more difficult to achieve than in the case of the RKKY scheme. It can furthermore be seen that via eqs. at least if the rare earth concentration in the compound is sufficiently high to still guarantee overlap of the 5d electron wave functions. That the d electrons are indeed expected to play a significant role was for instance shown by band structure calculations performed on Gd by Harmon and Freeman (1974). (11). it does not necessarily mean that the contributions of the former model to the 4f-4f coupling are less important compared to the latter. (8) and (10) sufficient contact is also made with experimental results available from various resonance techniques such as NMR. this model in its present form is less well suited for comparison with the experimental data. A different coupling scheme between the localized 4f moments was proposed by Campbell (1972). Such a comparison is in general only restricted to ferromagnetic Gd compounds where moment reductions due to crystal field effects are absent. This implies that the 4f induced positive d electron polarization does not remain restricted to the particular atom in question but has a much larger spatial extent. and the mutual interaction between the d electrons (involving also d electrons on other rare earth sites) is in many respects similar to that encountered in normal d-transition metals. The 4f electrons . This scheme involves the 5d electrons of the rare earth elements. It is sometimes possible to check the fulfillment of these two requirements by experiment. Apart from the fact that it predicts positive values of 0p. Crystal field effects In an intermetallic compound the composing elements lose their valence electrons to the conduction band. The d electrons are by far less localized than the 4f electrons. (5). implying a dominant role in the 4f moment coupling by the d-like electrons. In general one can speak therefore of a lattice of positive charges immersed in a sea of conduction electrons. (15) may be restricted to k _. Deviations from free ion behaviour can be expected therefore whenever the temperature decreases below a value smaller than the total splitting of the ground state after removal of the degeneracy mentioned. for points close to the origin at the rare earth ion in question. can be given by V(r) = rl" (13) The perturbing crystal field Hamiltonian then is 3~ = .e 2~-~ c2q ~ Zj fR(~jR ). while the term with A ° is irrelevant. once the . The electrostatic potential Vc(r) due to charges Zj located at a distance R s. t~) are the standard normalized spherical harmonics.H. This crystal field Hamiltonian is most conveniently represented by a series development in Tesseral harmonics f~ through k ~0 = ~ ~ A~ Y~fkq(r. The unrenormalized fkq are defined through Ckofko(r) = rkyOk(O. since otherwise the matrix elements are zero. The total angular momentum can therefore be taken as a good quantum number and the effect of the crystal field can be regarded as a small perturbation on the (2J + 1) fold degenerate wave functions (J. Since the spatial extent of the 4f wave functions is rather small.J. following Stevens' (1953) conventions. Oh) Ckqfkq(r) = 2-112rk[Y k~(O. (17) The point symmetry causes a number of A~ to vanish and requires. In the more restricted point charge model the electric charges Zj are identified with point charges located at the sites of the surrounding ions.) k=0 q=0 i (15) where the summation over i is to be performed again over all the 4f electrons.e ~_. are then given by 4Ir A~ = . oh) + (-. The lattice coefficients A~.308 K. Jz[ of the ground multiplet.6. For the rare earth elements the summation over k in eq. The effect of this electric field on the 4f wave functions leads in general to a complete or partial removal of the (2J + 1) fold degeneracy of the ground J multiplet level. BUSCHOW residing on a given rare earth ion will experience the electric field produced by the screened charge of the surrounding ions. the crystal field splitting is small compared to the spin orbit interaction. V(ri) i (14) where the summation extends to all 4f electrons at ri forming part of the rare earth ion considered. Most of the fkq along with their normalization constants Ckq are given in the review by Hutchings (1964).1)q Y ~(O. th)] (16a) (16b) where Y~(O. A somewhat different notation has been introduced by Lea et al. the remaining A~ to differ by constant factors. where a is the lattice constant (cubic compounds). In order to exclude also the variations of the quantities (r k) from ion to ion one may use the reduced crystal field parameters A4a 5. The quantities Ok are multiplicative factors. while values of (r k) have been calculated in the paper by Freeman and Watson (1962). (18) reduces to ~ = B4(0°4 + 50~) + n 6 ( o ° . for the general case that one wishes to include ground. characteristic of a given rare earth element. etc. for a cubic field with z II [001] Zc = A°4[f4o+ 5f44] + A°[f6o . The matrix elements can then be derived by Stevens' (1953) method of operator equivalents via E fkq(ri) = Ok(rk)O~ i (20) where O~ are operators in terms of Jx. (1962). very often only the abbreviations a i. An alternative notation for the Stevens multiplicative factors is o2=(sllalls). It has become common usage to represent the strength of the crystal fields by means of the coefficients Bk = Ak(r k) SO that eq. has been reviewed by De Wijn et al. For instance. (18) In a hexagonal field the expressions are more complex in general. For instance. (15) now reads ~ c = 7~ ~ B~O[.210~) -.RARE EARTH COMPOUNDS 309 quantization axis (z-axis) is chosen. A6a 7.] representation. J.21f64]. Detailed information on such calculations can also be found in the book of Wybourne (1965). (22) . In these expressions fkq is the shorthand notation for (19) x fi~(ri). k~O q~O (21) The coefficients Bk. through Ok. These authors considered crystal fields of cubic symmetry with z I[[001] for which eq.as well as excited J-multiplet levels. Jy and J~. for rare earth ions residing at sites of point symmetry D6h (such as in CaCu5 type compounds) the Hamiltonian for z tl [0011 is ~ = A°f2o + A°f4o + A~6o + A~66.. Values of Ok are listed in the review by Hutchings (1964). (1976a). In some cases it is sufficient to consider only the ground J-manifold of the 4f electrons.---(311f311J) and 06= (sll'/llJ). Better quantities to specify the intensity of the crystal field in a given crystal structure are A4(r4). o.B404 + B606. i The calculation of the matrix elements of fkq in the (J. still contain the specific properties of a given rare earth ion and hence are not constant in going through the rare earth series. [3j and 7i are used. A6(r 6) etc. Depending on whether one uses eq. (17)]. For ligands containing d electrons in particular the charge distribution will not be the same in the various crystallographic directions. 1974a. Extremely large deviations from the point charge model can be expected if there is a high density of 5d electrons at the rare earth site itself (Williams and Hirst 1969. These 5d electrons will therefore occupy almost exclusively the symmetry state(s) having the lowest energy after the crystal field splitting (Williams and Hirst 1969). The parameters W and x are related to the B4 and B~ coefficients by Wx = B4F4 and W(1 . symmetry and strength of the actual crystal field felt by the 4f electrons will in this case predominantly be determined by the charge distribution associated with the lowest crystal field state of the 5d electrons rather than by the ionic lattice. Dixon 1973.[xl)OdF6] (23) where W is an energy scale factor and x represents the relative weight of the fourth. Devine 1974).310 K. 0 < x < 1. are preferred to first principle calculations by means of point charges [eq. BUSCHOW This Hamiltonian was re-written by Lea et al. (21) or eq. into the form ~c = W[xOJF4 + (1 . a rather fundamental problem regarding the applicability of eq. (17) is that in a metal the assumption of even screened point charges is highly unrealistic. Bucher and Maita (1973) showed that for simple ligand systems a correlation exists between the crystal field splitting associated with a given sign and magnitude of the ligand charges on the one hand and the electronegativities of the ligand elements on the other. At this point it is perhaps desirable to comment further on the fact that analyses of crystal field effects in terms of adjustable parameters.Ix l) = B6F6. (1962). Morin et al. In the first place it is rather difficult to predict the charge of a given element in a given compound on the grounds of its valency.H. These authors also give a schematic representation of the energy levels as a function of W and X. charge transfer takes place and the charge of a given ion is dependent for these reasons on the nature and the concentration of the partner element. The quantities F4 and F6 are numerical factors common to all matrix elements and values of these have been listed for all rare earths by Lea et al. (23) the eigenfunctions and energies are obtained with A~(r k) or W and x as parameters. The eigenfunctions and energies corresponding to the crystal field split states of the ground J-multiplet can be calculated by diagonalization of ~c. In recent years it has become possible to obtain direct information on the level scheme of the crystal field split ground state by means of neutron scattering experiments. crystal field splitting of the 5d electron states will be much greater than that involving the 4f electrons. so that the strength of the actual crystal field may differ from that due to the point charges on the lattice sites. Eagles 1975. such as those mentioned above. Due to their large spatial extent. In view of the close proximity of the 5d electrons. Due to the differences in electronegativity of the composing elements. The Ak(r k) parameters responsible for a given level scheme can .J. Apart from this rather trivial difficulty. respectively.and sixth-order terms. For the latter case the eigenfunctions have been listed for various x by Lea et al. keeping the quantities Ak(rk) and H~x as parameters. It will therefore be necessary to include H~x in the diagonalization procedure. Here the crystal field splitting can lead to a singlet ground state with zero magnetic moment. a consistent description should be obtained for all the observed easy directions within a series of isostructural RMn compounds. T). The total perturbing Hamiltonian then becomes ~ t = ~ c + ff(ex(25) In routine computations the diagonalization is usually performed for many different directions n of H~x. T) = -kBT In Z(n.RARE EARTH COMPOUNDS 311 then be compared with point charge calculations. There are two main features that will make crystal field effects manifest in the experimental data. The first of these is a reduction of the rare earth's magnetic moment (in the sense of a definite decrease of the rare earth's moment length). Estimates of the magnitude of Hex can often be obtained for the compound considered from magnetic data available for this or related compounds in literature. with a given set of Ak(r k) values. The exchange energy is determined by the Hamiltonian ~ex = 2/~aHex • S (24) where H~x represents the exchange field exerted on the R spin by the surrounding R. This. Buyers et al. For these reasons it has become no longer fashionable to analyse experimental data on crystal field effects by means of point charge considerations. even though the magnitude of the actual moment may be close to the free ion value. In the case of a non-negligible exchange interaction between the localized moments this can lead to interesting collective excitation behaviour (Wang and Cooper 1969. can give rise to a reduction of the bulk magnetic moment. 1974a. 1977. The second feature is an often pronounced magnetocrystalline anisotropy. 1975).and M spins. Furrer 1975). too. In almost all cases the rare earth moment has been reported to be below the free ion value. Direct information on the magnitude of the rare earth moment can be obtained from neutron diffraction experiments. Limits for the parameters Ak(r k) may be set by the requirement that. Very often it was found that the point charge model prediction is incorrect by more than an order of magnitude. or even by its sign (Morin et al. (26) The direction of easy magnetization at a given temperature is the direction of n in which the free energy has its lowest value. T) and the Helmholtz free energy F(n. In the tables it has been indicated on which compounds neutron diffraction data have been performed. Gross et al. In order to describe the magnetocrystaUine anisotropy in terms of crystal fields one has to take account of the fact that due to the presence of exchange interactions the Zeeman splitting and crystal field splitting may be of comparable magnitude. . The resulting energy values Ei are subsequently used to calculate the partition function Z(n. A special case is formed by rare earth ions with an even number of electrons. Compounds of the series RB2 seem to be stable only in the case of rare earths with an atomic number smaller than that of Tb. RB6 and RB~2. Unlike the series RB2 and R2B5 listed in table A. 2.3. It can be derived from eq.2a the series RB4 is fairly complete. T) in these expressions with F(n. The only alternative then left is a coupling via the RKKY mechanism (see section 2. (28) are subsequently calculated for a number of different directions of n after which the quantities K~ can be derived by a fitting procedure. In the first place it seems less likely that the 5d electrons contribute significantly to the indirect coupling between the localized 4f moments in RB4 since a large 5d electron density is improbable in view of the diamagnetic character of LaB4 and LuB4. 2+ 0[ 2 2 + K20[ 2 2 2 + 0[20[3 10/3) 1012013 4 4 4 + K3(0[ 4 1012 "Jr-0/20[3 "t. Both sides of eq. BUSCHOW Usually the bulk magnetocrystalline free energy E(n. . are not included in the above treatment. The only exception is PrB4. The temperature dependence of K~ can be obtained by repeating this treatment for different values of T.3. (5) that the sign of Op in the RKKY approach is determined by the lattice sum E~ F(2kFR~).2a.1. (26) (Atzmony et al. We note that temperature dependences of K~ of a more general character. are also ferromagnets (see table A. 1973a). This suggests that the other RB2 compounds of this series. shows that this compound is a ferromagnet below Tc = 151 K with an easy direction of magnetization parallel to the c-axis of its hexagonal AIB2 structure (Will 1977a).J. T) of a cubic system can be expanded into a power series of the direction consines 0[ of the direction of magnetization n with respect to the cube edges E(n. RB4. such as considered for instance by Akulov (1936) and more recently by Callen and Callen (1971).H. T) = Ko + Ki sin2 0 + K2 sin4 0 + K3 sin 6 0 + K4 sin6 0 cos 6 ~b where 0 and ~b are the polar angles of n relative to the c-axis. . Magnetic properties 2.312 K. giving rise to a large intrinsic coercive force. The data available have been collected in table A. which is ferromagnetic at low temperatures.T)=Ko+KI(0[~0[~ . Neutron diffraction performed on TbB.2a). Compounds with group III elements Magnetic investigations have been performed on rare earth boron compounds of the following compositions: RB2. The change in sign of the magnetic coupling within a series of rare earth compounds is highly uncommon and needs further comment. in each of which a positive paramagnetic Curie temperature has been reported (Buschow 1977d).0/40[ 4) "~" . T) of eq.1). This . (27) (28) For a hexagonal system the free energy expression becomes E(n. It is seen in the table that all magnetic rare earth elements give rise to antiferromagnetic ordering in RB4. The anisotropy constants Ks can be obtained by comparing E(n. R2B5. The results obtained on TbB2 have furthermore shown that a considerable magnetic anisotropy can be present. However. do not vary according to S ( S + 1) or (g . 1973) neutron diffraction (Schfifer et al. it appears that the contribution of the Bloembergen-Rowland type interaction is only moderate.g)Qi010 + C2nQ2121 + 2(g .g)CnQi021]. The series RB6 forms by far the most interesting series of the borides since it comprises compounds which are diamagnetic (R = La). Wood 1971).g)Q1001 + 2(g . Geballe et al.1) is present in these compounds. In all these investigations the value of kF was considered as a parameter since. Finally we note that a rather complex situation is found in SmB6. A more . with R being trivalent. The relative importance of the two types of interactions was estimated by Glausinger (1975) on the basis of EPR in EuB6. (29) The quantities Qplk. No evidence of any appreciable s-d exchange interaction was found. 1976a). The change in sign of 0p within the RB4 series seems therefore in conflict with the RKKY model. Levy's extension of the RKKY approach has been used by Buschow and Creijghton (1972) to explain the sign reversal of 0p in the RB4 series. Gd. Nd. the Bloembergen-Rowland interaction (Bloembergen and Rowland 1955) seems more appropriate in the case of EuB6 (Fisk 1971. (12)] can be expected. from EPR performed on Gd~Laj-xB6 (Sperlich et al. The decrease of the lattice constants will therefore leave the products kFRi more or less unchanged (this holds strictly in cubic structures and only approximately in structures of lower symmetry). Effects of short-range ordering in RB6.1)(2 . Dy and Ho) and ferromagnetic (R = Eu). 1973). however. The values observed for 0p in RB6.1)CnQ0m + 2(2 . 1971) are discussed by Taylor (1975) and Fisk et al. derived from EPR and resistivity data (Fisk et al. Pr. 1970. This would suggest that an additional coupling mechanism involving the rare earth 5d electrons (see section 2. According to Levy (1969) this leads to an expression of the paramagnetic Curie temperature 0p given by Op= (3kB)-lJ(J + 1)[(g . The exceptional behaviour of EuB6 is a result of the fact that this compound is a semiconductor (Matthias et al. antiferromagnetic (R = Ce.1)2j(j + 1) as expected on the basis of eq. (5) and are defined in Levy (1969).RARE EARTH COMPOUNDS 313 sum is subject to scarcely any changes if one proceeds through the whole series from LaB4 to LuB4 because kF is proportional to a reciprocal lattice vector. 1968. Tb. Confirmation of the applicability of an RKKY type exchange mechanism has also been derived from results of NMR (Creijghton et al. no straightforward relation of kF to the formal number of valence electrons [eq.1)2Q0101+ (2 . Chazalviel 1976).p2k2are generalizations of the term J(0) 2Ei F(2kFRi) in eq. (5). (1971). for instance GdB6. in view of the presence of B-B bonds. Kaplan and Lyons (1963) have shown that the presence of an orbital momentum on the rare earth atoms can lead to a modified exchange interaction between the 4f moments. where Sm occurs in a so-called mixed valence state (Cohen et al. They originate from pair interactions described by orbital and spin tensor operators of ranks p and k. Instead of the normal RKKY mechanism responsible for the antiferromagnetic exchange in. 1968). Results of magnetic dilution studies performed with Gd3A12 are discussed in terms of the RKKY approach in Buschow (1975a). 1974). The magnetic properties of most of these compounds have been reported in the literature and the results are gathered in table A. 1971). 1975a. Macroscopically the existence of these narrow walls becomes manifest through the presence of large intrinsic coercive forces with a pronounced temperature dependence. With the exception of CeAl2 the values of A4 a 5 and A6a 7 listed in table 2 do not vary by more than a factor of about 2 from compound to compound. In Tb3Al2 the domain walls are extremely thin and extend over a few interatomic distances only. This has been attributed to a minimization of the crystal field energy (Barbara et al. 1977c). It is apparent from the large number of references listed in table A.H. Most of the results of magnetic investigations performed on these compounds could be explained by the presence of a ferromagnetic coupling between the 4f moments in conjunction with a crystal field splitting of about the same order of magnitude. 1974) and by measurements of the magnetization in various directions on single crystals (Barbara et al. Kaplan et al. Barbara e. can lead to a new type of magnetization process. It is well known that minimization of the magnetostatic energy requires that in zero applied field a ferromagnet decomposes into magnetic domains separated by walls whose thickness is determined by a compromise between the coupling energy and the anisotropy energy. 1973. ~ al. 4 and 5). In part this is due to the simple crystal structure of these compounds. There is a considerable difference in energy between positions in which the centre of the wall coincides with an atomic layer and positions in which the centre falls in between two atomic layers. (It was found that several of the RA12 compounds undergo a spontaneous cell distortion at low temperatures.2b for RA12 that the compounds of this series have received considerable attention. In Gd3A12 the Curie temperature is even close to room temperature. Deenadas et al. b. in conjunction with the comparatively low coupling strengths between the localized moments. Rather high magnetic ordering temperatures are exhibited by the first members of the R3AI2 series. obtained by measurements of the specific heat (Hill and Machado da Silva 1969. It is also known that it is relatively easy to prepare RAI2 samples in single phase condition. inelastic neutron scattering (Houmann et al.314 K. Movement of the Bloch walls therefore involves the surmounting of an energy barrier. is given in Buschow (1977d). Consequently the magnetization process needs thermal activation. (1971a) showed that the high magnetocrystalline anisotropy in Tb3Al2. A relatively large error may be involved with the parameters of . The number of intermetallic compounds occurring in the various R-A1 systems is considerable (Buschow and Van Vucht 1967).2b. the A127 NMR (De Wijn et al. 1973).J. 3 and the parameters listed in table 2 are based primarily on the single crystal data. For the characterization of the crystal fields in these compounds a reasonably consistent set of data is available. Cock et al. This feature will be discussed in more detail in connection with TbGa below (see figs. The level schemes shown in fig. including the RBI2 compounds. BUSCHOW detailed review of the magnetic properties of rare earth boron compounds. e. 1977a. Level scheme of the crystal field split ground J multiplet of several rare earth compounds of the type RAI2.RARE EARTH COMPOUNDS 315 200- %(2) 2rr t6 ~2 Ir I I0o ~4F 8 4r8(I) 3r3(2] 4r~(I) W 3r4 ' ' \ I r2 . (1973) Buschow et al.44 -0.5 4.150 K d e r i v e d f r o m t h e c o m b i n a t i o n o f N M R d a t a ( D e W i j n et al.4.2). 5 6..4. (1974) Houmann et al.7 8. T h e d a t a o f SmA12 l i s t e d i n t h e t a b l e a r e b a s e d o n A4(r4)/k = 150 K . Purwins et al. 8. 1973.69 1. (1973a) Barbara et al. 1976b.~3cU) 2r6 Nd3+ ~ r4 2~(I) 4~{el 4 2~ Ce 3+ .1..2.013 -0. (1976) SmAI2. The degeneracy of the various levels is indicated by the left hand index of the level symbol. Deenadas et al..0 . 1974) ( s e e s e c t i o n 2.32 -0. 11. TABLE 2 Crystal field parameters of various cubic Laves phase compounds RAI2.~.8 55 36 22 43 42 54 A6a 7 (106 meVA) (104 meV~) References 240 .26 W (meV) 1.0 .16 0.6 -4. . The level schemes correspond to the parameters given in table 2. A4a5 3. 2.025 7. -0. 9.10 3.. (1971) 4. 10 11. 10. K a p l a n e t al.3 . (1973) 5. 0. 0.4 -6.3 1. 1973) a n d m a g n e t i c m e a s u r e m e n t s ( B u s c h o w e t al.3 -3. T h e c r y s t a l field a n a l y s i s h a s t h e r e f o r e to be based on a mixing of excited ] levels into the ground J multiplet due to the p e r t u r b i n g i n f l u e n c e o f c r y s t a l fields a n d e x c h a n g e fields ( D e W i j n et al..38 0.88 40 0. A6(r6)lk = . Kaplan et al.5 I.44 .~(I ) 2r3 II~I 3~') Ho3+ 4~131 Er3+ 0 pr 3+ TbS+ Fig. (1976) 6.4. (1975a) 2. (1974) De Wijn et al.020 . -0.70 -0. Cock et al.10 . F o r S m 3÷ t h e s e p a r a t i o n b e t w e e n t h e m u l t i p l e t J l e v e l s is r a t h e r c l o s e c o m p a r e d to t h e c r y s t a l field s p l i t t i n g . 5 4. 3. 3 4.8 -2. For a definition of the quantities listed see section 2.37 0.9 4.25 . (1977d) Barbara et al.91 .64 -1. M a l i k e t al. Hill and Machado da Silva (1969) 3. Barbara et al. Easy Compound axis CeAI2 PrAI2 NdAI2 SINAI2 THAI2 DyAI2 HOA12 ErAI2 [111] [100] [100] [111] [11!] [100] [100] [111] B4 (10 -4 meV) B6 (10-4 meV) 0 . x 1 0. 1960. . BUSCHOW 1973a). 1976). In general it can be said that most of the experimental data show cerium to be trivalent in CeAl2. Dormann et al. This was correlated by these authors with the small helical antiferromagnetism superimposed on the ferromagnetic moment arrangement in DyA12 (Nereson et al. Sankar et al. Barbara 1975a) and the fact that its electrical resistivity (van Daal and Buschow 1969. 1966). 1977b. Magnetic dilution experiments (Buschow et al. A further manifestation of higher order terms in the exchange Hamiltonian in RA12 compounds was found in HoAl2 where. A relatively large participation of d electrons to the exchange interaction finally follows from a comparison of the values of Tc and H~ (eqs. For this reason we will postpone an evaluation of the validity of the RKKY approach in RAI2 and give it together with an evaluation of the coupling mechanism in other compounds in section 2. that the interaction of the 4f and 5d(6s) electrons of Ce in CeAl2 is nevertheless different from that in the other RAI2 members. This deviation might be closely connected with the electronic structure of cerium in this compound. (1973) found evidence for the existence of about 10% anisitropy in the s-f exchange constant J(0). however. This was explained by Levy as being a result of orbital contributions to the s-f exchange and spin orbit coupling of the conduction electrons (Levy 1971). (5-10)] was found to vary slightly across the RAI2 series. The s . 0973) also found that the conduction electron polarization around a 4f spin moment decreases less strongly with distance than expected on the grounds of the RKKY picture. it leads to a change in easy direction (Barbara et al. It is to be noted that the sixth order contribution is a consequence of the above-mentioned mixing and would otherwise be absent for J = ~ 2 ions. 1973. The fact that CeAl2 is the only RAI2 compound which orders antiferromagnetically (it has two phase transitions at 3.H. Dormann et al.5. Evidence for the existence of a large anisotropic exchange contribution in DyA12 was also derived from single crystal data (Barbara et al. Other experimental data support the notion that the magnetic interactions in the RAI2 series are much more compounded than the simple R K K Y approach outlined in section 2.4 and 4.1. The parameter A4a 5 of CeA12 does not fit in the series of values of the RAI2 compounds. McHenry et al. (1973a) were led to assume the presence of spin polarized d electrons residing in a narrow band in order to explain their EPR results on Gdl-xLa~Al2.5 K (Walker et al. well below To. Maple 1969) and NMR data (Kaplan et al. 1973. Maple 1969) has a remarkable temperature dependence suggests. 1967. An analysis of their data clearly shows a long-range oscillatory character of the exchange interaction but quantitative agreement with RKKY predictions is lacking. respectively) in various rare earth compounds (Dormann et al.316 K.3. 1972) seem to favour an interpretation of the magnetic properties of RA12 in terms of the RKKY formalism. 1976).J.1 would suggest: Magnon dispersion relations were studied by Bfihrer et al. Davidov et al. (1973) on a single crystal of TbA12. Some of the features sketched above were encountered in a variety of compounds other than RAI2. 1973. Jaccarino et al. Kaplan et al. 1975b.f exchange integral [eqs. 1977). (5) and (7). 1977b) and from EPR measurements on Gdl-xDyxAl2 (Nguyen et al. I .RARE EARTH COMPOUNDS 317 It can be seen from table A. like CeAI2. Neutron diffraction performed on some of these compounds shows that at low temperatures the moment arrangement is not simply ferromagnetic (Barbara et al. The results disagree with the level scheme arrived at earlier by means of specific heat data (Mahoney et al.o.J O TEMPERATURE Fig. The highest ordering temperatures are observed in RGa. In CeA13 the resistivity increases with decreasing temperature and after reaching a maximum at about 35 K decreases steeply. 1976).4 t-z = (D O0 _. which describes Kondo exchange scattering of the conduction electrons in the presence of localized moments with a crystal field split ground state (Maranzana 1970).and c-directions) of TbGa.. Evidence for the presence of crystal field splitting of the required magnitude (Maranzana 1970. Alternative explanations are based on scattering on virtual bound 4f states of widths narrower than the crystal field splitting (Andres et al. 1974). Inelastic neutron scattering experiments have been reported for PrA13 (Alekseev et al. The magnetization processes are governed by the presence of narrow walls leading to a strongly temperature dependent intrinsic coercive force. 1971b).£3 I. 1976). 4. 1971a) and Ce3Alll (Van Daal and Buschow 1970c). Andres et al.2c. 1977). . 1975a) was obtained from inelastic neutron scattering experiments (Murani et al. • 5 0 0 I 50 I ///" 100 I 150 200 K 250 300 0 0 U. The compounds CeAI3 (Buschow et al.. A typical set of data (Barbara et al.I- <~ =E 2 . show a rather anomalous temperature dependence of their resistivity. The magnetic properties of rare earth gallium compounds are listed in table A. 1975a). It falls outside the scope of this book to review all the experimental and theoretical material accumulated on CeA13 and related compounds. The same holds with respect to the so-called mixed valence compounds YbAI3 and YbA12 (Klaasse et al. 4 >- . Attempts have been made to explain this behaviour by means of the Kondo side band model.2b that the ordering temperatures of the compounds RAI3 and R3AIII are much lower than in RAI2.7 m z 8I I-_1 rfff- I't5 CL o 5 I-. Temperature dependence of the magnetization and the reciprocal susceptibility (measured in the a. 1971b) for a system containing narrow walls is shown in figs. wall movement will no longer be possible from a given temperature on.) . is frozen-in.H. When the magnetization (tr) is measured with increasing temperature in an applied field smaller than the coercive field the tr versus T curves behave in a way similar to that shown in fig. 1971a) prior to the measurements: At temperatures of sufficiently high thermal energy the field applied can remove all the walls from the sample so that the net magnetization is large.J. (Taken from Barbara et al. the typical initial rise in the cr versus T curves is generally absent if the sample is cooled in the presence of a magnetic field (Barbara et al. At the lowest temperature the thermal energy is not yet strong enough to surmount the energy barrier needed to move the narrow walls. 1971b. Furthermore. Upon subsequent cooling. in the same way as the latter. Due to the presence of the energy barrier. BUSCHOW and 5. below which wall propagation is impeded. decreases strongly with temperature (see the inset of fig. The inset shows the temperature dependence of the critical field. The temperature at which tr rises strongly will be higher the lower the applied field. The origin of the presence of narrow walls is a high magnetocrystalline anisotropy energy. A further characteristic feature of a system composed of narrow walls is the rather field independent nature of the first part of the curve of initial magnetization at low temperatures (fig.:77K / z=E1 :~°o r~ mQ: I z_~3 z 4 5 _o I i-m Z 7 I I I 22 t8 14 2 6 10 10 6 2 MAGNETIC FIELD H [kOe] 14 18 22 Fig. 4.1"Tb-~-i2 K l • . 5). corresponding to a high net magnetization. This critical field is close to the coercive field and. comparable in magnitude with the magnetic coup"' nnn~ LU a. wall propagation will become possible only above a critical field.2 K and 77 K. Increase of the net magnetization will only be possible by wall movement in directions corresponding to an increase in size of those domains for which the net magnetization is parallel to the applied field. This leads to the absence of an appreciable net magnetization in the low temperature region. 5. so that a situation with aligned moments. (/) z hJ 7 6 5 " 4 3 o T=4.318 K. 5). Magnetic isotherms of TbGa at 4. In rare earth intermetallics the former energy is the result of the crystal field interactions of moments containing an orbital contribution. The rare earth rich R . 1977) too. Inelastic neutron scattering performed on Pr3T1 has shown that the lowest crystal field level is a (non-magnetic) singlet (Birgenau et al. The compound Pr3T1 can be characterized as an induced moment ferromagnet (Andres et al. Barbara et al. unpublished). In PrTI3 (having the antistructure of Pr3TI) a singlet level is lowest (Gross et al. 2. No such effects are therefore expected in Gd compounds (L = 0 for Gd) and this is in keeping with experimental observations (Buschow and Van den Hoogenhof 1976. An enhanced interaction of 4f and conduction electrons also becomes apparent from the Kondo-like resistivity anomaly reported for this compound (Van Daal and Buschow 1970). 1972). (5) section 2.2. 1972) in which the singlet ground state is spontaneously polarized below about 11 K due to a slightly overcritical exchange interaction (Cooper 1972). Compounds with group I V elements Data of the magnetic and crystallographic properties of compounds between rare earths and Si or Ge are listed in tables A2. 1969a) (eq. (1964) from the thermal . The overall splitting was found to decrease from In to Sn.f and A2. The values of the effective moments (/~en) and the paramagnetic Curie temperature (0p) of Ce-Si and Ce-Ge compounds were derived by Ruggiero et al. In the equiatomic and indium rich R . 1971a). Pb. 1972). It can be inferred from the data shown in table A. The compounds RGa2 have extremely low magnetic ordering temperatures.1). It has been found impossible to describe the magnetic properties of these compounds by means of the R K K Y model (Buschow and Van den Hoogenhof 1976). Barbara et al. (1971c) report that DyGa2 and HoGa2 show metamagnetic behaviour below TN.I n compounds magnetic ordering is antiferromagnetic. The rather few rare earth thallium compounds whose magnetic properties have been studied are listed in table A.2e. Sn).g. Prln3 and Ndln3 and ascribed the observed change in sign of the crystal field parameters A4(r 4) and A6(r 6) to an increasing energy difference between the 4f levels and the conduction band in this sense. If one compares the 0p values and the ordering temperatures T~ of the various RIn3 compounds one finds that the values of Celn3 are greatly in excess of the expectations based on the DeGennes relation (Buschow et al.3. This suggests that the exchange interaction between the 4f electrons and the conduction electrons in Celn3 differs markedly from those in the remainder of compounds. 1977) and Ndln3 (Lethuillier and Chaussy 1976a) were determined by inelastic neutron scattering and the results were compared with the crystal field data in other RX3 (X = In. Lethuillier and Chaussy (1976a) compared the crystal field data available for CeIn3. Crystal field splittings in Prln3 (Gross et al.2d).I n compounds order ferromagnetically at fairly high temperatures (table A.RARE EARTH COMPOUNDS 319 ling energy (Barbara et al. but the low exchange interaction between the Pr moments leads to Van Vleck paramagnetism only at low temperatures and magnetic ordering was found to be absent (Buschow.2c that the ordering is antiferromagnetic. TI. (30) is given in Havinga et al. Again. 1964) precludes a further analysis of this interesting class of compounds. The tendency of the magnetic isotherms at 4. Rather high magnetic ordering temperatures are reached in RsSi4 (Holtzberg et al. It is remarkable. the positive 0p values show that the antiferromagnetic interaction may be rather weak. 1970. In contrast. Very often the temperature of the magnetization exhibits a cusp-like behaviour.A E ] k B T ) ] (30) and where N denotes the concentration of Ce atoms. BUSCHOW variation of the reciprocal susceptibility in the temperature range 100-500 K. In the model based on interconfigurational fluctuations (Hirst 1970) c ( T ) is replaced by c ( T + 0) and the positive quantity 0 is a measure of the transition rate between the two valence states (Sales and Wohlleben 1975). 1976. which indicates that Ce in this temperature range is primarily trivalent. (1973) and in Jefferson and Stevens (1976).H.2 K of GdsSi3 and various RsGe3 compounds to saturate in high field strengths (Ganapathy et al. however.J. This agrees with the positive sign of the values of Op observed. The susceptibility is then X4t(T) = Ntt2f~c(T)/3kB(T + 0) where c ( T ) = (2J + 1)exp (-AE[kBT)[[1 + (2J + 1) exp ( . Presumably the magnetic structure of these compounds is. having an effective moment equal to zero and a degeneracy equal to 1. The Curie temperature of GdsSi4 is even above room temperature and exceeds that of Gd metal. even though they have positive Curie-Weiss intercepts. 1971) has shown that these compounds order . Unfortunately the absence of low temperature susceptibility data (Ruggiero et al. Buschow and Fast 1967) shows that the antiferromagnetic interactions in these compounds are relatively weak. Neutron diffraction performed on several equiatomic rare earth silicon compounds (Whung et al. 1967). Alternatively the deviating magnetic properties of the Ce compounds could be due to an intermediate valence state of the Ce ions.54/xB. The reported/~¢n values are not far off from the free ion value of Ce 3÷ (2. Magnetic studies performed on compounds of the type RsSi3 and RsGe3 other than R = Ce show that these compounds do not order ferromagnetically at low temperatures. that the 0p values are very often strongly negative. A different interpretation of 0 in eq. even though the 0p values of the other (isostructural) rare earth Compounds of the corresponding series have positive 0p values.54t~n). rather complex. indicative of antiferromagnetic ordering. It can account for the often large negative values of the Curie-Weiss intercepts observed for 0p. where an excited valence state with an effective moment / ~ and degeneracy 2J + 1 is lying at an energy A E above the ground state. According to this expression Curie-Weiss like behaviour should be observed at high temperatures with an effective moment close to the Ce 3+ free ion value/x~n = 2. the RsGe4 compounds have rather low ordering temperatures (N6el type). This may point to a coupling scheme which for the Ce 3÷ moments is different from that of the other R 3+ moments in these compounds.320 K. At about 135 K there is a broad maximum in the susceptibility followed by a rapid rise below about 3 0 K (see fig. by the occurrence of at least four different structure types and in some cases by an off-stoichiometric composition of the compounds (Parth6 1967).6 K. Shenoy et al. The compounds PrGe and NdGe behave differently. Borsa et al. (5) in section 2. 1967.S n and R . Cooper et al.1). Recent high pressure susceptibility data show that the thermal expansion is not responsible for the magnetic-non-magnetic transition in CeSn3 (Beille et al.2g). Magnetic ordering in these compounds occurs at rather low temperatures and is antiferromagnetic (TN < 25 K). This sign reversal of 0p within the R G e series shows that the magnetic interactions in R Ge cannot be described by the simple RKKY approach (see eq. Antiferromagnetic order has also been reported (Buschow and Fast 1966) to occur in the compounds R G e with rare earth elements of an atomic number higher than that of Nd. LaGe2. In CeSn3 no magnetic transition was found down to 1. 1976). NdSn3 and NdPb3 the magnetic structure has been determined by neutron diffraction (Lethuillier 1974). 6). 1970. The tt9Sn Mrssbauer spectra obtained on this compound did not show significant changes of the isomer shift and the quadrupole interaction around 135 K (Shenoy et al. Sekizawa 1966. Sekizawa and Yasukochi 1966a). In contrast to the compounds with a rare earth of a higher atomic number the paramagnetic Curie temperature of PrGe and NdGe are positive and the temperature dependence of the magnetization points to ferromagnetism. In the high temperature region (T > 200 K) Curie-Weiss behaviour is followed with /~en= 2.2h. Magnetic properties of rare earth compounds with tin and lead are listed in table A.P b compounds has been focussed mainly on compounds of the relatively simple AuCu3 structure. The magnetic susceptibility of this compound exhibits a rather peculiar temperature dependence (Tsuchida and Wallace 1965.RARE EARTH COMPOUNDS 321 antiferromagnetically. YGe2 and ScGe2 have been reported to become superconducting at low temperatures (Matthias et al. EuSn3 and GdSn3 (Sanchez et al. 1964). In SmSn3 the magnetic structure is antiferromagnetic of the first kind (like in PrSn3 and NdSn3) whereas it is more complicated in EuSn3 (doubled unit cell) and in GdSn3 (helical spin structure). The sign reversal of 0p in the RGe2 series is again indicative of a coupling scheme of the localized moments not describable in terms of the R K K Y approach. however. The occurrence of the susceptibility maximum was first attributed to a Ce 3÷~ C e 4+ partial conversion associated with the thermal contraction of the lattice (Tsuchida and Wallace 1965). ferromagnetism has been reported in several members of the series RGe2 when R is a light rare earth element (see table A. The study of the magnetic properties of these compounds is considerably hampered. Henry 1962). 1958.78txa/Ce and 0p-203 K (Ruggiero et al. magnetic ordering seems to become antiferromagnetic (Yaguchi 1966. Apart from PrSn3 and NdSn3 conclusions about the magnetic structure type could be derived by means of Sn Mrssbauer spectroscopy in SmSn3. 1977). It is interesting to note that the compounds LaSi2. 1970).1 and the discussion given in section 2. On the other hand. It can be seen from the table that the study of magnetic properties in R .3. In the compounds RSi2 and RGe2 involving heavy rare earth elements. 1971). In PrSn3. . is an explanation of the peculiar x(T) behaviour in terms of an intermediate valence state. This does not seem to preclude a temperature dependent valence state change in CeSn3 since these two parameters appear to be hardly affected by the valence state of the R ions in RSn3 (Sanchez et al.2 i I ' I K. . - 2. If the ground state corresponds to Ce 4+ and the excited state to Ce 3+ eq. BUSCHOW ' I i I ' I i I ' I cesn 3 3. expected in compounds of Sm to occur close to 300 K. 1974).. 1974). therefore. This agrees with the temperature dependence of the Sn Knight shift observed in CeSn3 (Malik et al. (30) does indeed predict a maximum in x(T) and furthermore can account for the large negative value of 0p without involving magnetic ordering.4 1.H. I 0 40 80 t20 t60 200 240 280 1. 1976).322 I 1.5 T(K) Fig. thermoelectric power and the specific heat.8 f 0. (1974) and by De Wijn et al. This has been explained as being due to crystal field induced mixing of the J = ~ multiplet into the J --.7 i I i I i I i I l I I I . The close proximity of the 4f level to the Fermi level in CeSn3 leads to interesting behaviour of the thermal variation of the electrical resistivity. proved to be absent.0 - 2. For more details we refer to the reviews by Malik et al. It is to be noted that in this picture a maximum is also expected for the thermal average of the spin moment.5 ~0 rO k. 6. (1974). The temperature dependence of the tl9Sn Knight shift and the magnetic susceptibility in CeSn3 (taken from Malik et al.3 1.0 0. (1976a). The sign reversal of the Sn Knight shift. Rather unusual magnetic behaviour is displayed by SmSn3.~ground state in the presence of exchange fields.J. These quantities have been reviewed recently by Malik et al. Most likely. An analysis of the magnetic properties in terms of the R K K Y model (Van Steenwijk et al. Pierre 1967.2j. 1964). Attempts to explain the magnetic properties by means the R K K Y model are based mainly on the results of a magnetic investigation of the series Gd(Ni. indicating antiferromagnetism at low temperatures. Attempts have been made to explain the magnetic properties of the CsC1 type R C u compounds by means of the R K K Y approach (De Wijn et al. Yashiro et al. The R K K Y approach does not seem quite satisfactory for explaining all of the data (including hyperfine fields) in the case of the hexagonal compounds (Van Steenwijk et al.~-l) with those of GdZn2 (0p=68. Neutron diffraction performed on R C u with R = Tb. . The results were compared with similar measurements made on the isostructural compounds ErAg and ErZn.A u compounds are listed in table A. De Wijn et al. 1964a. Cu)2 (Poldy and Kirchmayr 1974). Most of the compounds have negative Curie-Weiss intercepts.5. 1971). 1972). 1968. Sekizawa and Yasukochi 1966b. 1968.2i that the equiatomic rare earth copper compounds occur either in the cubic CsC1 structure or in the orthorhombic FeB structure. Buschow et al. Most of the compounds investigated show metamagnetic behaviour (Sherwood et al. driven by the strain coupling of the singlet crystal field states of the Pr 3+ ion (Wun and Phillips 1974. 0) (Cable et al. Chao et al. The sixth order term derived from these measurements exceeds the value obtained via point charge calculations by one order of magnitude (see also section 2. Ho and Er showed that in all cases the magnetic structure is antiferromagnetic.3.5).A g and R . ½. Although most of the changes in magnetic behaviour of this series can be explained satisfactorily.~ -1) since the picture proposed predicts a strong reduction of 0p if the conduction electron concentration is increased in going from GdCu2 to GdZn2. With the exception of LaCu2 all compounds RCu2 have the orthorhombic CeCu2 structure. This will be discussed in more detail in section 2. With the exception of EuCu5 magnetic ordering in RCu5 compounds occurs at rather low temperatures. b.3. Pierre 1970). The splitting of the crystal field levels in ErCu was studied by means of inelastic neutron scattering (Morin et al. some difficulties are encountered when comparing the data of GdCu2 (0p = 11 K. Magnetic properties of R . 1977). together with the results of band structure calculations (Belakhovsky et al. 1970) is hampered by the change in crystal structure from hexagonal to cubic between EuCu5 and GdCu~. kF = 1. The properties of PrCu2 are unique in this series in that at low temperatures a cooperative Jahn-Teller effect occurs. Burzo et al. 1969. Compounds with group Ia elements It can be seen from table A. Andres et al. 1964. 1976. Winterberger et al. Dy. Winterberger et al. the magnetic propagation vector being q = (½.50. Pierre 1969). kr = 1. 1971. In all three cases the parameters A°(r 4) and A°(r 6) were found to be negative (Fs quartet level lowest).3. 1972.39 . 1974a). 1976). although a N6el type transition in the thermal variation of the magnetization has been discerned only in relatively few of these compounds (Walline and Wallace 1965.RARE EARTH COMPOUNDS 323 2.3. 1977. This seems to disagree with the view expressed by Sekizawa and Yasukochi (1966b). Ihrig et al. 1976). The compound PrAg is antiferromagnetic below about 11 K but undergoes a spin-flop transition in fields in excess of about 5 kOe (see fig.324 K.H. unpublished). BUSCHOW Since the R A u and RAg compounds have similar electron concentration and crystal structure as the CsCl-type RCu compounds it is predicted by the R K K Y model that the magnetic properties of RCu. A closer analysis of the data. Ihrig and Methfessel 1976b). The first members of this series are nevertheless not far off structural instability.2j shows indeed that the magnetic properties of GdCu and GdAg are not very different. The same then holds with respect to the values of 0p and/~eu derived from such data. RAg and R A u should be the same for a given R. (1976). however. Polarized neutron experiments on CeAg have shown that this compound undergoes a distortive cubic to tetragonal transition at 21 K. On the other hand it cannot be excluded that the occurrence of a phase transformation upon cooling from room temperature to 4. This follows from investigations on pseudobinary RAgl-xInx compounds (Ihrig and Methfessel 1976a. 1975). Comparison of the corresponding Gd compounds in tables A. which is only slightly above the magnetic ordering temperature (Radhakrishna and Livet. 1974b) revealed that the net exchange field on a Pr atom does not vary linearly with the magnetization M but also contains a substantial negative term in M 3. Unlike the case with the R A u compounds. Cubic to tetragonal transformations in these compounds are ascribed either to a bandor to a molecular Jahn-Teller effect associated with the e s levels of the rare earth 5d electrons.J. the sign of 0p is no longer negative. In GdAu. and that a distortive phase transition can also be driven by the 4f electrons in these compounds. 1975. This was . This difference in structure could partially account for the difference in magnetic properties between GdAu and GdAg or GdCu. Extensive bulk magnetic and neutron diffraction measurements were made on PrAg by B r u n e t al.2 K and vice versa. indicating that ferromagnetic interactions prevail in this compound. together with the magnetic transition it has been described by means of a spin Hamiltonian involving dipolar as well as quadrupolar interactions (Ray and Silvadiere. 1976b). however. using crystal field energy levels for Pr 3÷ derived from inelastic neutron scattering experiments (Brun et al. can lead to deviations from the true temperature dependence of the susceptibility associated with either one of the two phases. More recently it was found by means of M6ssbauer effect spectroscopy that the CsCI structure in the R A u compounds is metastable and undergoes a low-temperature martensitic phase transformation to a close-packed FeB-like structure (Kimball et al. It seems. no martensitic type of structure transformation has been found in RAg compounds (Goebel et al. if extended over a relatively large temperature region. 7).2i and A. b. where 0p is considered to be a slightly decreasing function when plotted versus increasing lattice constant in pseudobinary series based on these compounds. that the situation can be even more complex in some cases. This transition has been ascribed to a cooperative Jahn-Teller effect involving the 4f electrons. the lattice constant of GdAu is in between those of GdCu and GdAg. Furthermore. t e H m J .5-- Pr Ag m 1. Temperature dependence of the magnetic moment of PrAg in various field strengths (taken from Brunet al. 1975). The analysis of the experimental data was based on a single-ion Hamiltonian similar to eqs. There are two antiferromagnetic transitions at low temperature between which the magnetic ordering entails a sinusoidally modulated magnetization wave. propagating in the (100) direction. (25) was expressed as ~'ex = .5- 0 10 T(K) 20 30 Fig. 7. ::L =0 0. . Tellenbach et al. taken as an indication that the spin Hamiltonian in the paramagnetic regime contains a positive biquadratic exchange term. however. (22-25) in section 2.RARE EARTH COMPOUNDS I 56 KOe I I I I 325 1./). of eq.. It is incommensurate with the chemical unit cell and is also temperature independent. A commensurate antiferromagnetic structure does exist. 1973). at temperatures below the lowest of the two transition points mentioned. Information on the crystal field splitting and the exchange interaction in HoAg and ErAg has been obtained from inelastic neutron scattering experiments (Furrer 1975. Further proof that the magnetism in the RAg compounds is not that simple comes from neutron diffraction studies performed by Nereson on HoAg and ErAg (Nereson 1963.2 but where the term ~c.0~ 0. The molecular field Hm in this equation was approximated by Hm = gj/~)t(.g. 1974b).q. B e compounds derived from model calculations is close to zero. 1972a. Furthermore the crystal field Hamiltonian had to be expressed with respect to an axis other than a symmetry axis in cases where the magnetic moment was tilted away from the z-axis. These values scale reasonably well with the corresponding TN values. Qualitatively these parameters display the oscillatory behaviour expected on the basis of the R K K Y formalism. J2 = +0. b. Here nr is the number of r'th nearest neighbours and Jr is the isotropic exchange constant with an ion of the r'th neighbour shell. Antiferromagnetic ordering also exists in the compounds of the type R Ag2 and RAu2 (see table A. The RBeL3 compounds. By considering only neighbour interactions up to r = 3 and using the A values corresponding to the paramagnetic. The energy levels were calculated by diagonalizing ~o = ~ c + ~ex and keeping Hm as a parameter. b. Numerous neutron diffraction studies performed on these materials by Atoji (1968a. therefore. Many of the compounds have more than one magnetic transition temperature and the magnetic structures are very often incommensurate with the crystallographic lattice. Compounds with Be. By means of fitting procedures.2k were obtained by Bucher et al.4. the jump fields are proportional to the exchange: For R B ~3with R = Tb. Sill et al. The positive value of 0p in the former and the peculiar magnetic isotherms found for some of the RAu3 compounds suggest that the magnetic properties are again not free from complexity. that the number of existing rare earth beryllides is rather limited. Most of the data listed in table A.049 meV and J3 = . Mg and group IIa elements A glance at the data in table 1 Shows that the heat of formation of R . respectively. 2. commensurate and incommensurate region. The occurrence of transitions from the antiferromagnetic via spin flop to the paramagnetic phase in relatively low magnetic fields is in keeping with the fact . Dy. involving the experimental results obtained in the magnetically ordered and paramagnetic regime. whose magnetic properties are given in table A. It is not surprising. 1969a. Furrer obtained the following results: Ji = . 0 0 4 meV. b. leading eventually to a paramagnetic phase in high applied field strengths. 5 and 3 kOe. 1970.3.0 . In the case of ErAg Furrer has used the following expression: H m = 2(gj/~B)-l ErnrJr(J).326 K.J. In low field strengths the magnetization of most of the compounds with heavy rare earth elements show a N6el type transition in their temperature dependence.2k are in fact the only stable rare earth beryllides known at present.2j). 1971). c) have shown that the magnetic structures of these materials can be rather complex. No clear indication of the magnetic ordering type could be derived from magnetic measurements in RAu3 and RAu4 compounds (Sill and Prindeville 1975.H. Ho the step-like jumps occur at about 8. Since the magnetocrystalline anisotropy energy can be regarded as appreciable compared with the exchange energy. These features are reminiscent of spin flop transitions. (1975). BUSCHOW where A is the molecular field constant. The magnetic isotherms studied well below TN are either concave upward or exhibit a step-like jump at some critical field strength.0 . the level schemes were obtained together with the corresponding molecular field parameters. 0 9 3 meV. separated by AE. where the lower and higher states correspond to Ce 4÷ and Ce 3÷. S c h ~ e r et al. The peculiar magnetic isotherm found for DyB~3. Aleonard et al. 1976) which is difficult to understand in terms of the R K K Y approach. (30). In the first place there is a sign reversal of 0p in going through the series (Buschow 1973b. with a Ce3+/Ce4÷ ratio depending on the temperature. In view of the anomalously low lattice constant (Bucher et al. S c h ~ e r et al. then qualitatively leads to the required temperature behaviour of the susceptibility. 1975. The exchange constant J(0) [see eq. saturation is not yet reached in the field-induced paramagnetic phase. Magnetic properties of rare earth magnesium compounds are displayed in table A. respectively. none of the compounds with heavy rare earths can be regarded as truly ferromagnetic. Presumably. (1976) and by Heinrich and Meyer (1977). points strongly in this direction and makes it clear that a description of the magnetic properties in terms of spin flops is too crude a picture. 1976. 1975) and the temperature dependence of the 9Be nuclear magnetic resonance and relaxation (Borsa and Olcese 1973) this x(T) behaviour was ascribed to an intermediate valence state of the Ce ions. I) reflection indicates some tendency to antiferromagnetic short-range order (Aleonard et al. Straightforward application of eq. Bloch et al. which could obscure the N~el type transition. This may be due to the presence of a large magnetocrystalline anisotropy and/or to a crystal field ground state with a moment smaller than g3/~B. Bucher et al. 1977) and DyMg antiferromagnetic with a collinear spin arrangement (Aleonard et al. report in addition that this quantity varies significantly across the rare earth series. in particular. 1976b). Bucher as well as Borsa and Olcese found a rather peculiar temperature dependence of the susceptibility in CeBem3 showing a maximum close to 140 K. The magnetic properties of compounds of the type R M g have rather unusual features. (1975) ascribe the step-like jumps mainly to additional admixtures of excited crystal field states into the ground state or to Zeeman level crossing of adjacent crystal field levels as the field strength increases. Magnetic ordering in HoMg also seems to be primarily ferromagnetic. Low-intensity antiferromagnetic reflection .RARE EARTH COMPOUNDS 327 that 0p in the compounds considered takes positive rather than negative values and is furthermore close to the values of TN. The discrepancy with the results of Bucher et al.2~. (1976b) report ErMg to be ferromagnetic at 4. Neutron diffraction measurements performed on several of these compounds show that TbMg is antfferromagnetic with a non-collinear spin arrangement (Aleonard et al. Furthermore. In the highest field strengths applied the magnetization corresponds to R moments smaller than the free ion values (gJ/~B). E P R investigations on rare earth beryllides have been reported by Bloch et al. 0. No further analysis of the x(T) curve in CeBe13 was given. S c h ~ e r et al. (10)] was found to be positive in both investigations. a diffuse antiferromagnetic (0. although such behaviour is suggested by the observation of paramagnetic-ferromagnetic transition temperatures. is very likely due to the application of too high a field strength in the magnetization measurements. Very probably the data can conveniently be explained under the assumption of two energy states.2 K. In their investigations of RBe13 compounds Borsa and Olcese (1973) reported the occurrence of ferromagnetism in GdBe13. 1976). In several compounds. primarily in TbMg and DyMg. More experiments are needed to clarify the situation.H. unpublished). EuMg2 has a N6el type transition rather than a paramagneticferromagnetic transition (Buschow et al.1. Since Eu in EuMg2 is divalent. (1976). 1978. For the RZn compounds in which R = Ce. Pr or Nd the neutron patterns can be described by antiferronagnetic structures having a propagation vector (0. There is some doubt about the prevailing ferromagnetism reported in GdMg3 and TbMg3 (Buschow 1976). approaching room temperature in the case of GdZn (see table A. High field magnetization measurements performed on Gd~-xLaxMg made it clear that the RKKY mechanism is not able to deal adequately with the magnetic properties of the RMg compounds (Buschow and Schinkel 1976). A determination of the crystal field parameters in RMg was made by Aleonard et al. Buschow and Oppelt 1974. 1975. (1976) via magnetization anisotropy studies on single crystals.2m).J.2e).2 to 1. 1977b). As was discussed by Morin and de Combarieu (1975).328 K. Doubling of the unit cell upon magnetic ordering can occur in more than one direction and lead to non-collinear spin structures. The ferromagnetic ordering temperatures are slightly lower than in the corresponding RMg compounds. No neutron diffraction data have as yet been obtained on these compounds. this possibly originates from a different conduction electron concentration. Morin et al. this solution is not unique for a description of the neutron diffraction results in cubic materials. 1976). since this may be due to a contamination with the corresponding RMg2 which can be suppressed by applying an excess of magnesium (Will et al. the magnetic isotherms at low temperatures indicate the presence of domain effects involving small domain walls such as described in the case of Tb3A12 and TbGa in section 2. BUSCHOW lines. Magnetic ordering in R Mg3 compounds occurs at rather low temperatures and is antiferromagnetic. not commensurate with the lattice and increasing in intensity from 4. were observed by Aleonard et al. 2 l) (Buschow et al. depending on whether R in R Z n belongs to the light or heavy rare earth elements. 1975c. 0. respectively. Magnetic ordering is antiferromagnetic or ferromagnetic. respectively. Morin et al. Buschow and Schinkel 1976. Crystal field effect considerations and results of .5 K. 1978). Only some of the RMg2 compounds are cubic (see table A.. This severely hampers the interpretation of the neutron diffraction results. where crystal fields are absent (Aleonard et al. Inelastic neutron scattering studies on ErMg led to the same result (Morin et al. They found A4(r 4) and A6(r ~) to be negative and positive. Alternatively it is possible that magnetic ordering in RMg3 depends strongly on deviations from the ideal site occupancy in the Fe3AI structure type. The too low saturation moments and the often peculiar temperature dependence of the magnetization below Tc indicate that the actual magnetic structure in RMg2 may be more complicated than simply ferromagnetic. The equiatomic rare earth zinc compounds have relatively high magnetic ordering temperatures. Pierre et al. 1979).3. Complex magnetic behaviour has also been observed in GdMg. This will be discussed in more detail in section 2. Debray et al. The decrease of the magnetic ordering temperatures was found to proceed much faster with x in Gdl_xLaxZn than in Gdl-xYxZn (Eckrich et al. The compounds RZn2 crystallize in the orthorhombic CeCu2 type of structure. Attempts have been made therefore to use an extended form of the RKKY theory which approximates the s-f exchange integral by the form factor of the local moment density and in addition considers a non-negligible interelectron interaction between the conduction electrons.RARE EARTH COMPOUNDS 329 specific heat measurements reported by these authors favour a non-collinear antiferromagnetic structure with the moments along (110) at temperatures between TN and 18 K. 8). 1976). Morin et al.2 is used in conjunction with eq. Field induced metamagnetic transitions have been reported by Debray et al. 1970a. Below this temperature the moments in the non-collinear structure are assumed to point along 011). First an approximate value of H~x was used in the diagonalization of eq. The effect of this extension is to shift the node of the oscillating RKKY function in the kF range appropriate to GdZn2 towards slightly higher kF values.5. I[ has been noted by Debray and Sakurai (1974) that the positive value of 0p in RZn2 is not expected on the basis of the RKKY approach if eq. (25) was put equal to -gl~BHexJ~. 1974b).3. (5) in section 2. thereby making 0p positive at the free-electron value kF = 1. DyZn: and TmZn2 (see fig.2 [eqs. Neutron diffraction performed on several of these compounds shows that the magnetic structure is in general rather complicated (Debray and Sougi 1972. (22-26)]. where H~x = nglxa{Jz}r. These results are in disagreement with a description of the magnetic properties of the RZn compounds by means of the RKKY formalism.50 A-1 (see for instance fig. Magnetic dilution studies have been reported of GdZn. From the level scheme a new value of the thermal average {J~)r was derived and used subsequently to solve the problem self-consistently in the various crystallographic directions. (25). (1975) to occur in EuZn2. 1973. An analysis of the experimental data was given in terms of a molecular field model including crystal field effects along lines analogous to those outlined at the end of section 2. The Hamiltonian ~ex of eq. 1976). 1976). 1973. and unpublished) and entails incommensurate sinusoidal magnetic structures which in some cases give rise to a first order transition to a commensurate structure upon further cooling. (12). It would be interesting to investigate how far this approach also leads to a consistent description for compounds of different conduction electron concert- . The crystal field parameters A°(r ~) and A°6(r6) derived from this analysis (Morin et al. Magnetization measurements on single crystals and specific heat measurements have shown that in the ferromagnets TbZn and HoZn a similar rotation of the magnetic moment with temperature occurs at 65 K and 25 K. 1974b) were found to be reasonably consistent with the crystal field parameters obtained by inelastic neutron scattering in ErZn (Morin et al. together with NMR data obtained on these materials (Eckrich et al. 1973. respectively (Morin and Pierre 1973. 1 in Debray and Sakurai 1974). even though the free electron kF values are much lower than in GdZn2 (kF = 1. ErZn2 and EuZn2. (1975). also detected by ESR measurements (Taylor 1975. respectively). 1971). 2 8 --I Euzn 2 6 p t~ en ::L m 4 ~ ¼1~ 0 T=4. Magnetization and electrical resistivity measurements performed by Stewart and Coles (1974) on the more dilute rare earth zinc compounds R2Znn7 and RZn~2 have shown that most o f these compounds order antiferromagnetically at relatively low temperatures. investigations into the presence of short-range order have been focussed mainly on the Gd compounds.330 K. 1971). Short-range order.2K / 0 lO I 20 I 50 I 40 I 50 60 Heff (koe) - Fig.2n) and that the ordering temperature of GdCd is almost the same as in . BUSCHOW 4 6 4 I <¢ _.38 ]~-1 and 1.H.TmZn2. The data are taken from Debray et al.' 8.40 A-1 in EuZn2 and GdCu2.1 _ o I. It is not surprising therefore that the RCd compounds are also ferromagnetic (table A. Since [0p[ in Gd2Zn~7 as well as in GdZn~2 is much larger than TN. Rare earth cadmium compounds of the composition R C d are similar in crystal structure and formal conduction electron concentration to the compounds RZn. tration such as EuZn2 and GdCu2. the presence of short-range order effects is not quite unexpected (Fisk et al.J. In these two compounds 0p is still positive.¢. In order to exclude effects of crystal fields. was found to lead to deviations from normal Curie-Weiss behaviour at temperatures appreciably in excess of the N~el temperatures (Stewart and Coles 1974). see also Fisk et al. Field dependence of the magnetic moment in DyZn2. The in- . Apart from those of GdCd. whereas the A6(r 6) term remains negative and of the same order of magnitude in all compounds. It should be emphasized that the progress made with respect to crystal field effects is predominantly in the experimental field. 2. Cu. It is gratifying that in recent years single crystals of some of the compounds have become available by means of which reliable data regarding the crystal field splitting could be obtained via measurements of the magnetization anisotropy. Seemingly of more importance are the Coulombic terms arising from the anisotropic charge distribution of the conduction electrons. In such cases information on the crystal field effects and the indirect exchange coupling could be extracted simultanously. Zn. (1973). No such behaviour is expected if one takes into account merely the effective ligand charges. such as for instance given in the paper by Morin et al. even if derived from APW calculations. The difficulties one has to cope with in setting up such a model are demonstrated in comparative studies.RARE EARTH COMPOUNDS 331 GdZn. Discussion It is obvious from the results described in the preceding sections that the magnetic properties of the various rare earth intermetallics are governed mainly by two different entities: the crystal field splitting and the indirect exchange interaction between the localized moments.5. (1976): the fourth order potential term A4(r 4) in various CsC1 type ErX compounds (X = Rh. 1967). Unfortunately the unfavourable neutron crosssection of natural Cd seriously hampers magnetic structure determinations by means of neutron diffraction studies in all these materials. Unfortunately this applies to a rather large number of the compounds discussed above. is rather large. In almost all cases the temperature dependence of the magnetization below Tc was found to exhibit pecularities not expected for a normal ferromagnet (Buschow 1974.3.2n. Rather compounded situations can be expected in cases where the crystal field splitting and the indirect exchange interaction are of the same order of magnitude. A unique model by means of which crystal field splittings can be predicted is still lacking. Pd. The few examples available in the literature are listed in the second part of table A. Alfieri et al. Mg) becomes less negative in the sequence Rh to Mg and changes its sign between Zn and Mg. Considerable progress in this field has also been made thanks to inelastic neutron scattering experiments. The same holds for R H g compounds. Magnetic data pertaining to the members of other R C d series are still rather incomplete. Most of the new data have contributed considerably in showing that the point charge model is less well applicable to the present compounds. Ag. though smaller than the crystal field splitting. A cooperative Jahn-Teller effect from cubic to tetragonal symmetry has been reported by Liithi et al. the magnetic properties of the other members of the R C d series appear to be more complex due to the presence of large crystal field induced magnetocrystalline anisotropies and incidentally also to transformations in their crystal structure. In some special cases such experiments have even led to useful results when performed in the magnetically ordered regime on compounds in which the exchange interaction between the localized moments. Freeman 1972. a consistent description by means of the R K K Y model of the Op sign reversal in series like GdAg~_~Zn~ or GdCul-~Zn~ necessitates a similar change in sign of the hyperfine field at the non-magnetic site. (2) over all the extremal surface calipers. the sign reversal in the series R Mg and the strongly non-linear Op behaviour in magnetic dilution experiments on Gdl-xLaxMg (Buschow and Schinkel 1976). leading to an oscillatory distance dependence of the exchange coupling between the localized moments. (7) or eq. 1970) as well as theoretical (Hasegawa and Kiibler 1974. proper cognizance should be taken of contributions due to the anisotropic exchange between the 4f electrons and the conduction band (Morin et al. 1969) and with the oscillatory behaviour of the coupling constant between localized moments derived from neutron scattering experiments (Biihrer et al.1. BUSCHOW creasing localization of the 3d(4d) electrons due to the X component. Most of the reported discrepancies pertain to CsCl type compounds. Tannous et al. 1976). The origin of the large A6(r 6) is still obscure. 1976).J. lead at least to the correct trend in the A4(r 4) values observed (Morin et al. Apart from the contributions mentioned above. 1975. In the last decade numerous attempts have been made to understand the magnetic interactions in rare earth intermetallics in a more quantitative way by comparing the magnetic properties with results of NMR measurements and using eq. Results of such analyses were satisfactory in general but mostly resulted in values of the parameter kF slightly different from those (k °) derived by means of the free electron model [eq. In such cases it is more appropriate to sample J(q)f(q) in eq. Instead of a singularity at q = 2k°v. Furrer 1975). 1976. 1976. Intuitively one would expect that the strong localization of the 4f electrons justifies a description of the coupling between 4f moments in terms of the R K K Y model discussed in section 2. as well as the progression in filling of the rare earth 5d band in the sequence Rh to Mg. 1972). Qualitatively these features are in agreement with the observation of different Knight shifts in compounds of more than one crystallographically inequivalent site (Van Diepen et al. (5) in combination with either eq. Davidov et al. Examples of experimental results on bulk material are: the sign reveral of #p in the series GdX with X = Cu. Gdt-xLaxZn and Gdl-xYxZn (Eckrich et al. 1968).H. This is not found experimentally (Oppelt et al. These discrepancies were ascribed to a non-spherical Fermi surface'. (12)]. Ag or Au. This model entails a non-uniform conduction electron spin polarization.332 K. 1973. so that J(0) as well as kF take the form of an average (see also Watson 1967). Ray 1974) indications have been obtained that the dis- . Recently numerous experimental data have been reported in the literature which are more seriously in conflict with the R K K Y approach. Devine and Ray 1977). Weimann et al. 1973. (8) and solving for J(0) and kF (see for instance De Wijn et al. 1973. Experimental (Goebel et al. Furthermore. singularities will occur at values both smaller and larger than 2k°v. Dormann and Buschow 1976. Similar information regarding IJ(0)[ and kF has also been extracted from neutron diffraction studies by calculating the kF dependence of the stability of various magnetic structures and comparing the results of these calculations with the trends observed experimentally (see for instance Pierre 1969). b) seem largely to depend on the electronic properties of the 5d electrons. Correlation between the paramagnetic Curie temperature (Op) and the transferred hyperfine field at the Gd site (HN) in various Gd compounds. respectively. . They found a strong correlation between the magnitude of 0p and the sign of the transferred hyperfine field Hs at the Gd site (see fig. Dormann et al.RARE EARTH COMPOUNDS 333 crepancies with the RKKY formalism originate from a relatively large participation of the rare earth 5d electrons in the indirect exchange interaction. too. (1977a) extended their NMR investigation to several ferromagnetic Gd compounds of the cubic MgCu2 type. This correlation is based on the fact that the hyperfine interaction constants of s and d electrons are positive and negative. In order to check how far the 5d electrons participate in the indirect exchange interaction in other than CsCI type compounds. t00 I Gd'l'r2 | GdRh 2 m 0 -3O0 --------I 0 HN (kOe) GdRh 300 Fig. The results of a further analysis of their data suggest that the RKKY interaction is much weaker than hitherto assumed and leads to magnetic ordering temperatures of only moderate strength. Reasonably large values are only obtained in the presence of a 300 - ! Gd GdZn 200 I-GdAI2 O. 9). These results are interesting in so far as in these CsC1 type compounds the crystal field splitting and the crystallographic structure transformations (Ihrig and Methfessel 1976a. 9. M compounds have been observed only when M represents Mn. The 4f-3d coupling then arises indirectly via the 3d-Sd interaction.R interaction. In the second scheme (Campbell 1972) the 5d electrons of the rare earth elements play an important role. 3. provided the latter do not belong to the first few members of the transition metal series.M interaction. In the case of transition metals of the 3d type stable R . From the discussion given above it would appear that the predictive value of the RKKY coupling scheme is actually rather limited and that for an a priori description of the magnetic properties in the rare earth intermetallics a knowledge of details of their band structure would be required. the R . The magnetic interactions in R . in general. The 4f-s interaction was taken to be of the spatial non-uniform R K K Y type.M compounds is given by the ordering temperatures in compounds in which there is no moment on the M atoms. BUSCHOW participation of 5d electrons in the indirect coupling between the localized moments. Initially rare earth intermetallics and their magnetic properties were believed to represent standard examples of the R K K Y coupling scheme. In a way all these results seem rather frustrating. Co or Ni.H.R coupling in R .R coupling will be weak but may reach somewhat higher values if the indirect exchange proceeds via the 5d electrons.R interaction is the weakest of the three types mentioned.M interaction and the M . Exchange interaction in metal systems containing d electrons It may be inferred from the data listed in table 1 that the combining of rare earths and d transition metals leads to the formation of stable intermetallic compounds. Through ordinary 4f-5d exchange the localized 4f spins produce a positive local 5d spin polarization. As a matter of fact it is similar to the indirect interaction between the localized 4f moments in compounds belonging to the group of intermetallics discussed in the preceding sections. These have ordering temperatures well below 100 K. Three different schemes have been proposed for the coupling between the R and M moments. An impression of the strength of the R . In the first scheme (Buschow 1971b.1.M compounds comprise therefore three different types: the R .334 K. In cases of a purely RKKY type exchange the R . the 3d-s interaction was assumed to be positive (Wallace 1968) or of the same type as the 4f-s interaction (Buschow 1971b).J. The R . Fe. Compounds with d transition metals 3. Campbell (1972) argues that with respect to the 5d electronic properties one can consider the rare earth elements as belonging to the first half of a d-transition . Such a situation is reached in several RNin compounds (n ~<2). The unpaired 3d electrons of the transition metal component give rise to a magnetic moment in most cases. Wallace 1968) the coupling is assumed to proceed via polarization of the s conduction electrons. The sign of the 4f induced s electron polarization at the transition metal site depends on the sign of J(0) as well as on the sign of the lattice sum Y. too. (1960) [which have shown the rare earth induced s electron polarization to be negative at the AI sites].RARE EARTH COMPOUNDS 335 metal series. Co or Ni belong to the second half of such a series.1). The magnetic moments corresponding to the "alloys" were calculated within the molecular field and Hartree-Fock approximations. and like iron. Possible exceptions to this rule may occur with Mn compounds since this element belongs to the first half of the 3d transition metal series. It is reasonable to assume that this electron transfer would be accompanied by a more complete filling of the 3d electron states of the Mn atoms. In R . too. making the overall 3d-4f spin coupling antiferromagnetic. Co and Fe.M coupling is sensitive to changes in crystal structure and electron concentration. one expects a negative 5d-3d interaction.M compounds. 1977). Since the elements M = Fe. A third coupling scheme has been proposed by Szpunar and Kozarzewski (1977). With a positive s-3d interaction the overall 4f-3d coupling would then be antiferromagnetic. The reason for this is that this scheme is based on analytical expressions of the RKKY type interaction like eq.1. In their model the localized rare earth spin interacts with d electrons that are accommodated in narrow bands formed essentially with the 5d and 3d states of the rare earth and transition element atoms. respectively. (4) in section 2. In general considerable electron transfer from the rare earths to Mn may take place in view of the large electronegativity difference between these elements (Miedema et al. It can be expected therefore that the R . It was found that the model leads to an antiparallel coupling between the rare earth spin and the transition metal moment in rare earth compounds based on M = Ni. In order to be able to apply the coherent potential approximation it was furthermore assumed that the average magnetic moments of the transition metal atoms and rare earth atoms do not depend on the various types of sites in which these atoms can be accommodated in the crystal structure of the R . see section 2. but contrary to the first scheme no analytical expressions have been used in . A model dealing with the temperature dependence of the magnetization of rare earth transition metal compounds has been given by Szpunar and Lindgard (1977). In this case. (4) of section 2.i F(2kFIr-Ril) appearing in eq. the exchange interaction has been taken to be independent of k and q (J(q) = J(0). independent of the R[M ratio. It is worth noting that also the model proposed by Szpunar and Lindgard bears some features of an RKKY type interaction.1. Guided by 2~AIKnight shift results on RAI2 compounds reported by Jaccarino et al. Wallace (1968) has proposed that a negative s electron polarization prevails also at the transition metal sites in R . In contrast to the second and third coupling schemes mentioned above no uniform behaviour regarding the sign of the coupling between the R and M moments emerges from the first scheme. cobalt and nickel give rise to an antiferromagnetic coupling between the R and M spin moments.M n compounds manganese might therefore behave as a 3d element belonging to the second half of the transition series.M compounds. 10a the Fermi energy is much higher than the top of the 3d band.H. In case (b) the Fermi level is low enough to allow for a partial depletion of the 3d band. For the sake of clarity. The relatively strong effective Coulomb repulsion between the 3d electrons in these bands can favour situations in which the number of spin up and spin down electrons is no longer equal and leads to the formation of a magnetic moment. The effective Coulomb repulsion between the 3d electrons can be too weak. where the integration extends from the bottom of the 3d band up to the Fermi energy. Spin down and spin up electrons are indicated by arrows. however. As a matter of fact the effect of atomic ordering of the R and M atoms into well-defined crystal structures has been disregarded completely. Sometimes tt is possible to distinguish experimentally between cases (c) and (d). (b) EF (c) (d) EF I E N(E) Fig. which leads to 3d electron bands rather than to 3d levels. in which N(E) is considerably lower. The position of the Fermi level is indicated by E~. A comparison of the shaded areas corresponding to the number of spin up and spin down electrons in situations (c) and (d) shows that in these cases /~ ~ 0. The result is no magnetic moment since the number of spin up and spin down electrons is equal. Possible situations are schematically represented in fig. to give rise to band splitting.336 K. A critical assessment of the validity of the three proposed coupling schemes will be given at the end of section 3. s electron bands.M interaction is by far the strongest one in the R . The M .M compounds. BUSCHOW which structural details are considered explicitly. . 10. indicated by horizontal bars. Schematic representation of the density of states N ( E ) of 3d electrons as a function of energy E. This is a direct consequence of the spatial extent of the 3d electron wave functions being considerably larger than the 4f electron wave functions. have been omitted in this figure. If by chemical substitution of a third (a) EF ~. The magnitude of the magnetic moment (/z) is proportional to foEF[N(E)'~N(E) ~ ] dE. The 3d electron wave functions of neighbouring atoms show a strong overlap.J. The relative filling of the bands is determined by the Fermi energy. both sub-bands are filled completely and/~ = 0. In fig. lO. T .M compounds the total number of electrons contained in the 3d band can be raised situation (d) always leads to a decrease of/~.1. 2A is determined by A ~. In view of the comparatively large spatial extent of the 3d electron wave functions it can be presumed that the effect of externally applied pressure leads to larger effects on the electronic and magnetic properties than in the case of systems containing 4f electrons.1 --. In the itinerant electron model the pressure derivative of the Curie temperature (Wohlfarth 1969. (33) The quantity K represents the compressibility and B is a parameter determined by the intra-atomic Coulomb repulsion and the shape of the 3d band at the Fermi level. The spatially oscillating electron density variation responsible for this coupling is shown in fig. In Friedel's model the coupling is not mediated by conduction electrons of s character but rather by conduction electrons of d character. This relation is strictly valid only for weak itinerant ferromagnets. In case (c) N(EF)~ is smaller than N(EF)~'.1). The Curie temperature is given in the Stoner-Wohlfarth model (Wohlfarth 1968) by T~ = T 2 ( I . In its simplest form the itinerant electron model predicts an exchange splitting between the two 3d sub-bands if the Stoner criterion (Stoner 1938) is satisfied I N ( E F ) . As a consequence/~ will show an initial increase. In many respects this coupling takes the same form as the RKKY coupling scheme.1 > 0 (31) I is the effective Coulomb repulsion between the 3d electrons and N(EF) is the (paramagnetic) 3d electron density of states at the Fermi level. A priori it is not known how far the 3d moments in these compounds are localized or are due to itinerant 3d electrons. (32) The degeneracy temperature TF in this expression depends on the first and second energy derivatives of N ( E ) at the paramagnetic Fermi level. where kv is measured now to the nearest 3d band extremum. If d is the . (1961) have proposed a model for the 3d electron magnetism in which aspects of the localized as well as aspects of the itinerant model are combined.~KB/T¢. Friedel et al. The position of the nodes r = A.l/kF. Upon further filling of the 3d band more electrons go into the spin up band thereby increasing the difference between the total number of spin up and spin down electrons. If they were strictly localized the same RKKY type description could be used as outlined for the 4f electrons in section 2. For the formation of localized moments on the transition metal atoms a similar criterion exists as that given by Stoner [eq.RARE EARTH COMPOUNDS 337 component into the R . Edwards and Bartel 1972) is given by dTc/dP = ]KTc . a behaviour which is opposite to that expected in case (d). 11. It will be shown below that numerous properties of rare earth transition intermetaUics bear features which can satisfactorily be described in the framework of the itinerant electron model. (31)]. The coupling between the localized moments is intimately related to the so-called Friedel oscillations that surround a transition metal moment. In the quasi spin model of Liu the 3d electrons reside in spin split energy bands in a way that there is a spin cloud around each atomic 3d site.2. antiferromagnetism (including collinear as well as helical spin structures) is predicted when d > A. (5). Magnetic properties 3.338 K. A model dealing with itinerant as well as localized aspects of the 3d electron magnetism has also been proposed by Liu (1976) and by Stearns (1973). In R2Ni7 and RNi3 the Ni moments are very small and fall below 0. That is is primarily the Ni-Ni .3a a substantial Ni moment is only found in R~Ni~7. The interaction between the quasi spins. Since the band electrons include not only the s electrons but also the d electrons the coupling between the quasi spins will in general be more complex than is describable by means of simple analytical expressions like eq. B U S C H O W Fig. interatomic distance between the transition metal atoms Friedel's model predicts ferromagnetism when d < A.H. in the large wave number limit.1/~B/Ni. In the various Ni compounds listed in table A.3.N i compounds the Ni moments are virtually zero. 3. It is understandable therefore that the magnetic ordering temperatures reach comparatively high values only in R2Ni17.1. Recent years have seen the publication of a large number of papers reporting studies of the magnetic properties of rare earth transition intermetallics by means of the M6ssbauer effect and NMR techniques.2.J. In the other R . takes the form of the RKKY interaction. Other models describing the 3d electron magnetism can be found in the papers of Edwards (1977) and Pettifor (1980). A detailed review of these results falls outside the scope of this chapter but has been given by Buschow (1977e). Compounds with 3d transition elements The magnetic properties of compounds with 3d transition metals are listed in table A. The moment per 3d atom is in general non-integral. When excited the spin cloud or quasi spin is assumed to precess rigidly. 11. Electron density variation Ap around a local perturbation centered at r = O. 1970b) has shown that the magnetic structures can be rather complex. In the R-rich R . This would lead to a more complete filling of the Ni 3d band as well as to a reduction of the effective Coulomb repulsion between the 3d electrons.RARE EARTH COMPOUNDS 339 interaction which determines the ordering temperature is shown by the results on Y2Ni17. 1977a). and that in the magnetically ordered state there should be an induced moment at the Ni sites in GdNi2 of the order of a few hundredths of a Bohr magneton (Dormann and Buschow 1977). Similar data obtained on Gdt-xLaxNi2 indicate. magnetic ordering in RNin with n ~<2 is primarily due to the indirect exchange interaction between the 4f moments. The results of magnetic measurements on GdNis±8 led them to suggest that the Fermi level in the 3d band in RNi5 is located at a minimum in the density of states and this prevents exchange splitting between the two 3d sub-bands. This has led B~cle et al. is the absence of a Ni moment in RNi5 (R = La. It indicates that the 3d band in RNi2 is virtually full and contributes nothing or only a small portion to the density of states at the Fermi level. on the other hand.5 millijoules/mole K (Wallace 1973). that the contribution of the Ni 3d electrons to the indirect coupling between the Gd moments cannot be completely neglected. N M R data (Dormann and Buschow 1977) obtained on GdNi and related pseudobinary compounds confirm this view. The absence of Ni moments in the compounds of lower Ni concentration than RNi2 is therefore not surprising. The magnetic properties of the R3Ni and R N i compounds are therefore determined to a very large extent by the strong crystal field induced anisotropy. The easy direction of the magnetization in various RNi2 compounds has been determined on Fe doped samples by means of the 57Fe MOssbauer effect (Arif et al. Neutron diffraction performed on several of these compounds (B~cle et al. Givord et al. Experiments performed with polarized neutrons on a TbNi2 single crystal have shown that in the paramagnetic state the nickel atoms do not carry a magnetic moment (Givord et al. for which Tc is above 150 K. Remarkable. This value is close to that observed in LaA12. 1976).N i compounds in particular. The large magnetocrystalline anisotropy explains why the domain walls in these com- . In view of the large electronegativity difference between Ni and the rare earths (Miedema et al. For the reasons mentioned above. Lu or Y). Specific heat measurements performed o n LaNi2 have shown the electronic coefficient of the specific heat to be equal to 12. also found that the Th atoms produce a spatially non-uniform polarization of the conduction electrons which indicates that a substantial part of the Tb-Tb coupling proceeds via an RKKY-type coupling scheme. (1970b) to assume that the exchange interaction between the localized 4f moments is no longer isotropic but contains anisotropic contributions. 1977) it is conceivable that considerable electron transfer may take place in the direction R .~ Ni. (1976b) showed that LaNi5 and YNi5 are Pauli paramagnets with an exchange enhanced susceptibility. however. Both effects result in a decrease of the Ni moment. Gignoux et al. the R atoms reside at crystallographic sites of low symmetry and crystal field effects are important. It is reasonable to assume that a similar situation is present in the compounds of higher R/Ni ratio. Roughly speaking. In compounds of lower Co concentration there are hardly any moments on the Co atoms or they occur only by virtue of the polarizing influence of the rare earth partner.3c. too. there are a still quite a large number of holes in the cobalt 3d band of YCo2. In the paramagnetic regime the temperature dependence of the Co sublattice magnetization was found to be in keeping with the enhanced paramagnetism model already referred to above (Bloch and Lemaire 1970. This leads to a complex magnetization behaviour (Gignoux and Lemaire 1974) similar to that described for TbGa in section 2. 12. see for instance Lemaire 1966a).J.3b and A.C o compounds is determined by the Co-Co interaction (see also Wohlfarth 1979). (1976a.H.3. however.N i compounds. Burzo (1976) does not state explicitly in how far the constant Vco is sensitive to variations in temperature within the magnetically ordered and paramagnetic regimes considered. (1975) and by Cyrot et al. the paramagnetic ferrimagnetic transition is of second order. where the exchange field due to the R moments is much stronger. 1977a. BUSCHOW pounds and related pseudobinary compounds are rather narrow. This leads to ferromagnetism for the light rare earth compounds (Y = L . . is reproduced in fig. The latter compound is a strongly exchange enhanced Pauli paramagnet. 1977a. This has been explained by Bloch et al.S). The magnetic properties associated with the Co sublattice in RCoe give rise to a first order magnetic transition when R represents R = Dy.C o and R . 1977a. In the cobalt compounds. In a more recent analysis Burzo (1976) uses a Co moment given by/~co = VcoHex(Co) where Hex(Co) is the exchange field experienced by the Co atoms. Givord and Shah 1972). Gignoux et al. b) have performed a polarized neutron study on various RCo2 single crystals.3c. When the temperature is lowered the R sublattice magnetization increases together with the Co sublattice magnetization. Depending on the polarizing power of the rare earth component the induced moment at the Co sites in RCo2 can become fairly large (Moon et al. Their energy depends on the position of the wall centre with respect to the crystal lattice and varies periodically. The magnetic properties of rare earth cobalt compounds are listed in tables A. In contradistinction to YNi2. Petrich and M6ssbauer 1968. a Co moment is only present at Co concentrations higher than in RCo2. There is a close correspondence between the 3d transition metal moments in R . Part of the data of Gignoux et al. Ho or Er (Lemaire 1966a. 1975) and to be inconsistent with the localized moment description formerly proposed by Burzo (1972). The proportionality constant Vco = 31 x 10-6/~B/G has the dimension of a susceptibility and this comes close to the description by Gignoux et al. 1976a. b) where Vco takes the form of a weakly temperature dependent susceptibility. the ordering temperature in these R . Rare earth cobalt compounds in which the Co atoms have a magnetic moment of their own are tabulated in table A.340 K. Gignoux et al. (1979) in terms of a model of itinerant electron metamagnetism. In GdCo2 and TbCoe. Magnetic measurements and in some cases neutron diffraction measurements can be interpreted on the assumption of a Co moment oriented antiparallel to the rare earth spin moment. Close to Tc the magnetization is primarily due to the Co sublattice magnetization. 1965. b) (about I/~B/Co in GdCo2.1.S) and to ferrimagnetism for the heavy rare earth compounds (Jr = L . (1976a. Bloch et al. Dependenceof the Co momenton the polarizinginfluenceof the Tm moments(Gignouxet al. In the cobalt rich R .and Co sublattice magnetizations are antiparallel. 1976.b). 1976a. mutual compensation of both sublattice magnetizations should occur at some intermediate temperature (Tcomp). Dublon and Atzmony 1977. Taylor 1971) in these compounds (for instance in Dy3Co and Dy4Co3 the low temperature magnetic isotherms suggest magnetization processes which are largely governed by narrow domain wall propagation. This holds afortiori in the cubic compounds RCth.C o interaction still determines the direction of easy magnetization. Since in these cases the R. The single ion crystal field anisotropy of the R component through the R . at low temperature in particular. Atzmony et al.C o compounds the effect of crystal fields is relatively less important. a s already discussed in section 2. 1975).2K 0 I I 2 I I 4 I 6 /-LTm (/J-B) Fig.50K75K / " -02 i 0 ~ 1 I I I I I I 4. Yakinthos and Mentzafos 1975. partly because the rare earth atoms reside at sites of higher symmetry and partly because a large portion of the magnetic properties is determined by the Co sublattice. Gignoux et al. 12.2c.6 ::L ~. where the Co sublattice anisotropy is negligible (Dublon 1976.1). 1979.3. . 1977a.8 TmCO2 / -0. Hendy and Lee 1978. The effect of crystal fields on the magnetic properties is comparatively large in the rare earth rich compounds where it not only gives rise to a reduction of the rare earth sublattice magnetization at low temperatures but in addition has a large impact on the magnetization processes (Lemaire et al. 1968. the former exceeds the latter at absolute zero.Values of Tcomp are also listed in table A.RARE EARTH COMPOUNDS i I ' I ' 341 -0. In RCo~ a substantial influence of the Co sublattice anisotropy (Schweizer and Yakinthos 1969. For several R-Co compounds in which R is a heavy rare earth. Temperaturedependence of the magnetic moment of several CaCu5 type compounds. full symbols: decreasing temperature (Ermolenko et al. (1976) found an anomalous change in the magnetization near the temperature where the transition from easy plane to easy axis magnetization occurs (see fig.: 3. Open symbols: increasing temperature. From a further analysis 3. 14a. 1976.0 o~ t00 200 30o 400 TIK) I" ~llltlilllllll itl|l 5O0 to 3{}{} 350 4 0 0 450 T(K) Fig.0 t. 1969) becomes apparent. At temperatures high compared to the overall crystal field splitting the single ion anisotropy is relatively small so that the easy magnetization direction is determined primarily by the Co sublattice anisotropy.5 4. In the stoichiometric compounds RCo3. Deryagin and Kudrevatykh 1975.0 3. In the case of TbCos. Experimental results obtained by different authors are shown in fig.2 Ermolenko et al. where the stabilization energy AF of a moment alignment in the basal plane is given for various values of the second order crystal field parameter A°{r 2} and the exchange field He~ (see eqs. 1976. 1976).0 Dyc05 •z ~ C /l ° ~k 2.342 K. The single ion anisotropy of the R sublattice can in general be analyzed by means of crystal field theory outlined briefly in section 2. Georges et al. Kren et al.5 z. In cases where the contributions of R and Co differ in sign this can lead to changes in the easy direction at some intermediate temperature (Lemaire 1966b. The compound SmCo5 is one of the few examples where the anisotropy due to both the R atoms and the Co atoms favours an easy c-axis. 13). This influence increases in compounds of still higher Co concentration such as RCo5 (Ermolenko 1974. (10) and (25) of section 2. whereas in R2Co]7 the easy magnetization direction is perpendicular to the c-axis. 14b. At low temperatures the single ion contribution prevails.2.o v 1. R C o 5 the Co sublattice favours an easy c-axis magnetization.-. 13.H. These can be compared with the results of numerical calculations (Buschow et al. R2Co7.J.2).0 " - III I | III I | II II|I III| O0 l~ICi • . . 1975. depending on the nature of the 4f wave function of a given R ion as well as on the nature of the site these ions occupy in the above compounds. BUSCHOW Yakinthos and Rossat Mignod 1972. This has been explained by these authors in terms of a molecular field approach taking account of the change in magnetic energy levels due to the presence of the anisotropy. Kazakov et al. 1975).~ and DyCos. 1975) and R2Co~7 (Miller et al. Irkhin and Rozenfel'd 1974). 1974b) in fig. Klein et al. It can favour an easy direction either parallel or perpendicular to the c-axis. Greedan and Rao (1973). 1975). Ce 4+. (1975). i ~ i''~ -I 0 300 600 900 0 TEMPERATURE(K} 300 600 900 Fig. (a) Dependence of the stabilization energy AF on the crystal field parameter A°(r 2) and the exchange field Hex. Several of the above-mentioned compounds are suitable candidates for per- . (1974h). Perkins and Nagel (1975). 14. is of little importance (Buschow et al. Even if A~(r6) were of the same order of magnitude as A°(r 2) the basal plane anisotropy is expected to be only a few percent of the axial anisotropy. Perkins and Str~issler (1977) and Deportes et al. (1977). as has been proposed by Orehotsky et al.. 1974b).RARE EARTH COMPOUNDS 250 343 50 200 U. In the compounds RCo5 where the R ions are represented by La 3+. This agrees with the fact that in SmCo5 basal plane anisotropy could not be observed experimentally (Klein et al. Szpunar and Lindg~rd (1979).4O <3 n. . (19) of section 2. (b) Temperature dependence of the anisotropy constant Kt in various RCo5 compounds (full lines: data of Ermolenko 1974. broken lines: data of Klein et al.7 were to adopt the divalent state. It is clear that the large single-ion anisotropy due to S m 3+ would he lost if Sm in SmCo5 and Sm~Co. due to the magnetically ordered 4f moment at low temperatures. 1975).2 are relatively less important. of the single ion anisotropy of S m 3+ it was derived that the higher order potentials appearing in eq. Streever (1979). It can be seen in fig. The parameters A°(r ~) and A~(r 6) were kept zero. ILl Z bJ Z 0 (b) 150 ~ / LaCo 5 i . 14b that in these cases the anlsotropy remains relatively small at low temperatures. Sankar et al. (1976). 1979).. Polarized neutron studies showed that the coupling between the Sm and Co moment remains ferromagnetic below 350 K (Givord et al. -30 SmC°5 ~ g -20 I N -J ~D 100 Z 5O 0 0 i . y3+ or Gd 3+. More details regarding the magnetocrystalline anisotropy and the saturation magnetization in RCo5 and R2Co17 can be found in Buschow et al. . The data of GdCo5 in particular show that the anisotropy of dipolar origin. single ion anisotropy contributions are absent. F e compounds could as well be explained on the basis of environmental changes. Moriariu et al. (1978) note that there seems to be no definite relation between Hen and the nearest neighbour F e .F e compounds in table A. Even in the cubic RFe2-compounds the single ion anisotropy can be appreciable. BUSCHOW manent magnet applications. information regarding the easy magnetization directions in R Fe2 compounds has been derived mainly from results of M6ssbauer effect spectroscopy (Atzmony 1977. such as a high coercive force. argue that the concentration dependent moment decrease in the R .F e compounds in which R represents Y or Lu have shown that the strength of the Fe sublattice anisotropy is in general rather modest. so that the easy magnetization direction in these materials is determined primarily by the single ion anisotropy of the R component. The concentration dependence of Tc has a trend opposite to that observed in R . Rosen et al. a measure of the magnetic moment of the corresponding Fe atoms.3d it is seen that the magnetic ordering temperatures increase with decreasing Fe concentration. respectively (nS = 1 .F e compound by means of the 57Fe M6ssbauer effect (Gubbens et al.F e separation at these Fe positions.344 K. 1973. the direction of the easy axis of magnetization is strongly temperature dependent and in a given temperature region does not coincide with one of the major cubic directions. under certain conditions. Dy. Since Hen is. Gubbens et al.J. It follows from these results that there is a considerable difference in effective hyperfine field (Hen) between the Fe atoms occupying crystallographically non-equivalent positions in R Fe3.N i and R . These plots are reproduced in fig. Atzmony et al. In many pseudobinary compounds. More information regarding this class of materials is contained in Buschow (1977e) and in Vol.N i compounds. 3/4.H. SmFe2 arid HoFe2.F e compounds).C o and R . Atzmony and Dariel analyzed . The magnetic measurements performed on R . studies on single crystals (Clark and Belson 1974. by K. 1973a. Atzmony and Dariel 1976. values listed for the Y . A more or less linear decrease or increase of Hen was found. but also in CeFe2. 15a (R is trivalent Er or Y) and fig. Van Diepen et al. Permanent magnets made from these materials have outstanding properties. when this quantity was plotted versus the relative number of first Fe neighbours (nFe) or versus the relative number of first R neighbours. of these handbooks (Rare earth based magnets. 1979) (R = Tb. is suggested by the results of numerous investigations of the R . 1978). 1976). R6Fe23 and REFel7. Ho and Er) made it clear that reliable values of the saturation magnetization cannot be obtained on polycrystalline samples even if the field strengths applied are in excess of 100 kOe. in terms of more localized 3d moments. however.J. An alternative interpretation. There is as yet no unique explanation for this peculiar behaviour (Buschow 1977e). a high energy product and a high temperature stability (Martin and Benz 1971. Apart from the above-mentioned studies on single crystals.rive). Gubbens et al. 1975). Strnat). even though the magnetic moments per Fe atom decrease in the same direction (this latter fact can for instance be derived from the p. Shut et al. 15b (R is tetravalent Ce or Th). From the results presented for R . 1976a. Abundi et al. The decrease in the Fe moment with decreasing Fe concentration can be ascribed to a weakening of the effective Coulomb repulsion and to the band filling mentioned earlier in connection with a similar 3d moment decrease in the R .C o series. A \ \ \ 0 4 rI-Fe (a) ~{~ \ \ \ \ (b) " ~ 300 "1- A\ \ \ 9\ 8 \Q 250 A _ 200 - 8 i 1. together with the rather impressive magnetostrictive properties of binary and pseudobinary R . b. Hcf. (20) in section 2. (1974) by means of ultrasonic sound velocity measurements. The magnetization versus temperature curves shown in fig.F e compounds.2. are discussed in more detail in chapter 7 of this book (Magnetostrictive rare earth compounds.50 i 0. (1979). The results show that the Fe atoms in this compound have a large stable moment of their own in addition to a small induced component due to the R .RARE EARTH COMPOUNDS 345 400 A Yx Fey o Er x Fey o Thx Fey v Ce x Fey A (Z-Fe °c. by Clark). Effective hyperfine fields. Gubbens et al. 1974a. In Tm2Fe~7 too. eqs. MOssbauer effect spectroscopy also proved to be useful in the determination of the easy magnetization directions in RFe3 (Van der Kraan 1975.M interaction. 16 may help to illustrate the various possibilities that exist. These properties. at the various Fe sites in RxFey as a function of the relative number of Fe neighbours (nFe= number of nn Fe atoms/[number of nn Fe atoms + number of nn R atoms]).75 nFe I 0. The curve shown for Er2Fen can be regarded as normal.50 nFe Fig. 1975) as well as in R2Fe~7 (Steiner and Haferl 1977.0 I 0. Several of the R2Fe~7 compounds are not simply ferro. (26-28)) and showed that the single-ion model actually predicts these directions. the comparatively low magnetization at 0 K is in . 1977) correlation could be established between the easy directions observed in the various compounds and the sign of the coefficient Ok of eq.or ferrimagnetic but have a non-collinear magnetic structure. Arif et al. Since the Fe sublattice magnetization still exceeds the Er sublattice magnetization at absolute zero no compensation temperature is expected nor is it observed. Elastic and magnetoelastic properties of RFe2 compounds were studied by Klimker et al.0 \o \ \ V 1 t. 1976. 350 .75 I 0. The decreasing magnetization well below Tc ~ 300 K reflects the increasing ordering of the Er sublattice.2. their data by means of crystal field theories (Atzmony 1977) (section 2. Polarized neutron studies were made on HoFe2 by Fuess et al. 15. 7compounds. whereas below 275 the magnetic structure is collinear (Givord and Lemaire 19"/2. Gubbens and Buschow 1973. The curve shown in the top part of fig. 1974). Barbara et al. 1974.0 3~o ~oo Temperature {K) Fig. In these cases the nearest neighbour F e . Tm. Magnetic ordering sets in close to the temperature where the M vs.F e distances correspond to negative exchange interactions on the N~el-Slater curve. Comparison of the lattice constant in the c-direction of the R2Fe~7 compounds shows that comparatively low values are reached in the compounds with R representing Ce. In Tm2Fe17 a helimagnetic structure has been observed only in the rather limited temperature range 275-235 K. These negative interactions stabilize a helical spin configuration below the ordering temperature. (1973) have correlated the presence of such short F e .J.346 K. Temperature dependence of the magnetization of three different R2E¢. respectively) are very short. In conjunction with an in- . T curve exhibits a small maximum. Narasimhan and Wallace 1974). agreement with an antiparallel coupling between the Tm and Fe moment. The decreasing effect on the total magnetization of the increasing order of the Tm sublattice is obscured in this case by the change in easy direction from perpendicular with the c-axis (T ~>70 K) to parallel with the c-axis (T ~<70 K) (Givord and Lemaire 1972.I as 4(0 and 6(c) for the Th2Ni~ structure and the Th2Zn~7 structure. 16.F e distance of the Fe atoms residing at the so-called dumb-bell sites (these are the sites indicated in table A. This agrees with results of neutron diffraction (Givord and Lemaire 1972. B U S C H O W 75 Yb2Fe17 50 T25 5O ~25 25 °o 1. At lower temperatures the strength of the negative interactions decreases as a consequence of the spontaneous magnetostriction.o 2.H. Yb and Lu. 1973. Elemans and Buschow 1974). According to these authors the short F e . In these cases the magnetic ordering is not of a simple type but entails helimagnetic structures as well as fan structures (Givord and Lemaire 1972). Yb2Fe17 and Lu2Fe17.F e distances with the occurrence of the non-collinear magnetic structures. 16 is more or less representative of the compounds Ce2FelT. It is reasonable to assume that the Mn sublattice magnetization in GdMn2 is also internally compensated by antiferromagnetic ordering of the Mn moments. so that essentially its magnetization is internally compensated. obtained by Oesterreicher (1971) in the cubic Th6Mn23 structure (Prd'r~Mnt9 or Pr6Pr3Mnz0) rather than in the hexagonal MgZn2 structure. Interesting results were reached in PrMn2.Mn23 the value 50/~e observed in Gd~Mn23 is much too low to be explained by ferromagnetic ordering (Gd and Mn moments parallel). The combination of the rare earth and manganese sublattices leads to a ferromagnetic spiral structure (Corliss and Hastings 1964). Since the saturation magnetization of the Mn sublattice should have a value close to that found in YdVlnz3 or Luc. From the results shown for YMn2 and LuMn2 it can be deduced that the Mn atoms do not have a magnetic moment of their own. The possibility of an induced moment exists in compounds where the R component possesses a sizable spin moment. Table A. Neutron diffraction studies of this compound have shown that the Mn sublattice itself is antiferromagnetically ordered. make it clear that the Mn atoms in RdVln23 bear a magnetic moment. The effective moments derived from the linear part of the temperature dependence of the reciprocal susceptibility in RsMn23 exceed the free R ion values considerably. Unfortunately the neutron diffraction results do not allow the moment of the Mn atoms to be fixed. From the results obtained in the magnetically ordered regime one can therefore reach no definite conclusions as to the sign of the R . In GdoMn~ the saturation moment is close to 50~B per GdsMn23 which corresponds to 8. 1965) do not point to a magnetic moment on the Mn atoms in these compounds. in TbMn2 (Corliss and Hastings 1964). even if one assumes that the Gd moments in the Gd sublattice are ordered ferromagnetically. They do have a magnetic moment. and also the results obtained on LuoMnz~ and YoMn23. Investigations of the 55Mn N M R on ErMn2 and TmMn2 by Barnes and Lunde (1975) as well as neutron diffraction studies on TmMn2 (Felcher et al. Measurements in the paramagnetic regime show that the reciprocal susceptibility in Gd~Mn23 is approximately linear several hundred degrees above the magnetic . The structural change led to distinctly different magnetic properties (given in parentheses in table A.M n interaction. This.3e summarizes the results of investigations performed on rare earth manganese compounds. The compounds RMn2 crystallize in either the cubic MgCu2 structure or the hexagonal MgZn2 structure. as in TbMn2.3e) with a magnetic ordering temperature (To = 448 K) close to that expected for compounds of the stoichiometric composition R6Mn23 (see table A. however.2/~B per Gd atom.RARE EARTH COMPOUNDS 347 creasing anisotropy this eventually leads to a transition from a helimagnetic structure to a fan structure. In view of the complicated magnetic ordering in R Mn2 compounds no definite conclusions can be reached regarding the sign of the R .3e). It is not possible therefore to derive values of the Mn moments from the saturation magnetization. even within rather wide limits.M n coupling. It also precludes simple ferrimagnetic ordering (Gd moments antiparallel to the Mn moments) (Buschow and Sherwood 1977b). The Tb sublattice consists of ferromagnetically coupled Tb moments. however.. (Taken from Desportes et al. The R and Mn sublattices are therefore not coupled magnetically and order more or less independently at temperatures T~ Y /k. No magnetic ordering in YMnn is suggested by its field. 1977. the change in sign of the asymptotic Curie temperature 0p in going from the light to the heavy rare earths in R6Mn23 would be indicative of an antiparallel coupling between the rare earth spin moment and the ferromagnetic moment component. 1977). Deportes et al. Magnetic structure of YMnn. 17. 7 x 10-3 emu/mole). 4 / z s .3e show that the magnetic ordering in these compounds is antiferromagnetic and occurs well below room temperature. that antiferromagnetic ordering occurs below TN = 120 K (Deportes et al.'Y \.J./ Fig. since it is not known how many different sublattices have to be included. y. Its form suggests ferrimagnetic ordering.. The mean magnetic moment per Mn is 0 . If one assumes for instance the presence of two antiferromagnetically coupled Mn sublattices in conjunction with a ferromagnetic R sublattice.// i.and temperature independent susceptibility ( X = 3 . induced by the R spin in the otherwise antiferromagnetically ordered Mn sublattice. (1977) note that the symmetry of the magnetic structure is such that the molecular field produced by the M moments at the rare earth site cancels.348 K.M n interaction in these compounds._. however. An analysis of the magnetic data in terms of a molecular field model seems impossible. Neutron diffraction has shown. 17. Y atoms on the sites 2(a) and Mn atoms on the sites 8(i) and 8(j) lie in the planes z = 0 (full lines) or z = 21(dashed lines). It is clear that further experiments are needed to reach definite conclusions regarding the sign of the R . A schematic representation of the non-collinear antiferromagnetic structure is given in fig.W.) "-. The magnetic data of RMn12 listed at the end of table A. M n atoms on the site 8(D lie in z = *4and z = 43.H..) . B U S C H O W ordering temperature only (Kirchmayr 1966). the positive 0p values in compounds of a composition R3Ru.3f shows that in the CsC1 type compounds a change from ferromagnetism (R = Gd. Davidov et al. Several of the cubic Laves phase compounds become superconducting at low temperatures (LuRu2. respectively (Tg ~ TN). Similar conclusions can also be drawn from the low electronic coefficient (~/) of the specific heat (ChamardBois 1974). Dy) to antiferromag- . The diamagnetic character of YRh (see table 4. Dy-Ru and Y . Re-entrant critical field behaviour was studied in more detail in GdxThl_~Ru2 (Davidov et al. Curie temperatures have been reported only for RRu2.R u has been determined (Loebich and Raub 1976a). too. Th. 1973c).M n coupling either.3f. Inspection of the data contained in table A. Unfortunately the data on the RMn~2 compounds do not reveal any information on the sign of the R . however. CeRu2. This was explained by assuming that the electrons which contribute to the superconductivity are also responsible for the thermal broadening (both properties depend on the square of the wave vector dependent exchange integral ([j(q)]2)). In view of the large difference in electronegativity between Y and Rh. the disappearance of the open 4d band can be understood in terms of electron transfer from Y to Rh (Tamminga 1973).RARE EARTH COMPOUNDS 349 and TN.2. Investigations of the magnetic properties of various Y-Rh compounds by Loebich and Raub (1975) have shown that the susceptibility of these compounds is lower than that of the parent materials and reaches a minimum for YRh. (1973b) investigated pseudobinary compounds of the type GdxRl-xRu2 (R = La. ThRu2) (Hillenbrand and Wilhelm 1972. although the stoichiometry of several of these compounds in the systems Gd-Ru.R u compounds are given in table A. From a further analysis of the neutron diffraction data Deportes and Givord (1976) conclude that the magnetic interactions between the Mn moments in RMn~2 vary strongly with the interatomic distance. None of this is true. Compounds with 4d and 5d transition elements Attempts to determine the crystal structure of the various rare earth rich ruthenium compounds have not been very successful.3f) suggests that no partly depleted 4d band due to the Rh atoms is left in this compound. with the possible exception of RRhs.2. 3. Charmard-Bois (1974) has used the band structure calculations available for the isostructural compound DyRh (Belakhovsky 1972) and attributed the low values of ~. and one might expect the magnetic properties of these compounds to be governed by the R K K Y mechanism. Guided by the magnitude of the magnetic susceptibilities of the various Y-Rh compounds one might assume that the 4d electrons of the Rh atoms do not make a significant contribution in the determination of the magnetic properties of the rare earth rhodium compounds. and X to the presence of a minimum in the density of states at the Fermi surface. Wilhelm and HiUenbrand 1971). Magnetic data of R . Tb. Rhodium behaves essentially as a non-magnetic partner element in the various R-Rh compounds. Ce) and found a correlation to exist between the normalized superconducting transition temperature and the thermal broadening of the E P R of the magnetic impurity. R73Ru27 and R2Ru suggest that these latter are ferromagnetic. Y or Lu shows that the effect of the 4d electrons of Pd on the magnetic properties can be regarded as being negligible in RPd3. This will probably also be the case in R . This change is incompatible with the RKKY coupling scheme. Tm) occurs. since GdsPd2 was not observed to crystallize in the cubic DysPd2 type (Fornasini and Palenzona 1974. 1977). The change in magnetic properties in going from GdRh to TmRh is probably a shift in the relative importance of these coupling schemes. The other R .350 K. Of particular interest is the compound EuRh2 and related pseudobinaries due to the intermediate valence state of Eu in these systems (Bauminger et al.H. Loebich and Raub 1973b). Furrer and Purwins have taken the absence of this transition as evidence that the 4f electron of Ce in CePd3 has to be described by a virtual bound state near the Fermi energy rather than by a localized state. In EuRh2-2xPtz~ the valence state of Eu was found to be strongly dependent on the local environment. Compounds obtained by combining rare earths with 5d transition metals have been the subject of only a few magnetic investigations.3f).3f have not been so fully investigated as those of the CsCl type. Furrer and Purwins (1976) have performed inelastic neutron scattering experiments on several of these compounds. (1975e) to obtain materials (primarily based on GdxErl-xRh) that have large heat capacities at low temperatures. 1974a). Extremely low magnetic ordering temperatures are observed in RPd3.R h compounds listed in table A. A comparatively high ferromagnetic ordering temperature is reached in GdsPd2 (T~ ~ 334 K. The diamagnetic character of the compounds RPd3 with R = La. A possible reason for this could be a difference in crystal structure. As can be seen in table . It is somewhat surprising that the magnetic ordering temperatures in the remaining RsPd2 compounds are much lower.P d compounds of even lower Pd concentration. Er. Compounds of the type RRh2 are ferromagnets whereas the data obtained on Gd3Rh and Gd7Rh3 indicate that metamagnetic behaviour prevails in R3Rh and R7Rh3 (Loebich and Raub 1975). even if one takes into account that the R component in these compounds has a lower spin moment than Gd. An intermediate valence state of the Ce ions in CePd3 had been proposed before on the grounds of susceptibility data (Fornasini and Palenzona 1974). Their measurements on PrPd3 and NdPd3 show that the energies and widths of the crystal field transitions are almost independent of the temperature. From the cryogenic point of view these results seem quite valuable since there is a lack of materials that have high heat capacities in the range 4-10 K.1) can be regarded as being small (Dormann and Buschow 1976).J. No crystal field transition has been observed in CePd3. The mentioned change from ferromagnetism to antiferromagnetism has been used in Buschow et al. see table A. Detailed investigations by means of spin echo NMR on GdRh and related pseudobinaries have shown that each of the two types of indirect exchange coupling between the Gd atoms (proceeding either via 4f-s or via 4f--d polarization as discussed in section 2. BUSCHOW netism (R = Ho. including neighbours beyond the nearest shell (Nowik et al. the width of the 4f electron state being comparable with or larger than the crystal field splitting. if M represents Col-xNix or Co~_~Cu~ the magnetization displays a collapse-like decrease with increasing x (for more details regarding these pseudobinary systems we refer to the original papers cited in the reviews by Taylor (1971). On the other hand. 1976). these investigations have been focussed mainly on the Laves phases ROs2. Fe) when the R / M ratio is increased. 3. it can be derived that there is at best only a very moderate contribution of the 5d electrons to the density of states at the Fermi level.P t binary systems can extend over an appreciable concentration range. where M is represented by Fel-~Cox.M compounds described in section 3. At the stoichiometric composition GdPt2 vacancies are believed to occur on Pt as well as on Gd sites (Harris et al.M compounds (M = Ni. Several magnetic studies on pseudobinary compounds RMn. 10c where the Fermi level of the 3d band is close to a minimum in the density of states of the spin down sub-band. including the composition RPt3 (R = La to Tb). Gd ~57 and Pt 195 performed on GdPtx and related pseudobinary compounds (Dormann et al. and from the fact that the compounds of Ir and Pt with either La or Y are weakly Pauli paramagnetic or diamagnetic. (1976). although they seem to indicate that the vacancy concentration is somewhat smaller than assumed by Taylor et al. 1977b) are in satisfactory agreement with the substitution scheme mentioned above.RARE EARTH COMPOUNDS 351 A. From the fact that LaOs2 is a superconductor. Wallace (1973) and Buschow (1977e). originates from a comparatively larger participation of the rare earth 5d electrons in the exchange coupling (Dormann et al. Discussion There are numerous experimental facts which favour an interpretation of the magnetic properties of the R .3g.2. For these reasons it can be expected that the 5d electrons of Os. (1973) have shown that the cubic MgCu2 type structure in several R . 1973. Harris et al. Spin echo NMR studies made on Gdl-~La~Pt2 have shown that the predominant interaction involves s conduction electrons (RKKY type). Results of spin echo NMR of Gd ~55. The somewhat higher ordering temperature in GdIr2. Taylor et al. if compared to GdPt2. Since initially more electrons go into the spin up band than into the . The X-ray diffraction measurements of the lattice spacing within this concentration range in GdPt~ have been interpreted by means of a model in which the Pt atoms substitute progressively into the Gd sites. Increasing x leads to a more complete filling of the 3d band. One of these is the gradual decrease of the transition metal moment in R .3. The above-mentioned concentration dependences of the 3d sublattice magnetization have currently been interpreted by means of a rigid band approach. b). 1977a. where the 3d electrons of the constituent 3d elements share a common 3d band: In the case of the pseudobinaries with M = Fe~_~Cox a situation exists similar to that sketched in fig. RIr2 and RPt2. have shown that the mean magnetic 3d moment passes through a maximum before decreasing with increasing x.1 in terms of itinerant 3d electrons. Co. Ir or Pt do not play a significant role in the exchange coupling between the rare earth moments. The (paramagnetic) density of states decreases towards the top of the band. Increasing x corresponds to a filling up of the spin down sub-band and a simultaneous decrease in the magnetization.H. The changes of the magnetic properties of R . one has . N ) = n I(N (34) The number N is determined by the crystal structure of a given series of compounds.352 K. in which the magnetization was found to vanish in the intermediate concentration range. Burzo et al. For each concentration x the probability of Co atoms having n Co atoms as nearest neighbours. (34) it is possible to calculate for each concentration x the number of Co atoms that is surrounded by at least j Co atoms as nearest neighbours from n=N P~(x) = Y.M compounds and their amorphous counterparts obtained under applied pressure by various authors have been discussed by Buschow et al. BUSCHOW spin down band this results in an initial increase of the magnetization. 18. to produce experimental evidence that favours a description of the magnetic properties of the R . A positive slope d T d d P is exhibited by the compounds with the highest Te in each system. so that eventually one reaches a situation where the Stoner criterion [eq. or it passes through a maximum with increasing 3d atom concentration (Th-Fe). In pseudobinaries based on M--Col-xNix or Col-xCu~ the situation in fig. Lower Tc values lead t o increasingly negative slopes. n. (33) but are difficuR to understand in a localized picture. N ) . P(x. is given by N -! n)! xn(1 . The itinerant nature of the 3d electrons is also supported by magnetovolume effects obtained on a variety of binary R . 10b). With eq. (1973. due to measurements of Brouha et al. 10d applies. It is also possible. it decreases with 3d atom concentration (Y-Fe). n. In each of these cases the values of d T d d P are seen to be dependent only on the magnitude of To. Of particular interest in this latter respect is the series Y6(Fe~-~Mn6)23. (1974) pointed out already that the collapse-like decrease of the transition metal moment in GdCo2-z~Ni:~ can satisfactorily be explained by means of a model due to Jaccarino and Walker (1965) in which the decrease in moment with decreasing x can be ascribed to a loss of moment in those Co atoms that have an insufficient number of Co atoms as nearest neighbours. n=i (35) Since Co atoms having less than j nearest Co neighbours are assumed to have no exchange splittings.x)t.. 1974) are reproduced in fig.r_.M compounds in terms of a localized model rather than in terms of itinerant 3d electrons. (1977).M compounds. P(x. Some representative sets of data. however. These features are explained in a satisfactory way by means of eq. out of a maximum number of N. (31)] is no longer satisfied and the band splitting disappears (as in fig. Three examples are shown in this figure: the magnetic ordering temperature increases with 3d atom concentration (Gd-Co).J. YCos-sxNisx and ThFes-s~Nis~ (Buschow et al.) in various R . taking also account of the mode of occupation of the shell of second neighbour 3d atoms (Besnus et al. . All these examples show that the magnetic state of a given 3d atom is primarily determined by the local environment. too. 1977). ti°i 20 P(kbar} 40 ThFes 700 600 Th z Fe7 ? 8'0 500 ~ " " ThFe3 400 300 20% 90 1000 20 ' Plkbarl 40 200 ot % Fe Fig.GdzCo17 1200 353 ?f 600 1 4~ t ~ Gd 03 ot % Co P(kbor) 1000 800 600 400 °°20 ' 6001- I/ -. Dependence of the Curie temperature (T.YFez 16°° ool 21 10040 ~ 60 80 1000 at % Fe 700 600 500 400 300 . (More sophisticated models. (36) Using the above formalism successful attempts to explain the concentration dependence of the 3d sublattice magnetization have been made in several other series of pseudobinaries such as LaCo5-sxCusx.RARE EARTH COMPOUNDS 1200 I tt . 18. i. /z (x) = xPj (x)/~ (x = 1).) In this connection it is interesting that a similar analysis can explain the concentration ..e. 1977) have been employed.M compounds on M concentration (left hand parts) and on applied pressure (right hand parts). 1978) or models where environmental changes lead to a stepwise decrease of the 3d moment (Van der Kraan et al. a ~ Th~zFel. its nearest neighbour shell. Finally it may be recalled from the results presented in section 3. found that the substitution of Co for Fe gives rise to a well-developed satellite structure. Without further analysis of the data the occurrence of this well-developed satellite structure reveals two important facts: (i) the 3d moments are fairly well localized. 1977). The Y atoms themselves do not have a magnetic moment. This also follows from results of 57Fe M6ssbauer effect spectroscopy performed on the same pseudobinary series by Luijpen et al. In these cases the occurrence of the magnetic structure types . Further support for the localized nature of the 3d moment comes from investigations using NMR or the M6ssbauer effect. 1976. In pure YFe2 all Y sites are equivalent. The relative intensities of the various satellites are in agreement with the probabilities of the Y atoms having a nearest neighbour [nn] shell consisting of 12Fe [nn]. Starting from ferromagnetic Y6Fe23. Investigations (Beckmann et al. (1976) the introduction of Fe into Y6Mn23 leads to a lattice contraction which enhances the antiferromagnetic Mn-Mn exchange. 1977). (1977) who found that an Fe magnetic moment persists for Fe concentrations as low as 2% (YCo2 is Pauli paramagnetic.1 that most of the R . These results made it clear that the rigid band approach. Oppelt et al. Therefore the hyperfine field observed at the Y nuclei is a measure of the exchange fields produced by the surrounding magnetic Fe and Co atoms (transferred hyperfine field).M compounds in which there is a moment at the 3d sites can be characterized by the presence of ferromagnetically ordered 3d sublattices.1 that the results of 57Fe M6ssbauer effect spectroscopy on R . Hilscher et al. It was already mentioned in section 3. (1976).F e compounds of different composition and crystal structure (see fig: 14) can also be regarded as a demonstration of the localized character of the 3d moments in these binary compounds. This in turn leads to a decrease of the magnetization and To.2. The ggy NMR in YFe2-aCo~ was investigated by Oppelt et al. M6ssbauer effect studies reported by Longworth and Harris (1975) on the analogous series CeCo2_2xFe~ even indicate the presence of an Fe moment for Fe concentrations as low as 13%. see section 2).J. and (ii) there is a considerable difference in the magnitude of the Fe and Co moments. The disappearance of the magnetization in the intermediate concentration region was shown to originate predominantly from the magnetically inhomogenous nature of these materials (Beckmann et al. 1976) of the system Y6(Fel-~Mnh3 made it clear that the disappearance of the 3d sublattice magnetization in the intermediate concentration range can also be understood in terms of localized 3d moments. The only exceptions were found in the iron rich compounds R2Fe17 and in R . lowering of the magnetization and Tc is due to the antiferromagnetic coupling of the Mn atoms with the host lattice.M n compounds. According to Beckman et al. 10Fe [nn] + 2Co [nn] and so forth.2.354 K.H. BUSCHOW dependence of the 3d sublattice magnetization in amorphous rare earth transition metal alloys such as Yi-xCox (Buschow et al. so that only a single Y resonance line is observed. 11Fe Inn] + 1Co Inn]. is less well applicable on an atomic scale. where the 3d electrons of Co and Ni share a common band. Neither the itinerant model nor the localized model are able to account fully for all aspects of the magnetic properties of the R . In the first scheme (Buschow 1971b.1 for the magnetic coupling between the 3d and 4f moments. Even if the s-3d interaction is taken to be the same in all the R . this means that the s electron polarization produced by the Fe moments at the rare earth sites is also negative. however small.M compounds (Wallace 1968) is not free from doubt. Wallace 1968) the coupling is considered to proceed via polarization of the s conduction electrons. Especially the premise that the 3d-s interaction leads to a positive's electron polarization in R . The 4f-s interaction in this scheme is essentially of the RKKY type. Three schemes have been mentioned in section 3. These results and those obtained by Crecelius et al.M compounds proceeds via 4f-s and 3d-s polarizations. it masks the negative contribution due to conduction electron polarization). (1976) haveshown that the hyperfine fields at the two crystallographic Y sites in this compound are both negative.R i l ) of eq. Recently the results of . The NMR results discussed above make it difficult to believe that the coupling between the R and M moments in the various R .1. McCausland 1975. always constitutes a certain degree of localization of the 3d electrons.2. As a matter of fact a glance at the data collected in table A. Spin echo NMR studies on YFe3 reported by Oppelt et al. 1977b). In the coupling scheme proposed by Campbell (1972) the 4f-3d coupling proceeds via polarization of the rare earth 5d electrons. (1977) seem to indicate that the degree of 3d moment localization becomes stronger in the direction Ni. Fe. in terms of the uncertainty principle. Arif et al. Mn.3a of Buschow (1977e) shows that a negative transferred hyperfine field at the rare earth site in R .M compounds. As argued by Oppelt et al. have a marked influence on hyperfine interactions in view of the fact that the hyperfine coupling constant of s electrons exceeds that of d electrons by an order of magnitude. These polarizations. the RKKY part may differ considerably in magnitude and sign from compound to compound in view of the expected differences of the lattice sum Y~iF(2ke" I r .M compounds.M compounds is rather the rule than the exception. the RKKY-based coupling scheme seems less suited to deal with the extensive experimental material. Since it was shown in section 3. (4) in section 2.M coupling is invariably antiferromagnetic. (A positive hyperfine field has been observed for Y as a solute in elemental Fe (Shirley et al. This is Undoubtedly inherent in the rather narrow 3d band in these compounds. In some cases it even leads to the wrong answer (Arif and McCausland 1975.RARE EARTH COMPOUNDS 355 observed was explained by exchange interactions between localized moments whose sign and magnitude is strongly distance dependent. This trend is also reflected in theoretical studies of 3d metals made by Pettifor (1980).1 that the R . Co. It will be clear from the above discussion that arguments can be given for the 3d electrons being either itinerant or localized. 1968). which. According to Stearns (1971) the positive sign of this field originated from the overlap of the too large solute atomic volume with the Fe matrix. F e compounds. It was already mentioned in the introduction that these ternary compounds differ from pseudobinary compounds in that all three constituent ele- . It follows from the results discussed in section 3. respectively. upon combination of these elements with strongly polarizing rare earth elements. than that of the 3d elements. The results of these calculations are indeed in favour of a strong coupling between the 3d electrons and the rare earth 5d electrons.1 Campbell's coupling scheme predicts an antiferromagnetic coupling between the 4f and 3d spin moments. (1977) disagree with the view of Gomes and Guim~trfies (1974) who assume a complete absence of d electrons at the rare earth site. The latter compound is Pauli paramagnetic but a moment on the Co atoms can be induced via the R . It.1). Pt.2 that there is virtually no influence on the magnetic properties of 4d or 5d electrons in rare earth compounds composed of Ru.M n compounds are not yet available. This is in agreement with the experimental data obtained hitherto on various R-Ni. as reviewed in section 2. BUSCHOW band structure calculations have become available (Malik et al. This latter effect presumably outweights the polarizing influence of the rare earth component and makes the 4d and 5d elements behave like non-magnetic components.356 K. In itself this is not surprising since the d electron interaction in the pure 4d and 5d elements is rather weak compared with that in the 3d elements.C o and R . As outlined in section 3. This means that the electron transfer from the rare earth atoms to the transition metal atoms would also be stronger. and in several cases leads only to exchange-enhanced Pauli paramagnetism rather than to magnetic moments.2. This is unfortunate in as much as in Campbell's coupling scheme the sign of the R . The results of these band structure calculations and results of a Mtssbauer-effect investigation by Tomala et al. One would then have a situation analogous to that in YCo2.M n interaction may differ from that of the interaction between R and Ni. Reliable data on the coupling between R and Mn in R . Antiferromagnetic coupling between 4f and 3d spin moments is also predicted in the calculations of Szpunar and Kozarzewski (1977) so that also in this case one can speak of agreement with the experimental data. These were made on several members of the RCo5 family under the simplifying assumption of all Co sites being equivalent. 4. In general magnetic moments could arise. 1977a).HJ. however. The electronegativity of the 4d and 5d elements is significantly larger. Indeed. Pd or Os.2.C o interaction as in GdCo2 (see section 3. Ternary compounds or hydrides In recent years a considerable number of investigations has been reported in the literature in which the magnetic properties of ternary rare earth compounds were studied. the compounds formed between rare earths and 4d or 5d transition elements have much more in common with the rare earth compounds involving a non-magnetic partner element. Co or Fe. R . independent of the RIM ratio and crystal structure. Rh. however. in terms of the R K K Y model (Buschow et al. 1971b. 1973b). A rather unusual variation of the paramagnetic Curie temperature 0p was observed in the series Gdl_xThxCuA1.R coupling. This spontaneous magnetization. RFe2Ge2. The magnetic properties of the most common types of ternary compounds are listed in tables A. As outlined in section 1. The magnetization was found to be composed of a small spontaneous magnetization superimposed on the normal rare earth sublattice contribution. 1973b). Antiferromagnetic ordering is seen to occur in most of these compounds. passing through a maximum for x = 0. those in RCo2Gee and RAu2Si2. As can be seen in table A. all having the tetragonal ThCrzSi2 structure. In both series the magnetic ordering temperatures are rather low and of the Ntel type. A fairly complicated situation seems to exist in the compounds RFe2Si2 and RFeeGe2. It can be seen in table A. The rare earth sublattice gives rise to antiferromagnetic ordering at temperatures slightly lower than. Neutron diffraction experiments performed on NdFe2Si2 confirmed the antiferromagnetic ordering within the Nd sublattice below TN = 15. together with 27A1 N M R data on GdCuA1. or at best only an induced moment in RCoeGez.RARE EARTH COMPOUNDS 357 ments occur at crystallographically non-equivalent positions. The data listed for RCo. In order to study the nature of the exchange interactions operative in these compounds magnetic dilution studies were performed on GdCuA1 and GdPdIn (Buschow et al.4. Compounds of the type RNiAI and RCuAI crystallize in the hexagonal Fe2P type structure (Dwight et al. Above the Ntel temperatures the magnetic susceptibility does not follow Curie-Weiss behaviour.3. Mtssbauer effect spectroscopy (Bauminger et al. all these compounds crystallize in a structure derived from the tetragonal BaAh type (see table A. The fact that LuCo2Ge2 and YCo2Ge2 are Pauli paramagnetic shows that Co has no moment. and a similar situation exists in compounds of the type RAu2Si2. 1974b) showed that actually only a very small fraction of the Fe atoms participates in magnetic ordering (about 5% in RFeeSi2 and about 20% in RFe2Gez) whilst the majority of Fe atoms remains paramagnetic.1) where the Fe and Si(Ge) atoms are preferentially accommodated at . has been ascribed to the Fe atoms. mentioned earlier (Felner et al.4b reflect therefore mainly the nature of the R . Rare earth metals and 3d transition metals can be combined in reasonably high concentrations in various compounds of the type RCoeGe2. but comparable to. RFe2Si2 and RMn2Ge2.4b that there is a close resemblance in magnetic properties. 1968). The compounds of both series are isotypic and have about the same conduction electron concentration.Ge2 in table A. Attempts have been made to explain these features. In the series Gdl-xTh~PdIn a change in the sign of 0p from positive to negative was observed at about the same Th concentration.4a most of these compounds give rise to ferromagnetic ordering at low temperatures. About the same fraction of magnetically ordered Fe atoms was found to be present and responsible for the spontaneous magnetization observed at high temperatures in RFe~Siz and RFe2Ge2.6 K but did not indicate the presence of magnetic ordering within the Fe sublattice (Pinto and Shaked 1973). 1975). also present in the cases where the R atoms do not carry a moment. 1971b. Due to the low net magnetization it has not been possible to derive the magnetic ordering temperatures from magnetization measurements. 1977). where. the rare earth sublattice becomes magnetically ordered. Such a small deviation from ideal site occupancy is in general very difficult to observe by diffraction measurements. (1979) did not detect magnetic ordering in DyFe2Si2 above 4.5/~B. Below TN the molecular field contributions due to the two Fe sublattices cancel at the rare earth site.F e distances with the Fe neighbours at the normal Fe sites. Apparently in their sample the site occupancies are rather perfect. Narasimhan et al. Magnetic ordering within the Fe sublattiee is antiferromagnetic. It is reasonable to assume that a very small fraction of Fe atoms has interchanged sites with Si or Ge atoms. In this connection it is interesting to note that G6rlich et al.4c. The moment per Mn atom in these compounds is about 1.2. The results reported for GdMn2Ge2 seem to indicate that in these compounds the Mn atoms tend to order antiferromagnetically. moreover. It is conceivable therefore that the Fe atoms having this shorter nearest neighbour separation are responsible for the observed "weak" ferromagnetism at temperatures much in excess of TN. In R Fe4Als the Fe atoms occupy the 8(f) positions. respectively. This situation is in fact not much different from that encountered in the binary compounds RMnn discussed in section 3.358 K. 17. The values listed in table A.1.1. A schematic representation of this structure is given in fig. (1975) conclude from their results that the magnetic coupling between the rare earth spin moment and the manganese moments is antiparallel.4b refer to ordering of the R sublattice. Nevertheless. . Analysis of the magnetic data was performed by means of a molecular field model involving three sublattices. However.2 K. The Curie temperatures listed for these latter compounds in table A. Compounds of the type RMn2Ge2 give rise to ferromagnetic ordering slightly above room temperature when R represents one of the light rare earth elements (Narasimhan et al. The main magnetic interaction in these compounds is due to the Fe atoms which carry a magnetic moment of about 0. ferromagnetic alignment occurs at lower temperatures.4c have been determined by means of 57Fe M6ssbauer effect spectroscopy (Van der Kraan and Buschow 1977. BUSCHOW the 4(d) and 4(e)sites. No TN values have been determined for RMn2Ge2 compounds with R elements heavier than R = Gd.7/~B/Fe.J. A somewhat different behaviour is displayed in compounds where R is a heavy rare earth element. Magnetic data obtained on ternary compounds of the tetragonal CeMmAIs type (Zarechnyuk and Krypiakevich 1963) are collected in table A. This leads to a more or less independent ordering of the rare earth sublattice at much lower temperatures (Bargouth et al.H. It was mentioned in the introduction that the CeMr~AIs type is derived from the tetragonal ThMnn type. The slightly smaller R factor obtained by Pinto and Shaked (1973) when considering 9. 1975). Two different Cu sites are present in the AuBe5 type listed in table A. The Fe atoms at Si(Ge) sites give rise to rather short F e . complete atomic ordering will only occur in an ideal case. Buschow and Van der Kraan 1978).8% interchange of Fe and Si in RFe2Si2 points nonetheless in this direction. the R sublattice and the two antiparallel coupled Fe sublattices. Magnetic data of these compounds are given in table A. In general these ternary hydrides can be obtained by the absorption of hydrogen gas by intermetaUic compounds of the type described in the preceding sections. Buschow and Van Diepen 1976. . 20. 1977).1 satisfy the mentioned requirements to form a stable hydride. This behaviour would be difficult to explain if an R K K Y coupling scheme alone were responsible for the magnetic interaction of the R moments in these compounds. CeFe2). Results obtained by Kuijpers (1973) on ternary hydrides of the type RCosHx are shown in fig. As can be seen in fig.M compounds described in section 3. A change in ordering type has been reported to occur in the R C u ~ g series (Takeshita et al. There have been relatively few magnetic investigations dealing with the hydrogen absorption in rare earth nickel compounds. Largely from N M R data concerning ternary hydrides based on LaNi5 and related compounds.9 K coincides with the occurrence of long range magnetic order (Matthias et al. The ternary compounds of the type RRI~B4 form a quite interesting class of materials. 1975). Instead of a complete survey of all the magnetic data available on ternary hydrides.4d. Hydrogen absorption in R . 1976. Halstead 1974. The magnetic ordering temperature may decrease (YFe2) or it may increase (Yt~Fe23. Buschow 1977). A stable hydride (with a dissociation or equilibrium pressure at room temperature close to or below Iatm) will be formed in most cases whenever one of the components of the original compound is strongly hydrogen attracting and if the compound itself is not particularly stable. 1976). 1968) and the original papers (Van Mal et al. ErRh4B4 becomes superconducting below 8. Van Diepen and Buschow 1977). Ferromagnetic ordering seems to occur in most of the GdAu4Ni compounds (Felner 1977). Halstead et al. For more details regarding these thermodynamic arguments we refer to textbooks (Mueller et al.7 K. Buschow et al 1975f). 1974. the 3d moment here considerably increases after uptake of hydrogen (Buschow 1976. Since it is known from X-ray diffraction measurements that a considerable lattice expansion occurs upon H2 absorption.C o compounds was found to give rise to a decrease in moment per Co atom and to a decrease in magnetic ordering temperature (Kuijpers 1973. 1977). These results contrast strongly those obtained after hydrogen absorption in rare earth iron compounds. E P R measurements performed on LaNi5 doped with Gd seem to indicate that hydrogen absorption leads to a reduction of the 3d band susceptibility (Walsh et al. All but the most M rich R .2. 1976.RARE EARTH'~ COMPOUNDS 359 Preferential ordering of different kinds of atoms on these two sites gives rise to the MgCu4Sn structure (Teslyuk and Krypiakevich 1961) adopted by several compounds of the type RCu4Ag and GdAu4Ni. it can be concluded that Pauli paramagnetism is preserved after hydrogen absorption (Barnes et al. The return to the normal state at 0. A separate class of ternary compounds is formed by the ternary hydrides. These results are in keeping with magnetization studies on LaNi5Hx reported by Busch and Schlapbach (1978). only the changes in magnetic properties accompanying the hydrogen absorption will be briefly reviewed. 19. For instance. Bauminger et ai. . .. broken lines: after H2 absorption.J... i. 3 e~ RCo5 0. _N 0 u. Malik et al.. transitions from ferromagnetism to Pauli paramagnetism (Y~Mn23).3 e d 1.. LuMn2.5 0 x (H/'RCos) Fig. ... 5 d) NdCosHo.i z ~ 80 . Results taken from Kuijpers (1973). The most drastic changes in magnetic properties are found to accompany H2 absorption in rare earth manganese compounds (Buschow and Sherwood 1977a. Most of the magnetically ordered ternary hydrides were found to exhibit pronounced thermomagnetic history effects at low temperatures (Bus- . 19. This is illustrated in fig. 120 80 ~'"~'. .5 ~ "~ 1. 21 where predictions regarding Tc in the hydrides can be made on the basis of the pressure effects reported by Buschow et al..0 ~ b) LaCosH3.. Change of the magnetic properties of various rare earth iron compounds upon H2absorption.. H-concentration dependence o f the Co moment in various RCo~ compounds and their ternary hydrides.. These encompass hydrogen induced transitions from Pauli paramagnetism to ferromagnetism (YMn2. 20. ThoMn~) but also the reverse effect.. Full lines: before HTabsorption.35 c) SmC051"t2. BUSCHOW a) LoCosH.. 1977b)..360 K. successful attempts have been made to correlate the changes in Tc with data on magnetovolume effects available for the pure intermetallics. YFe3 CsFe2 4O 0 ! i 0 200 400 600 0 T (K) 200 400 600 800 Fig. b.H. (1977)... Y6 Fe23 Y Fe2 _~ 4o I.... ..e. that this coupling can be reduced considerably (Gualtieri et al. chow and Sherwood 1977b). Buschow 1977c.2a-n and A. hydrogen compressors. YFe2 and CeFe2. Buschow 1977). edited by A. the latter to intermetallics in which the second component is a d transition metal. Evidence was obtained. 1976. however. no change seems to occur in sign of the magnetic coupling between the rare earth. It was noted. These features have been explained on the basis of partial atomic disorder originating from the metastable character of the ternary hydrides. 1980). Although it falls somewhat outside the scope of this review it is worthwhile to mention that several of the hydrogen absorbing compounds are important materials for several technical applications.4a-e. Magnetic characteristics of binary rare earth intermetallics are given in tables A.F. . 1 some details of the most common structure types encountered in rare earth intermetallics are listed. Andresen (1978). predicted from the magnetovolume effects available for Y6Fe23. however. For more details the reader is referred to the various contributions on this subject contained in the book Hydrides for energy storage.and 3d spins (Kuijpers 1973.3a-g. The former table pertains to intermetallics with non-magnetic partners. in Buschow and Sherwood (1977) that the hydrogen absorbed may also exert its influence on the magnetic properties by means of electron transfer. cold accumulators and hydrogen based batteries.RARE EARTH COMPOUNDS H2 ABSORPTION EXTERNAL PRESSURE 361 600 n YFe~ YFI 5 500 4OO X 300 200 t00 -e--.AV/V 0 10 P [kbor) 20 30 Fig. even after the drastic changes in electronic properties associated with the hydrogen absorption.M n compounds and the corresponding hydrides. Attempts have been made to correlate the presence or absence of a magnetic moment on the Mn atoms with a critical Mn-Mn distance in the R . Magnetic properties of several series of ternary rare earth based intermetallics are listed in tables A. energy conversion in solar heating and cooling. It is interesting to note that. These comprise hydrogen storage. Appendix In table A. 21. Effect of the hydrogen absorption on the magnetic ordering temperature. YFe3. N O e~ N ~ r °. •- ~ ~ ~ ~ ~ ~ *G 362 . e~ 0 0 ~g °~ 363 . Tc and TN are reported. ~. Tc and TN reported by different authors in literature are dissimilar. lower and higher limits have been listed. . The referenc.H. BUSCHOW TABLES A. since these latter may depend strongly on the amount of localized moment impurities present in the samples. The magnetic structure types are indicated by F (ferromagnetic). The values given for X of Pauli paramagnetic compounds are room temperature values and not values attained at 4. The first reference pertains to literature of the crystal structure and lattice constants. The values of the effective moments ( ~ ) and saturation moments (/~) are expressed in Bohr magnetons per rare earth atom.es comprise three groups separated by semicolons.J. The references after the last semicolon correspond to neutron diffraction work.364 K. Values for the paramagnetic Curie temperatures (0p) Curie temperatures (To) and N6el temperatures (TN) are given in K. Since in most cases the values of /~c~. Usually only one reference has been chosen out of the collection of references available. AF (antiferromagnetic) or by C (complex). Details pertaining to the structure type listed in columns 3 are given in table A. 0p. 1.2 K. /~.2a-n Magnetic properties of intermetallic compounds of rare earths and non-magnetic metals. 0p. The references given between the two semicolons pertain to the literature in which the values of ~¢a. HOB.7-22 7-7.47 0p 151 33 25 9 14 14 ~ 4.49 -76 3. u n p u b l i s h e d B u s c h o w a n d C r e i j g h t o n (1972) Buschow. 10.015 x 10-3 cm3/mole no C-W behaviour 3.30-9. 1.59 -68--44 3.5-18 23 21 9 10. 12. 14. 4 X = -0.11 10. 3 4.7 20. 11 17. 12 9.28-8. 11 17.2 10. 9. 7 4. 8 4.161 3.8 . (1970) M a t t h i a s et al.52 -10-15 7. I1. 9.5 6.. 1 I. (1977a) B u c h e r et al. I. ErB 4 TmB4 YbB4 LuB4 YB 4 tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr UB4 UB4 UB4 UB4 UB4 UB4 UB4 UB4 UB 4 UB4 UB4 3.7 10.61 . (1971) P a d e r n o a n d P o k r z y w n i c k i (1967) Sales a n d W o h l l e b e n (1975) G s c h n e i d n e r (1961) . i1-13 9. 3-6. I. cub cub cub cub cub cub cub cub cub cub cub cub cub cub cub cub cub CaBs CaBs CaBs CaBs CaBs CaBs CaBs CaBs CaBs CaBs CaBs CaBs CaB6 UBI2 UBI2 UBl2 UBI2 X = -0.2-25 NdB4 Stub4 GdB4 TbB4 DyB4 . 4 4. 11. 2. 1 I. 12 9. 16. 3-7 4.032 x 10-3 cm3/mole LaBs CaBs PrBs NdBs SmB6 EuBs GdBs TbB6 DyBs HoBs YbBs LuBs YB6 DyBI2 HoBI2 ErB12 TmBI2 1.6 .07 -66--50 9. 4 4.5-10. 3 3. 10 9. 3 3. 6. !.72 -43--22 10.68 -23-3 -440 X = 6.3 43-44. 4.2 2 ..RARE EARTH COMPOUNDS 365 TABLE A.046 x 10-3 cm3/mole -0. 1.53 5-27 1.3 13-15 !1. 9. 3.43 10. II. 4 4. 17. 4 ilion tetr tetr tetr 15. 1. (1968) P a d e r n o et al.0 7 8.54 24.96 10. I. 11. 12. 1. (1967) Gebaile et ai. 3-7. I1 9. 3.56-3.0 5.2 9. 5. 3. 4 4.5 5.94-8. (1968) H a c k e r a n d L i u (1968) C o l e s a n d Griflith (1961) C o l e s et al. 11.5 7.2a Rare earth boron compounds Crystal structure AIB2 AIBz AIB2 AIB2 Magne~ structure F Compound TbB2 DyBz HoB 2 ErB 2 Pr2Bs Nd2Bs Sm2B5 Gd2B5 LaB4 CeB4 PrB4 Symmetry hex hex hex hex mon mon mon ~eu 9.26-10. 2.061 x 10-3 cm3/mole 2.2 1 . 1.1 32. 11.7 9. 15. 7 4. 16 9.8 10 AF AF 4. (1962) L a P l a c a et al. 15.12 no C-W behaviour 7. 14 9. 3-6 4.. 3 4. 3-6 4.6 13.63 -35 -21 . 3-6 4. I..01 -55--60 9.4 7. 3 3.85 -23 6.6-7. (1961) 9. 7.5 50 UB4 UB4 UB 4 X = -0. 1. 11-13 9. 3. 8. 11 B u s c h o w (1977d) Will et al. 2 1.45-8. 1 3. 12 9. E t o u r n e a u et ai. unpublished F i s k et al.5 4.7 23.85-7 31-57 42-45. 17. 12.54 -42 no C-W behaviour 8. 1.1 Tc 151 55 15 16 TN l~erences I. 3. 13. 1. 5 17. 12 9.1 8-9 8. 08 x 10-3 cm3/mole 2.0523-28 7. 10.56 64 30-36 14-16 15 168-182 105-121 62-70 27-42 12-24 F (F) F F TmAI2 YbAI2 LuAI2 YAI2 LaAI3 CeAI3 PrAI3 NdAl3 SmA!3 cub cub cub cub hex hex hex hex hex MgCu2 MgCu2 MgCu2 MgCtl2 Ni3Sn Ni3Sn Ni3Sn Ni3Sn Ni3Sn 4.2b Rare earth a l u m i n i u m c o m p o u n d s Crystal structure Ni3Sn NisSn Ni2Si Ni2Si Zr2AI 3 Zr2AI3 Zr2Al3 Zr2AI3 Zr2AI3 Zr2AI3 Zf2A~ 3 CeAI CeAI DyAI DyAI DyAI DyAI DyAI DyAI DyAI DyAI DyAI CrB MgCu2 MgCu2 MgCu2 MgCtl2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 Magnetic structure Compound Symmetry Ce3Al Pr3AI Pr2Al Gd2AI Gd3AI2 Tb3AI2 DY3AI 2 Ho3AI2 Er3AI2 Tm3Al2 Y3AI2 LaAI CeAI PrAI NdAI SmAI GdAI ThAI DyAI HoAI ErAI TmAI YAI LaAI2 CeAI2 PrAl2 NdAI2 SmAI2 EuAI2 GdAI2 ThAI2 DyAI2 HoA!2 ErA!2 hex hex orb orh tetr tetr tetr tetr tetr tetr tetr orh orh orb orh orh orb orb orb orb orb orb orb cub cub cub cub cub cub cub cub cub cub cub /zetf 2. 29 18.2-9. 30. 14.84-8.6 10.59 30-32 70 2. 4 5.58 1-11 3. 9.6. 26. 6 5~6 5. 29. 6.6 7. 13 10. 12 10.64 -33-9 3. 47 18:22 19. 27 16. 7. 49.45-10.7 9. 2 3. 31 8.62-9. 36.92-'/. 39. 40.52-3. 2 3.27 32.89 9. 22.46-3.15 17-22 9.05-7.2 10. 12 16.103 x 10-s mS/mole X = 0. 10.1 8. 13 10.26. 50 1.47 0.366 K.53 -4-13 5.32. 37 18. 30 18. 6. 13 I0. 37 18.05 -2-0 7.16-9. 6 5.92 31-37 61-76 120-122 9-10 19-20 25-29 42 72 20 26 13 10 C C C C C C 4-4.19-4 3.14 4.HJ. 7. 4.15 17-25 10. 12. 6 5. 6. 17 4. 44-46 18.41.74 . 8 5.8 no C-W behaviour X = 0.11 +5 no C-W behaviour 7 . 14 10. 28. I I.49 19.26. 11. 32-35 18. 2 I. !1.34-2. 14. 29 16.94 168-180 9.8 0p -24 2 4 150 280-302 125 31 10 -3 . 38. 13 10.22.52 3.290 203 76 33 9 3 C C 2.6-9. 22.075 × 10-3 cma/mole X = 0. 49 19. 22.69-8.6-11.02 7.1-8. 7 5.9 9.06 x 10-3 cm3/mole 2. 16. 6. 14.0-10. 6.53-2. 11. 26. 6. 6 10. 22. 6.62 3. 26. 22.9 275.8-11. 6.6 F F no C-W 7.59 8.27.52-2.79-1.9 9.12-10.2 0. 43 18.60 2.54 . 6.25 5.9-7.7-11.27-2.5 3.49 19.7 i0. 6.1-3.70 -2 X = 0.18-25 16. BUSCHOW T A B L E A.11 10-24 10. 22 18. 35.1-7.81-9.63 -46--25 3.22.52 64-260 10.21 6.18 7.2 9.42. 6. 15 10. 26.16 16 18 7.10 ~ Tc TN References I. 27.82 108-110 9. 48 19. 10.90-8. 29. 15 10. 2-2. 30.52 4 0.5--89 10. 35. (1972) Oestereicher and Pitts (1972) Barbara et al. 44. 53. (1973) Barbara et al.50-3.52.16 7. (1973) Klaasse et al. 46.2. orb orh tetr La3AIH La3AIH BaAI4 X = -0.67 3. 24.55 hex rh rh rh Ni3Sn BaPb3 HoAI3 HoAI3 ErAI3 TmAI3 YbAI3 YAI3 La3AIIj Ce3AIII cub cub cub rh orh orb Cu3Au Cu3Au Cu3Au BaPb3 La3Alll La3AIII 8. (1978) . 44. 41. 56.29-8. 52. 36. 53 1. 12.35 -99. 15. (1972) Barbara et al. 40.49 19. (1976) Oestereicher (1973a) Purwins et al. (1968) B u s c h o w (1969) B6cle and Lemaire (1967) Kissel and Wallace (1966) Niculescu (1972) B6cle (1968) Van Diepen et al. 10. 22. (1967) Buschow and Fast (1966) De Wijn et al. (1968) Cock et al. (1974) N e r e s o n et al.2b (cont. (1966) DeWijn et al. (1972) S c h ~ e r et al. 9. ! Magnetic structure References 19. (1977b) Barbara et al. 5. 17. (1977a) Barbara et al. 31. 21. 2.3 13 Buschow and Van Vucht (1967) Mader and Wallace (1968a) Buschow and Van der Goot (1971a) Buschow (1975a) Buschow (1965b) Barbara et al. (1962) Van Daal and Buschow (1970b) Walker et al. (1967) Chouteau et al. 16. 27. (1974) Milhouse et al.49. 46 49 19.7. 6-9 12. 56 1. (1969) Van Daal and Buschow (1970c) Wernick et al.87 . unpublished Van Diepen et al. 48.48 x 10-3 cm3/mole 2. (1973) Mader and Wallace (1968b) Buschow et al.49 19. 3. 4.88 .0 -64 10. 20. (1967) Hacker et al. 26. 31.85 -51 10. (1973) Iandelli and Palenzona (1972) Buschow. 19. 49 19. 43.51 19. (1967) Buschow (1968) Sales and Wohlleben (1975) Van Diepen et al.75-7. 34.62 -9 7. 38.61 3. 13. 43 19. 25.79 12-14 29. (1975a) Swift and Wallace (1968) N e r e s o n et al. 33.53 1.53 -24--25 0. 32. 6.62 -300 AF Pr3AlH Nd3Allt EuAI4 1.RARE EARTH COMPOUNDS T A B L E A. (1970) Wernick and Geller (1960) Buschow. 47.19 4. unpublished Harris et al. 11. 42. 54. 1. 53. 55.49 19. (1976) Will and Bargouth (1972) Havinga et al. 23. 51. (1968) B/:cle et al.) Crystal Compound Symmetry structure GdAI3 TbAI3 DyAI3 HoAI3 367 ~cff 0p /~ Tc TN 17 21 23 9 5-5. 18. 37. 28. 2. 39. 50. (1965) Van Vucht and Buschow (1965) Van Vucht and B u s c h o w (1964) Van Daal and Buschow (1970a) Williams et al. 49. 54.89 -26 9. 8. 45.5i. 7. (1971a) Stalinski and Pokrzywnicki (1966) Barbara et al.53 20. 14. 86 5. 10 9.6 5.89 6. 6.6 3.51 2. cub tetr tetr orb orh orb orh orb orb orh orh hex hex hex hex hex hex hex hex hex hex hex hex hex /~ee 2. Cable et al. 10.48 10. 6 5.28 9. ! I.7 8. 12 80 53-55 1. 7. 6 5. 2. 10 9.39 4.23-8.2c R a r e earth gallium c o m p o u n d s Crystal structure Cu3Au CrsB3 Zr3AI2 CrB CrB CrB CrB CrB CrB CrB CrB AIB2 AIB2 AIB2 AIB2 AIB2 AIB2 AIB2 AIB2 AIB2 AIB2 A1B2 AIB2 AIB2 Magnetic structure Compound Symmetry Ce3Ga GdsGa3 Ce3Ga2 Gd3Ga2 CeGa NdGa GdGa TbGa DyGa HoGa ErGa TmGa LaGa2 CeGa2 PrGa2 NdGa2 SmGa2 EuGa2 GdGa2 TbGa~ DyGa2 HoGa2 ErGa2 TmGa2 YbGa2 1.4 5.368 K.15 -20 -6 -2 /t Tc 7N References 1. (1972) .93 9.8 10.H. (1964a) B a r b a r a et al. 1I 9. 8 5. 9.J. (1971b) H a s z k o (1961) B a r b a r a et al.2. 8. 4.04 7. 2 9. II.93 6.5 2.12 5. 9. (1971c) Iandelli (1964) K l a a s s e et al.18 9 10 6 .40 8.51 7. (1976) C o l o m b o a n d Olcese (1963) B u s c h o w and V a n d e n H o o g e n h o f (1976) Crystal s t r u c t u r e u n k n o w n H a c k e r and G u p t a (1976) D w i g h t et al. 10 9. I 2.47 10.70 9. 3. C C I1 14 18 15 10 AF AF no C-W behaviour 7. 1 2. 9.74 8. 2 3. 5.7 10.72 2. 6.7 Op -56 25 -4O -32--23 -21 34 208-210 152 88 60 18 10 .23 9. 11. 10 9.6. (1967) B a r b a r a et al. 12.76 3.8 5. BUSCHOW T A B L E A.2. 10 9. 1 9. I 5.42 45 190-200 155-158 116 68 34 15 F. 6 9.64 8.18-8. 6 5.73 3. 78 -17--12 no C-W behaviour 10 8. 8 6. (1974) U m e z a k i et al. 3 5.21.8 10. 10.4 1. AF !1 6.22 17. 2 9.75 -10 7. cub cub cub cub tetr Cu3Au Cu3Au Cu3Au Cu3Au CuTi3 369 /tea 0p /t Tc TN Magnetic structure References 1. 9 9. (1973) Stalinski (1974) Crystal structure u n k n o w n P a l e n z o n a (1968) K a w a n o et al. 13.15 13. 13. 20. 2. 22. 8. 21.4 8. 3 1.1 0 .13 13.63 8. 3.29× 10-3 cm3/mole 12. 2.27× 10-3 cm3/mole 2. 13 17. 7.G u e g a n (1976) Sekizawa a n d Y a s u k o c h i (1964) Cable et al.5-62 i14 213 138 51 185 112 28 145-190 120 42 F 183 95 +6 -66-18 16 AF 10 8 2.7 2.72 .48 3.8 5.3 5.4 9.65 -18 9. 9. 3.67-3. 14 13. (1970) Lethuiilier a n d C h a u s s y (1976a) Lethuillier (1974) K u z m a a n d Markiv (1964) Harris and R a y n o r (1965a) Crangle (1964) Arnold a n d N e r e s o n (1969) K l a a s s e et al. 13 13. 3 6. 7. 5. 19 13.4. 14.6 2. !1 9. (1974) . 2 I. 17. (1974) Lethuillier a n d P e r c h e r o n .15.8-7 16 4.58-3.9.20 -85 10. 9 5. (1973) Stalinski et al.. 11. 16 13. (1969a) H a v i n g a et al. I1.2 56.4 13. 13 13.9.54 -46 3. 16.1 -33 9-22 10 196 113 31 . 12 13.43 0. 19. 9. 13. 16 13.8 10. 4. (1966) C o l o m b o and Olcese (1963) H u t c h e n s et al. 13.4-3. 13. (1964a) Iandelli (1964) B u s c h o w et al.78 -35 10.37 5.62 9.RARE EARTH COMPOUNDS T A B L E A. 2 hex hex hex tetr tetr tetr tetr hex cub cub cub cub cub cub cub cub cub cub cub cub cub cub Ni21n Ni21n Ni21n Thin Tbln "loln Thin Caln2 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AnCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCus 2. 7 I. 13.73 -8 7.2 5. 2 12. 13 13.10 9.5-10 45-48 36 23 11 6 AF AF AF AF 6. 14 Moriarty et al. 6.79 +8 X = 0.9 3. 15.20 13.05 -62 10.6 -6 no C-W behaviour X = 0.2d Rare e a r t h indium c o m p o u n d s Crystal Compound Symmetry structure La31n Ce31n Pr31n Nd3ln Gd3ln DY31n Er31n Ce21n Tb21n Ho2In Celn Gdln Tbln Dyln Holn Ce21n 3 Euln2 Lain3 Celn3 PrIn3 Ndln3 Smln3 Eulu3 Gdln3 Tbln3 Dyln3 HoIn3 ErIn3 Train3 Ybln3 Luln3 YIn3 1. 17. 13.68 3.1 1. 18. 18. 5 12-13 11 AF A n d r e s et al. 10 12.6 -0 X = 0. 5.28 x 10-3 cm3/mole 7.2 3. 10 11. (1972) Crystal structure u n k n o w n C o l o m b o and Olcese (1963) Iandelli (1960) Iandelli a n d P a l e n z o n a (1965) B u s c h o w .C 220 11. (1974) . 11. 12. 10. (1972) Birgenau et al. 4 6.58 . (1970) Stalinski et al.J. 7 6. 12 13. 4 9. 4. B U S C H O W T A B L E A.29 -20 no C-W behaviour 8.5-6. 13 0.22 7. 6 6. 13.65 -33 2.2e Rare earth thallium c o m p o u n d s Crystal Compound Symmetry structure La3TI Pr3TI Ce2TI CeTI EuTI GdTI YbTI EuT12 CeTI3 PrTl3 EuTI3 GdTI3 DyTI3 YbTI3 cub cub cub cub cub cub hex cub cub hex cub cub hex 1. 9.77 4 7. 7.1. 7 10.10 -4 !1 F.H. 8 4. 6 8. 4 5. unpublished Iandelli (1964) G s c h n e i d n e r (1961) Stalinski (1974) B r u z z o n e a n d Ruggiero (1963) Olson et al.40 3.67 .370 K. 2. 3. 1. 6. 12.7 2. 5. Cu~Au Cu3Au CsCI CsCI CsCI CsCI Caln2 AuCu3 AuCu3 Ni3Sn AuCu3 AuCu3 Ni3Sn ~e~ 0p ~ Tc Ts Magnetic structure References 1.78 2. 11 hex tetr hex hex hex orh orh orh orb orh orh orh orb orh orh orh tetr tetr orh orh orh orb hex 1. 4. 8. 8.38 7.47 8. 2 3. 4 3. !1 6.3 10.55 10.17 -8 -5 0 /~ Yc TN References 1.23 10.5 7. (1970) N g u y e n V a n N h u n g et al. Ni21n Cr~B3 MnsSi3 MnsSi3 MnsSi3 SmsGe4 SmsGe4 SmsGe4 SmsGe4 Sm~Ge4 FeB FeB FeB CrB CrB CrB ThSi2 ThSi2 GdSi2 GdSi2 GdSi2 GdSi2 A]B2 7.RARE EARTH COMPOUNDS T A B L E A. 4 3. 9 10. 1I 6. N g u y e n V a n N h u n g et al.08 7.55 2.5 0p -60 -46 -43 53. 3. 6.7 97 90 349 216 133 69 26 -7 5 -8 2 -5 10 -299 -58--47 .2f Rare earth silicon c o m p o u n d s Crystal structure Magnetic structure 371 Compound Symmetry Ce3Si Ce2Si CesSi3 NdsSi3 GdsSi3 DysSi3 GdsSi4 TbsSi4 DysSi4 HosSi4 ErsSi4 CeSi GdSi TbSi HoSi ErSi TmSi CeSi2 PrSi2 GdSi2 TbSi2 DySi2 HoSi2 ErSi2 /tel[ 2. 5 3.7.3 9.45 2.61 3. 5 6. (1967) G a n a p a t h y et al.15 9.0 AF AF AF AF Crystal s t r u c t u r e u n k n o w n Ruggiero et ai. 4 6.2 6.64 9. 8.24 6. 5.81 9.50 8.7 6. 5 3. 2 6. 2 I.44 6. 8 6. 4 3. (1971) Matthias et aL (1958) Y a g u c h i (1966) S e k i z a w a and Y a s u k o c h i (1966a) .5 27 17 17 18 6. 8 6.94 7. (1964) S m i t h et al.7-7.90 2.06 9. 11.34 10.67 8. 10.35 11. 8. ! 1 6. 2 3. (1967) Parth6 (1967) 7.49 7.5 3. ! I 6.1 10.12 336 225 140 76 26 50 57 25 10 10 10. 9.8 10. 10. 2.58 2. 8 6. 2 6. 5 3. (1976) H o l t z b e r g et ai. 92 45 48 85 40 10 31 15 30 40 21 7 10 1. 6 7.76 10 2.54-2. 9.H. H o i t z b e r g et al. 7 7.80 10 3.372 K. I. 3. 10 10. 7 7.10 8: 9.0 -15 2. 2 8: 9.1 -54 9.2g Rare earth g e r m a n i u m c o m p o u n d s Crystal Compound Symmetry structure Ce3Ge LasG¢3 CesGe3 PrsGe3 NdsGe3 Sm5Ge3 GdsGe3 TbsGe3 DysGe3 HosGe3 ErsGe3 GdsGe4 TbsGe4 DysGe4 HosGe4 ErsGe4 LaGe CeGe PrGe NdGe SmGe GdGe TbGe DyGe HoGe ErGe YGe CeGe2 PrGe2 NdGeq StaGe2 GdGe2 TbGe2 DyGe2 HoGe2 ErGe2 ~eff 0p ~ Te TN Magnetic structure References 1: 2 3. 3 3:3 3. 7 7. 3 5. 3 3. 7 7. 4-.J. (1967) B u s c h o w and F a s t (1966) Parth6 (1967) Matthias et al.74 16 9.98 93 10. 7.73 20 no C-W behaviour 8. 3 3:3 3.7 7.7 7.7 -4 9.10 10 9. I0 hex hex hex hex hex hex hex hex hex hex orh orb orb orh orh orh orh orh orh orh orb orh orh orh orh orh tetr tetr tetr tetr orb orh orb orh MnsSi3 MnsSi3 MnsSi3 MnsSi3 MnsSi3 MnsSi3 Mn5Si3 MnsSi3 MnsSi3 MnsSi3 SmsGe4 SmsGe SmsGe4 SmsGe4 SmsGe4 FeB FeB CrB CrB CrB CrB OrB CrB CrB CrB CrB ThSi2 ThSi2 ThSi2 ThSi2 2.74 + 18 no C-W behaviour 8. BUSCHOW T A B L E A.46.47 45 11.48 35 8. (1964) B u s c h o w and F a s t (1967) Buschow. 2. 4.9 -26 10. 7 7.64 39 28 40 62 48 36 18 7 2.51 .7 3'.77 -5 10.18 19 3.57 -41 X0= 0. Crystal structure unknown Ruggiero et al. 10.3 3. 6 5.42 70 9. 6 5.10 10. unpublished Smith et al. 8.19-0 3. 7 7.6 28 42 28 1! 1. (1967) 6. 6 5.10 -3 cm3/mole 2.46 5 3.9 -48 10.58 43 10.21 -13 9. (1958) S e k i z a w a (1966) .76 -5 10.15 94 9. 2 3. 5. 2.63 80 10. 8. 10 10. 4 3.66 -50--26 3.69 +30 3. 6 5. 7 7'.7 7 no C-W behaviour 8.73 1.4 20 12 1. 10 10.10 8. 7 7. 10 10.4 3.6 22 3.60 ~0 10. 173x 10-3 cm3/mole 2 . (1973) Stalinski (1974) Stalinski et al. 11. 2 17. 10. 7 4 .13 no C-W behaviour 2. 20.5 16. 6 4. 8 -203 3. 7. (1967) S h e n o y et aL (1970) Lethuillier a n d C h a u s s y (1976a) Lethuillier 0 9 7 4 ) Lethuillier et al.13.18 16. 7 8 . 22 24. 18 19. 22. 5. 7 -10--8 3. 14. 7. 3. 18.14 4:6 2.2.I 14x 10-3 cm. 5 hex tetr cub cub cub cub cub cub cub cub hex orh cub cub cub cub cub cub cub cub cub cub cub cub I. MnsSi3 Sm2Sn 3 LaSh3 CeSn3 PrSn3 NdSn3 SmSn3 EuSn3 GdSn3 YbSn3 Ce2Pb Eu2Pb CePb LaPb3 CePb3 PrPb3 NdPb3 SmPb3 EuPb3 GdPb3 TbPb3 DyPb3 HoPb3 YbPb3 YPb3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 Ce2Pb PbCI2 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 2.9.2h Rare earth tin and rare e a r t h lead c o m p o u n d s Crystal structure Magnetic structure 373 Compound Symmetry Ce2Sn SmsSn3 C¢2Sn3 P-eft 0p p Tc TN References I.6. 12.6 -7 2. 2.RARE EARTH COMPOUNDS T A B L E A. 3 .2 3 .20 -29 10. 7. 24. 8. 2. 8 4. 9.21 -55 10.20 17. 6. 6 . 2 3.18. 2 16. 6 3 -34--22 no C-W behaviour 7. 15. 23. 16: 18. 9.4 -! 10.0 .5-3.61 -25--22 no C-W behaviour 7. 6. 16. 5 4.6-4.. 18 24.55 --8 no C-W behaviour Xo= 0. (1973) L o e w e n h a u p t (1973) Buschow.21.7 9-12 38 ~35 AF AF 32-42 2.9. (1975) L o e w e n h a u p t and Hfifner (1969) P e r c h e r o n et al. (1970) T s u c h i d a ' a n d Wallace (1965) B o r s a et al./mole 2 . 18 24. 6. 3 I.7. 12.17 no C-W behaviour Xo= 0. 21. 8. 14. (1964) .to = -0.81 -66--25 7. (1974) M c M a s t e r s a n d G s c h n e i d n e r (1964) K u z m a et al.3 6 .5-8.55 .65 -75--60 8. 10.3 . 2. 17. 15 16.18 16.085x 10-3 cm3/mole 13.2 .025 x 10-6 cm3/mole 2. 9. I I.10--5.6 4. II 8.42-3. 6.49 I Xo= 0. 3 4. 2. unpublished G s c h n e i d n e r (1961) M c M a s t e r s and G s c h n e i d n e r (1967) H u t c h e n s and Wallace O971) Structure type n o w k n o w n LethuiHier et al. 10 4.2 .6 -60 9. (1964) P e r c h e r o n a n d Lethuillier (1972) Harris a n d R a y n o r (1965a) H a v i n g a et ai.17 3 . 18 24.1 I.0 -73 . 19.3 . 18.57 .5-7.7 6 19-22 17 15 I1 3. II 4: 3. 5 8 . 22 23. 18 24. 2 3.7 AF Crystal s t r u c t u r e u n k n o w n Ruggiero et al. 4. 7.73 -13--18 7.21 16. 17. 5. (1976) 374 16. 21.4-8 3.51 -10 3. Storm and B e n s o n (1963) S h e r w o o d et al.59 -48 3.8 -6 10. 1. 14. 3.4 8. 1. 17. (1976) Pierre (1970) Cable et al. 28. 9.01 7. 29. 12.52 58 20 2 2 -0 -0 ~0 -40--30 12 -4 . 26 22. 25 22. 17. (1970) B u s c h o w a n d v a n der G o o t (1970) Coldea a n d P o p ('1974) A n d r e s and B u c h e r (1972) . 29 27.2 0. 1 1. I.2.8 9.6 4. (1964a) Pierre a n d P a u t h e n e t (1965) Winterberger et al.5 (7.95 40-72 7.59 3. 17. 15. 26 27.4 8. 6.4 II 9. 17.20 16. 26 22. 23 24. 27. 10.9 0. 17. 1 3.7 7. 22. 13 3.5. 15 16.41-7.2 5. 17.60 -38-0 3. 23. 12.5 -6 9.7 9.II 3. 26. (1977) B u s c h o w et al. (1968) Pierre (1969) B u r z o et al.49 -4 no C-W behaviour 0. (1964) De Wijn et al. 17. 11. 16. 2.2 5.35 4 7.61-10. 1. 18.9) 40 41-140 114-177 61-64 28 17-33 I1 AF AF AF AF 13-15 41 54 24 9 !I 57 25 15 7 Walline a n d Wallace (1965) Olcese (1963a) C h a o et al.3-8.2 1. 28 27. !. (1964b) D e b r a y et al. 1.56 -2 no C-W 7.89 9.9 10. private c o m m u n i c a t i o n W i c k m a n et al. 4.48-2.56 -8 no C-W behaviour 2.3 1.4 6.8 6.75 5 10.6 7. 13.19 16.T A B L E A. 25.19 16.4 2. 8. 19.19 16. 26 22. orh orb orh orh cub cub cub cub cub cub orh hex orb orh orb orh orh orb oth orb orh orh orh orh orh hex hex hex cub cub cub cub cub orb orh orh orh orb FeB FeB FeB FeB CsCI CsCI CsCI CsCI CsCI CsCI FeB AIB2 CeCIl2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CaCu5 CaCu~ CaCu5 AuBe5 AuBe5 AuBe~ AuBe5 AuBe5 CeCu6 CeCu6 CeCu6 CeCu~ CeCu6 ~td 0p ~ Tc TN 2. 24 22.15-2.8.19 16. 17. 17 16.8 -26--18 10. 28 27. (1972) Sekizawa and Y a s u k o c h i (1966b) Pierre (1967) Yashiro et al.3) (4. 24. 20.52-9.68 -22--20 10.46 -75--26 9.69 -2 no C-W behaviour 8. (1968) K l a a s s e (1973) B u s c h o w and v a n der G o o t (1971b) A n d r e s et al.19 16. (1971) Cable et al.9.66 .0 7. 28. 17.17 16. 10 3. 2. 24. 17-19 16. 17 22. 28 27.6) (7. 26 22. I !. 9-11 3. 28 2.1 5.8 2. (1975b) V a n Steenwijk (1975a) V a n Steenwijk et al. I 15.19 16.19 16.59 3. 14 3. (1964) T a m m i n g a (1973) Sherwood.2i Rare earth copper c o m p o u n d s Crystal Compound Symmetry structure CeCu PrCu NdCu SmCu GdCu TbCu DyCu HoCu ErCu TmCu YbCu LaCu2 CeCu2 PrCu2 NdCu2 SmCu2 EuCu2 GdCu2 TbCu2 DyCu2 HoCtt2 ErCtl2 TmCu2 YbCu2 LuCo2 PrCu5 EuCu5 GdCu5 TbCu5 DyCu5 HoCu5 ErCu5 TmCu5 CeCu6 PrCu6 NdCu6 SmCu6 GdCu6 1.7 Magnetic structure References 1.15 7.6 10. 64 -3 no C-W behaviour 8. 24.0 8.1 7 . 7-9. 1.4.24-8.19 3.3 3. 26.29 29 9.3 19 AF C C C no C-W behaviour 7. 3 21. 36 1. 24. 3 -6 1.83 -21..32 -5 no C-W behaviour -92 20 8..2-9 1! .5 -5. 35 1. 14 I. 27 28. 4 I.13. 22 37.45-10.53 .55 6.5 12 24.58-23 9. 35. 3 1. 16 I.13.5I-2.14 22 138-150 106 55-63 32-33 18-21 9.93-10. 30 37.2j Rare earth silver and rare earth gold compounds Crystal structure CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI FeB CsCI CeCu 2 MoSi2 MoSi2 MoSi2 MoSi2 MoSi2 MoSi2 CeCu2 CaCu5 CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI FeB CeCu2 MoSi2 MoSi2 MoSi2 MoSi2 MoSi2 MoSi2 MoSi2 7.45 7. 35 1.4 no C-W behaviour Xo= 0.13.0 5. C AF.7 .03 31.4 9.7 C C C C C .5 -25 .40-10.50 0 9. 38. 1.5 < 1.4.4. 38. 16 I. 3 37. 4. 25 26.13. 43 24-34 10 13-19 8-19 Magnetic structure Compound LaAg CeAg PrAg NdAg SmAg GdAg TbAg DyAg HoAg ErAg TmAg YbAg YAg CeAg2 EuAg2 GdAg2 TbAg2 DyAg2 HoAg2 ErAg2 TmAg2 YbAg2 EuAg5 CeAu PrAu NdAu SmAu EuAu GdAu TbAu DyAu HoAu ErAu TmAu YbAu CeAu2 EuAu2 GdAu2 TbAu2 DyAu2 HoAu2 ErAu 2 TmAu2 YbAu2 Symmetry cub cub cub cub cub cub cub cub cub cub cub orh cub orb tetr tetr tetr tetr tetr tetr orb hex cub cub cub cub cub cub cub cub cub orh orh tetr tetr tetr tetr tetr tetr tetr /te~ 0p /~ Tc TN References 1.RARE EARTH COMPOUNDS 375 T A B L E A.15-7.38 -31.22 7 10. 40 37. 24. 28 29. 17 33.6 -13-24 10. 35. 30 18.13.4. 37 40.44 2-6 3.13 17.52-10. 27 37.62 4. 38 37. 41 37. 31. 31 32.2 1.0 10.25 .5-10 AF AF AF AF AF.42 -4 7. 38.43 2. C 10.0 .22 -9.54 23 10.22 23.2 6-7. 19 20.2-5. 24.4-35 9-15. 24.086 • 10-3 cm3/mole 2. 15 I. 17 18. 10 I.2-3.4.0 9.60 19 -38 8. 35. 8 1.6 34. 30.56 -20.4.5 < 1. 36 1. 24. 38.5 48-49.t6-5 3. 24 25. 24.6 55 31-33.6 -84--70 9. 38.. 26.41 14 -47 -31. 36 17. 32 33.97 9. 1. 39 37. 29 30. 34.0 0.7 6.8 9-9.0634 cm3/mole 2.0 -4.5 -8.11-13 I.15 -36--11 10. 35 I.42 Xo= 0.5-15 7.95 1. 24.4.35-4. 09 8. 3. 26. 4. (1963) Goebel et al. 37. 24.90 10. 31. 38. (1976) Moriarty (1966) Weimann et ai. 18. 5. 6.45 44. 12. (1973) Atoji (1968b) Atoji (1972b) Atoji (1972c) Iandelli and Palenzona (1969a) Crystal structure not known Sadagopan et ai.42. 20. 39. 34.3-4. 2. (1975) Olcese et al.21 3.42. (1975) Atoji (1968a) Miura et al. (1974a) B r u n e t al. 7.6 14 Chao et al.32 orb orh orb orb orh orh orh tetr tetr TiCu3 TiCu3 TiCu3 TiCu3 TiCu3 TiCu3 TiCu3 MoNi4 YbAu4 EuAu5 1.5 -6 # Tc T~ Magnetic structure References 43. (1976) Van Steenwijk et al. 36.2j (cont. BUSCHOW TABLE A. 10.64 9. (1968) Sill and Prindeville (1975) Sill et al. (1964a) Arnold et al.5 9.7 26.8 23. tetr hex MoNi4 MoNi4 CaCus 8. (1976) B r u n e t al. (1972) Sekizawa and Yasukochi (1966b) Pierre and Pauthenet (1965) Cable et al.) Iandeili and Palenzona (1968).3 21.45 44. (1967) Nereson (1963) Debray et al.36 10. 41. 17. 3 44.46 44. 19. 43. 30. 44. (1963a) Walline and Wallace (1964) Olcese (1963b) Ihrig and Methfessel (1976a) B r u n e t al.5 -9-15 7. 45. 23. 35. (1971) . 11. 14. 40. (1971) Atoji (1969a) Atoji (1969b) Atoji (1972a) Atoji (1970) Kiaasse et al. 42.10-33.99 7.9 6. see K6ster and Meixner (1965) Kissel and Wallace (1966) Chao (1966). 6. 21.2 -6 4.45 44. (1977) Crystal structure not known Complex crystal structure. 15.0 10. 46. Sill et al.8 0p 6 17.376 K.45 44. 28.46 44.) Crystal Compound Symmetry structure CeAu3 GdAu3 TbAu3 DyAu3 HoAu3 ErAu3 TmAu3 YbAu3 ErAu4 TmAu4 #e~ 2.45 44:45 44. 31.78 13 25.3 . 29.J. 33. 27.46 32. (1975a) Burzo et al. (1972) Crystal structure unknown K6ster and Meixner (1965) Van Steenwijk (1976) Baenziger and Moriarty (1961) Kaneko et al. (1974b) Buschow et al.95-4. 9. 32.45 44. 22. 8. 16.42 7. (The Ts values listed are derived from resistivity measurements. 13.H. 1 1.2k Rare earth beryllium compounds Crystal structure NaZnl3 NaZnl3 NaZn13 NaZn13 NaZn13 NaZnl3 Nagnt3 NaZnt3 NaZnl3 Nagn13 NaZnl3 NaZnl3 NaZnl3 NaZnl3 Magnetic structure Compound LaBer3 CeBel3 PrBel3 NdBel3 SmBel3 EuBe) 3 GdBe13 TbBe13 DyBel3 HoBet3 ErBe~3 TmBet3 YbBel3 LuBe13 Symmetry cub cub cub cub cub cub cub cub cub cub cub cub cub cub ~tef~ 0p # Tc TN References 1.RARE EARTH COMPOUNDS 377 TABLE A.8 19-22 25. 1 1. B o r s a a n d O l c e s e (1973) 3.125 x 10-3 cm3/mole 2. 1 X= -0.5 13 9.82-7.94 25-45 6.47-10.55 1 no C-W behaviour X = -0.0 10. 1. I I.58 -8 3. I 1.57 6 9.3 9-9.97 9.71 14. 1-3 1.9 10.5 1.3 5.63 8.7-9.4. 1. 2 1.5-25 no C-W behaviour no C-W behaviour 7. D o m n g a n g a n d H e r r (1973) 5. B u c h e r (1975) 2.4 I.67 2.53 6 7. I I.7 15. 1.2. 1.37 1.45 2. (1971) 4. 1.4 1.57-3.4-2.024 x 10-3 cm3/mole no C-W behaviour 3. 1. 1 I.0 9. C o o p e r et al. H e i n r i c h a n d M e y e r (1977) . 1 1. 0 -124 no C-W behaviour 8.90 100 10. 4 1. 8 8.8 8. 6. 9. 5.7 1. 4.H. b) A i e o n a r d et al.119 10.C 0.I I 83 10.69 5. 2.94 83-84 10. 1. 5 I. 1.23 5.1.84 8. 3. 8.7 6.7-7. 11.57 3.9 7.1 4. 2. 8 8.58 1. 2 I.171 x 10-3 emu/mole x = 0.66 . 9.2. 12.81 -240 9.39 -11--9 3. 12 B u s c h o w (1973b) A l e o n a r d et ai.2. 2 1.05 4.5-16 < 1.73-9.60 9-15 x = 0.18 × 10-3 emu/mole 2.19 3.8 -42 5.86 7 7.34 7 3.6 I.26-9.7 -46 3.82 56 10. 10 12.54-10.378 K.2. (1978) B u s c h o w (1976a) Will et al.6 26 26 30 7.2. (1977) 7. I.4 6. unpublished .10. (1977b) K r y p i a k e v i c h et al.74 23 9. 4.77 24-25 9. (1976) M o r i n et al. I. BUSCHOW T A B L E A. 3 I. 8 8.5 10. 4. (1975) B u s c h o w et al. 9 9.2 13 4 7.9.36 108-120 9.03 6.55 5. 8 8.8-8. 8 8. I.14--9 no C-W l~haviour 8.5 9.51 .6-7.3 2.7 2. 12 I1. 12 ll.49 1. 8 8. (1978a.5 AF AF C C AF C F.56 -110 8. I.55 .46 3 X = 0. 8 2. 8 8'.2e R a r e earth m a g n e s i u m c o m p o u n d s Crystal structure CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgZn2 MgCu2 MgZn2 MgZn2 MgZn2 MgZn2 MgZn2 MgZn2 MgZn2 Fe3AI Fe3AI Fe3Al Fe3AI Fe3AI Fe3AI Fe3AI a-Mn a-Mn o~-Mn a -Mn a-Mn Th2Nit7 Magnetic #e~ 0p /t Tc Ts structure Compound Symmetry LaMg CeMg PrMg NdMg SmMg GdMg TbM8 DyM8 HoMg ErMg TmMg YMg LaMg2 CeMg 2 PrMg2 NdMg2 SmMg2 EuMg2 GdMg2 TbMg2 DyMg2 HoMg2 ErMg2 TmMg2 YbMg2 YMg2 LaMg3 CeMg3 PrM83 NdMg 3 SmMg 3 GdMg3 TbMg3 GdsMg24 Tb~Mg24 DysMg24 HosMg24 ErsMg24 TmsMg24 Eu2Mgt7 cub cub cub cub cub cub cub cub cub cub cub cub cub cub cub cub cub hex cub hex hex hex hex hex hex hex cub cub cub cub cub cub cub cub cub cub cub cub hex 1. (197613) B u s c h o w et al. I.32 26 no C-W behaviour 8.10 9. 9.7 25-48 10.29 x 10-3 emu/mole 2.9 9. 12 12.08-8.4-6. 2 8. (1975c) Sch/ifer et al. 2.66 39 11 3 -20 18-20 45-47 48-64 5. 8 8.72 119-120 81 22-46 21-25 5. 11. 12 11.47 -10--5 3. 10. I. 8 8.52 19 8. 8 8. (1960) Buschow. 9 9.12 II.9 9.J.7 81 88 66 27 19 6. 1.6-10. 9 9. 8 8.5 16 20-26 AF 7. S c h ~ f e r et al. References I.11 × 10-3 emu/mole X = 0. 8 8. 2.02 7.2. 3 I. 21 24.5-45 8. 25.2 9.2m Rare earth zinc compounds Crystal structure CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI CsCI CeCu2 CeCn2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CaCu5 CaCu5 Magnetic structure Compound LaZn CeZn PrZn NdZn SmZn EuZn GdZn TbZn DyZn HoZn ErZn TmZn YbZn LuZn YZn LaZn2 CeZn2 PrZn2 NdZn2 SmZn2 EnZn2 GdZn2 TbZn2 DyZn2 HoZn2 ErZn2 TmZn2 YbZn2 l.72 -38-24 3.3.28-3.84 11. 17 19.3.12 8. 29 28.25-2. 16 19.54 7.5 9.48 70 9. 3. 19-21 13.8 6.27 28.26.1-8.64 7.01 10. 21 22.17.0 8.2 AF C 6. 3. 13.5-6. 8.10-3 cm3/mole 2.17.82 24 45 20-30 68 55 35 12 13 5.56 14 3. 3.71 26 9.5 -4 7 7-7.2 110-140 80 5-25 9. 5.uZn2 CeZn5 EuZn5 Symmetry cub cub cub cub cub cub cub cub cub cub cub cub cub cub cub orh orb orb orb orb orb orh orh orh orh orh orh orh orh hex hex /tea 0p ~ Tc T~ References I. 8. 5 3.8 29-36 66-148 110-125 268-270 204-207 139-145 75-80 0-50 AF AF AF F X = 0. 1.22 13.14-2. 17. 17 13.5.7 6. 29 28.43 10-13 3.3.11 3.7 3.40 28 no C-W behaviour 7.84 9. 21 13.10.62 58 10.08 9. 17 13. 29 28.29 28.44 30-45 no C-W behaviour 7.008. 14 15.19 × 10-3 ¢m3/mole . 18 13.29 X = 0.5 no C-W behaviour 2.48 1!.64 0 -44 -24--78 0 -53 -17 -14 .9.63 7.10 3.11.82 14 268 7.21. 16. 6 3..9 10. 3-5.19-9.2 190-203 8.23 13.l' = 10-5 emu/cm 3 2.29 28. 2 3. 5 8.18--2 3.5 1.26-3.73.91 C C C 10 10 28 Ce2Znl7 Gd2Znl7 Tb2Zn17 DY2Znl7 Ho2Znl7 Er2Znl7 Tm2Zn17 Yb2Znl7 rh rh rh rh rh rh rh rh Th2Zfll7 Th2Znl7 Th2Znl7 Th2Znl7 Th2Znl7 Th2Znj7 Th2ZIlI7 Th2Znt7 .5.10 8.48 . 8.18.5.23 26. 8 3.RARE EARTH COMPOUNDS 379 TABLE A. 5. 17.21.99-8.3.06 2.2 10. 19.45 31.5 9. 15 13. 3. 29 28.5. 15 13. 9.10 3.59 5. 16 28. 19 C 28. 29. 25. 20. 28.) Crystal Compound Symmetry structure CeZnnn YbZntn Smgni2 Pefr 2. BUSCHOW TABLE A. (1970b) Debray and Sougi (1973) Buschow et al. 26.30 28. 11. 16 14 2. 3.29 28. ThMn. 2.8 3. (1975d) Wickman et ai. 8. 12. 9. 24. (1968) Debray et al. 21. 27.50-7.14 -38 9.2m (cont.67 -3 7. unpublished Michel and Ryba (1965) Lott and Chiotti (1966) Olcese (1963d) Iandelli and Palenzona (1964) Iandelli and Palenzona (1969b) Stewart and Coles (1974) Forsyth. 18. (1964a) Debray et al. 16 28.74 Op 26 -27.29 19.380 K. 5. 15. (1975) Eckrich et al. 22. 23. 30.29.29 GdZnl2 TbZnl2 ErZal2 EuZnu3 tetr tetr tetr cub 1. (1976) Morin and Pierre (1973) Cable et al. 19.40 -58 10.2 ThMnl2 ThMn12 NaZnl3 8. (1975c) Iandelli and Palenzona (1965) Yashiro et al. 10. 17. (1975) Debray and Sougi (1972) Debray et al. (1964) Goebel et al. 14. 7.. (1970a) Olcese (1963c) Debray et al.27 Chao et al. (1976) Olcese (1963c) Kanematsu et al.54 0 0..J.H. unpublished Buschow et al. 6. unpublished . 19. 4. (1976) Fornasini and Merlo (1967) Debray and Sakurai (1974) Debray et al.8 P Tc TN Magnetic structure References 28.94 2-18 16.29 tetr tetr tetr BaCdtI BaCdn0 ThMnt2 15 28. 13. (1969) Morin et al. 1 3.00 2.9 -12 0. 2 6. 7. 12.8 9. 13.89-7. 8 12.RARE EARTH COMPOUNDS T A B L E A.97 . 2 10. 6 6. 1. 8. 1.3 10-11.1 9.05 7.13 2.2-3. 15. cub cub cub cub cub cub cub cub cub cub cub cub cub hex orh hex cub hex cub hex cub cub tetr tetr tetr cub cub cub cub hex hex hex hex cub #eft 0p # Tc TN References I.18 -75 7. 2 12. 8 8. 7 8.53 44-49 1.03 7.50 10-14 0.3. 2 17.8 8. 1.82-7.18 -52 7. Iandelli (1955) Iandelli and F e r r o (1954) Iandelli and P a l e n z o n a (1964) Cable et al. 3. (1964a) O i c e s e (1963d) B e r n d t (1967) C r y s t a l s t r u c t u r e not k n o w n B u s c h o w (1974) O l c e s e (1963c) Alfleri et al.40 129 2. 1. 9. 9 6.7.060 x 10-3 cm3/mole 2. 6 2.87 -7-18 2.73 8.2n Rare earth c a d m i u m c o m p o u n d s and rare earth m e r c u r y c o m p o u n d s Crystal structure CsCI CsCI CsCI CsCI CsCI CsC[ CsCI CsCI CsCI CsCI CsCI CsCI CsCI CdI2 CeCu2 Cel 2 BiLl3 Ni•Sn y-brass Pu2Zfl 9 GdCd6 GdCd6 BaCdll BaCdlu BaCdll CsCI CsCI CsCI CsCI AIB2 AIB2 MgCd3 MgCd3 CeaHg21 Magnetic structure 381 Compound Symmetry LaCd CeCd PrCd NdCd SmCd Eu6Cd5 GdCd TbCd DyCd HoCd ErCd TmCd YbCd CeCd2 EuCd2 GdCd2 CeCd3 GdCd3 GdCd4 Gd2Cd9 EuCd6 GdCd6 CeCd. I.2-9. 14 6.46 -6 8. 4. 8 I I. 8 7.78 (2.1-2.16 7.93 7. 11. 16.03-0. 15 16.47 32 7. I.2 9.94 166-177 7.2 15-36 7..95 35-50 7. 17.3 6-7. I. 3 I.79 -33 +29 -53 -69 -55 10 10. 3 I.33 × 10-3 cm3/mole 2. 1.2-9. 5.3. 3.7 3.63 11 12-14 50 105-121 194-196 30 254-265 166-185 90-105 19-30 4-14 (50) 75 35. (1974) K 6 s t e r and M e i x n e r (1965) IandeUi and P a l e n z o n a (1965) B u s c h o w and V a n S t e e n w i j k (1977) B r u z z o n e et ai.73 -32 7.1I .82 70-83 2. 2. 2 13.63 3. C o m p l e x crystal s t r u c t u r e . (1973) . see ref.3 I. 2 8. 13.50 2 54 7.3 I .56-7.65 3 2.2 1. (1967) S t e w a r t et al.8 I.1) (-42) 2. 15 X = 0.05 8. 13 I I.7 80-92 8.44 -29 7. 3 I.7 8. 6 2. 7.69 -4-10 7. 6.4 5.3-3. 7 I. (1971) Lfithi et al. I 1. 6. 3 6.5 80 Xo= 0. PrCdll EuCdll CeHg EuHg TbHg YbHg CeHg2 EuHg2 CeHg3 EuHg3 CesHg21 EuHg5 1. I-3 I.10. 2 13.80 .5. 14.76 12 7. 7.0p.382 K. ~[/~. 3. 6 7. 8.40 4.2 15 4 3. The values given for X of Pauli paramagnetic compounds are room temperature values and not values attained at 4. The values of the effective moments (~etf) and saturation moments (p~) are expressed in Bohr magnetons per rare earth ion and per formula unit.4 7.6-3.3-5 I. 14 15. 12 7. 6 6.7 Tc TN 2 15 100 62 33-35 20 5-9 Magnetic structure References 1. Usually only one reference has been chosen out of the collection of references available.0-9.8.. 3.3-5 1.30× 10-3 cm3/mole 3. 4 6. 7.1 6.9 .55 23 C 12 NdTNi3 LaNi CeNi PrNi NdNi SmNi GdNi TbNi DyNi HoNi ErNi TmNi YbNi LuNi hex orb orh orb orb orb orb orb orb orb orb orb orh orh ThTFe3 CrB CrB CrB CrB CrB CrB CrB CrB CrB FeB FeB FeB FeB 3.3 7.4. 3. The references given between the two semicolons pertain to the literature in which the value of ~J~eff. 4 1.6 0 no C-W behaviour 8. The magnetic structure types are indicated by F (ferromagnetic). 7.16 13 3.75 7. 8 8.and Fe rich compounds give rise to a compensation temperature a t which the rare earth and 3d sublattice magnetizations cancel.0 -5 10.2-7.6 6. 7. 3.6 orh orh orh orb orh orb orh orb orh orh hex hex hex Fe3C Fe3C Fe3C Fe3C Fe3C Fe3C Fe3C Fe3C FeaC Fe3C Th7Fe3 Th~Fe3 ThTFe 3 ~(= 0. I0 II. The references after the last semicolon correspond to neutron diffraction work.2-5. Tc and TN reported by different authors in literature are dissimilar.8. respectively. 7.4 1. Details pertaining to the structure type listed in columns 3 are given in table A.9 7. These temperatures are listed under Tcompand are given in K.7.2 9.7 no C-W 8.8-9.7 -24 3.8-8.26-2. 3-5 1.T¢ and Ts are reported.1-8.6 29 I1.I.1-8.8.74× 10-3 emu/mole 13.6 .1 3.3a Rare earth nickel compounds Crystal Compound Symmetry structure La3Ni Pr3Ni Nd3Ni Sm3Ni Gd3Ni Tb3Ni Dy3Ni Ho3Ni Er3Ni Tm3Ni LaTNi3 CeTNi3 Pr7Ni3 Ite~ 0p tt 0.3-7.7. 8 7.4 I.4-10.3 7. lower and higher limits have been listed. 4. The references comprise three groups separated by semicolons.2 K since these latter may depend strongly on the amount of localized m o m e n t impurities present in the samples.I-5.7 9.4 0 X = 0.4. LaNi2 CeNi2 cub cub MgCu2 MgCu2 X = 0.72 0.33 48 0 2. Several of the Co. T A B L E A. F F (ferrimagnetic) (AF (antiferromagnetic) or by C (complex).8 7.1 60 10.4 7.3a-g Magnetic properties of intermetallic compounds of rare earths and d-transition metals.2 8.10 5.5 7.23-0.3-3. 0p. Since in most cases the values of/~tr.7-9 7.7 5.1-2.1 -6 9.J.H.7. Values for the paramagnetic Curie temperatures (0p) Curie temperatures (To) and N6el temperatures (TN) are given in K. 16 .8 10.3 2. The first reference pertains to literature of the crystal structure and lattice constants.74 0.8 10.0-7.8.4 4. 7 7.7 5. ~t. B U S C H O W T A B L E S A. 4 7.7-5.5 23 24 77 40 64 36 13 21-22 27-35 45-47 71-73 50-52 48-62 32-37 11-13 8 F C C C C 6.3-5 1.7 3.7-10. 8 7.7-9. 4. 4 1.9 3. 7.25 x 10-3 emu/mole 2. 10 7.2 I. 17 15.7-7. 2.65 10. 9.8 58 rh rh rh hex hex hex hex hex hex hex hex hex hex Gd2Co~ Gd2Co7 Gd2Co7 CaCu5 CaCu5 CaCu5 CaCu5 CaCu5 CaCu5 CaCu5 CaCu5 CaCu5 CaCu~ 9.4 7.7 6.17.RARE EARTH COMPOUNDS TABLE Crystal structure MgCu2 MgCu2 MgCu2 MgCu2 MgCu 2 MgCu2 MgCuz MgCu: MgCu2 MgCu2 MgCu2 MgCu2 PuNi3 CeNi3 PuNi3 PuNi3 PuNi3 PuNi 3 PuNi3 PuNi3 PuNi3 PuNi3 PuNi3 PuNi3 Ce2Ni7 Ce2Ni7 A. 33. 37 15.8 13 27-33 27 20 18-23 FF 10.35 15. 33. 30.57 1. 28 26.36 4. 32 15.17 15. 38 15.5-16 0.5 8 26.56 22 12.9 7 7. 9.17. 17-19 15.61-3. 34. 9.5 3.17. 27 26. 9. 30 26.19. 27. 20.4-10.84 7. 14.40-7. 34.64 12-18. 34.) tt Tc TN Magnetic structure References 15.82-7. 27 26.84 5. 34.7 F 10. 14. 32 15.80 15. 14. 30 26.65 -120--90 no C-W no C-W no C-W 7.17 15. 26. 17 26. 2.2-3.18 15.27 0.5 35-45 7.2 6.14 20 27 85 I15. 37 .20-0.21 15.34. 27.57 11.75-9. 30 26.26 4.56 0-2 X = 0.9-8.16 0.19.77-6. 37 2.71-9.98 9.17.27 21-22 7. 29 26.3a 383 (cont. 9.1 1 7. 30 15.28-7.6 x 10-3 emu/mole -24 0 60 29 -6 -5 -5-15 0 9. 27 26. 28 1!. 39 15.19.0-7.5 77-78 35-44 0. 37. Compound Symmetry PrNi 2 NdNi 2 SmNi 2 GdNi2 TbNi2 DyNi2 HoNi2 ErNi2 TmNi2 YbNi2 LuNi2 YNi2 LaNi3 CeNi3 PrNi3 NdNi3 SmNi3 GdNi 3 TbNi 3 DyNi3 HoNi3 Erlqi3 TmNi3 YbNi3 YNi3 La2Ni7 Ce2Ni7 Pr2Ni7 Nd2Ni7 Sm2Ni7 Gd2Ni7 Tb2Ni7 DY2Ni7 Ho2Ni7 Er2Ni7 Y2Ni7 LaNi5 CeNi5 PrNi5 NdNi5 SmNi5 EuNi5 GdNi5 TbNi~ DyNi5 HoNi5 cub cub cub cub cub cub cub cub cub cub cub cub rh hex rh rh rh rh rh rh rh rh rh rh hex hex Ite~ 3. 31 26.57 3.27.94 30-31 2. 24 15.72 13. 25 15.14. 14.2 77-85 6.41 116-118 98-101 80-81 70 67-74 58 C X = 2 x 10-3 emn/mole -2.5 9.37-9.47 × 10-3 cm3/mole X = 0. 33 26.17. 28 26.I16 98-100 69 66 62-66 43 <20 30-33 48 85 87 F C C C F C F F mixture of hex(CeqNi 7) and hex(Gd2COT) 6. 27.53-3. 30 26.2-7.4 3. 19 15. 28 26: 27.86 20 0.5-10. 30 26.55 6.30 12. 14. 27.14.27. 27.86 1.88 0. 37.2-2. 29 27. 22 15. 23 15.34 23-30 16-22 16-21 13.0-6.6-2.0 0.7 7.62 23-28 10.55-9. 14. 36 15. 28 26.8 1.33 6. 37 15. 30 26. 30 26. 26. 26. 2.75-1.2 x 10-3 cm3/mole A'= 0.83-9.82 0p 4-8 I0-16.74 no C-W 7.72 1 0 .5 5.0 7. 43. 7. (1968) Farrell and Wallace (1966) McMasters and Gschneidner (1964) K. 43. 41. 6. 41. 9. 49.31 5.5-5.2 178 8.05-14. (1980) Wallace and Aoyagi (1971) Busehow et al. 2.43 44. (1970) Primavesi and Taylor (1972) OIcese (1973) Abrahams et al. 15. 46 41. 42. 47 42. B U S C H O W T A B L E A.7 6. 49 X = 2 x 10-3 ema/mole 4. hex hex hex hex hex hex hex hex hex hex hex hex hex hex hex CaCu5 CaCu5 CaCus CaCu5 CaCu5 Th2Nil7 Th2Nil7 Th2Ni17 Th2Ni~7 Th2Nil7 Th2Nit7 ThzNil7 Th2Ni~7 Th2Nit7 Th2Nil7 geff 9. 42. 9.8 138 130 96 73 53 25 8. 46.5-12.384 K.J.42.43. 11.46.7 168-170 12. unpublished results Burzo and Laforest (1972) Crangle and Ross (1964) Voiron (1972) Felcher et al. 4. (1968) B~cle et al. (1976) Mansey et al.43 41.8-9. 17. 30.J.2-13. 25. 42. 46. 44. 28. 22. 47 ll.43.H. 27.88 12 60 0p 7. (1976b) Gignoux et al. (1976) Gignoux and Givord (1977) Gignoux et al. 33. 42.36 186 187-205 FF FF FF FF C F 8. 34. 13. 10. 43. (1978) l_~maire and Paccard (1970) Corliss and Hastings (1964) Buschow (1966) Laforest et al. 31. 16. 21. 12. (1971) Lemaire et al.3a (cont. 14. 34 15. 19. 39. (1962) Oliver et al. 47.) Crystal Compound Symmetry structure ErNis TmNi~ YbNi5 LuNi5 YNi5 Sm2Nit7 Eu2Nij7 Gd2Ni17 Tb2Ni17 DY2Nit7 Ho2Nil7 Er2Nij7 Tm2Nii7 Yb2Niz7 Lu2Nir~ Y2Ni17 1. (1967) Carfagna and Wallace (1968) Terekhova et al. 32. (1976a) Andres et al. (1976) Yakinthos (1977a) Yakinthos and Roudeaux (1977) Yakinthos (1977b) .H. (1973) Buschow (1972) Klaasse et al. 15. 5.l-ll. (1965) Givord et al. 48 41. 42. 47 41. 29. 40 . 20. 45. (1975c) Nesbitt et al. (1975) Nowik and Dunlap (1973) Scrabek and Wallace (1963) Buschow and van der Goot (1970) Paccard and P a u t h e n e t (1967) Yakinthos and Paccard (1972) Paccard et al.43. 43.0 4. 36. 42. 37. 38. 49 41. 24. 43.45. 162 166 152 (601) 151-170 Lemaire and Paccard (1967) Buschow (1968) Ferron et al.25 12. 43.7 ~ Tc 12 22 TN Magnetic structure References FF 15. (1964) Walline and Wallace (1964) Parviainen and Jaakkola (1975) Barbara et al. (1967) Yakinthos and Rentzeperis (1974) Gignoux et al. 8. Busehow.2. 35.8 9. 3.0 7. 23. (1967) Steiner and Hrubec (1975) Steiner et al. 48.85 7.42.67-5 26. 32. 18. 37.42. 40. 37 41. 17. '20. 17.6 7. 3.3. 7 8. 18.9-8. 9 8.56 2. 17. 4.8 n0 0. 7 7.RARE EARTH COMPOUNDS T A B L E A. 24.31-5. 17.4 5. 4 7.6 9. I 1 10. 30. 16.2-8.7 7.6 6-6. 20-25 10. 2.17-8.3 4. 5.6 240-242 62 50 28 7 5 <2 <2 230-233 C 44 25 <2 <2 50 97-126 211-259 395-420 226-256 123-169 74-111 FF FF X = 1. 21.5. 17. 4 1. 3.4 5.3h Rare earth cobalt c o m p o u n d s Crystal Compound Symmetry structure La3Co Pr3Co Nd3Co SmaCo Gd3Co Tb3Co l)y3Co Ho3Co Er3Co Tm3Co Lu3Co Y3Co Gd4Co3 Tb4Co3 Dy4Co3 Ho4Co3 385 #off 0p /~ T~ TN Magnetic structure References 1. 3. (1970) Givord a n d L e m a i r e (1971) B u s c h o w (1970) L e m a i r e et al. 1977a.5-6. b) B u s c h o w (1972) B u s c h o w a n d v a n der G o o t (1969a) B u s c h o w (1971a) Ferron (1970) Y a k i n t h o s (1977a. cub cub cub cub cub MgCu 2 MgCu2 MgCu2 MgCu2 28 5. 3. 19.8 1. 23.2 7. (1976a. (1968) M c M a s t e r s a n d G s c h n e i d n e r (1964) Buschow and Sherwood. 2. 2 1. 7. 12-18. L e m a i r e (1966a) Voiron a n d Bloch (1971) D u b l u n et al. 1978) B u r z o (1972) G i g n o u x et al. 7 8.1 1.9 8. 26.3 ~0 ~0 6.0 7 14 127-143 76-82 45 23-24 13 7. 12-15 10. 3. 9.12-14. (1975) B u r z o (1975) B u s c h o w (1977b) G i g n o u x et al. 19 10.7 6. 3-5 1. 13. (1965) C a n n o n et al.8 32. 19 10.72-7.21. 5. 29.27. 25.14. 9.4 1. 28. 6.5.2 3.72x 10-3 emu/mole 107 8. (1972) Chatterjee and Taylor (1971) T s u c h i d a et al.5-5. 11.04 10.3 1.3 228 129 F (FF) (FF) ErCo2 TmCo2 YbCo2 LuCo2 YCo2 1.5 × 10-3 cm3/mole X = 3.38-6. 21 10. 9.13.0 4.6 10.4-3.7 10. 26. 14. 8. 4 8. 25.12-14. 28.6 5. 29 30 10.03 2. 4. 7.02 1!. 22.20. 5. 20. 2.3 1. unpublished Farrell a n d Wallace (1966) Crangle and R o s s (1964) Wallace and Skrabek (1964) B u r z o (1973) .21.98-3. 20.13-17. (1975) Steiner a n d O r t b a u e r (1975) D e p o r t e s et al.14.16 Er4Co3 Lu4Co3 Y4Co3 CeCo2 PrCo2 NdCo2 SmCo2 GdCo2 TbCo2 DyCo2 HoCo2 orh orb orh orh orh orh orh orb orb orh orb orh hex hex hex hex hex hex hex cub cub cub cub cub cub cub cub Fe3C Fe3C Fe3C FeaC Fe3C Fe3C Fe3C Fe3C Fe3C Fe3C Fe3C Fe3C Ho4Co3 Ho4Co3 Ho4Co3 Ho4Co3 Ho4Co3 Ho4Co3 Ho4Co3 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 X = 48 × 10-3 cm3/mole 18 35 159 85 65 44 20 0 1.1 5.5. 10.33 (FF) FF MgCu2 X = 3. (1974) Schweizer (1968) G i g n o u x et al. 4 1. 19 10.5-48 7 . 9 8.58 10. 15. 19 10. 5.12-14. 6 . 12. 27. 20.7 x 10-3 cm3/mole 16.3-8 5. 12-15 10. 21.9 5. 14.4-6. (1976) M o o n et al. 9 10.9-7.26-2.6-7. 4 1. 386 K.93r 0.10. 16. 22-24. 21 15.5 3.1-2.57-0. 3. 8. BUSCHOW T A B L E A. 28 F F 400 326-330 224 1t5 FF FF FF FF F 428 410 380 230 140 F F F 99-120 93-170 71 FF FF FF F . 26.6 12. 19 20.5 1.16 !.6 5.5-1. 14. 21 20. 24. 17. 2.0 7.0 0. 4 1. 3. 2.18 1.3c Rare earth cobalt c o m p o u n d s Crystal structure PuNi3 PuNi3 PuNi3 PuNi3 PuNi3 PuNi3 PuNi3 PuNi3 PuNi3 PuNi3 PuNi3 PuNi3 PuNi3 Ce2Ni7 Ce2Ni7 Ce2Ni7 Ce2Ni7 Ce2Ni7 Gd2Co7 Gd2Co7 Gd2Co7 Od2Co7 Gd2Co7 Od2Co7 PrsCol9 Pr5Col9 PrsCol9 PrsCol9 CaCu5 CaCu5 CaCu5 CaCu5 CaCu5 CaCu5 CaCu5 CaCu5 CaCu~ CaCu~ CaCu5 CaCu5 Magnetic structure Compound CeCo3 PrCo3 NdCo3 SmCo3 GdCo3 TbCo3 DyCo3 HoCo3 ErCo3 TmCo3 YbCo3 LuCo3 YCo3 La2Co7 Ce2Co: Pr2Co7 Nd2Co7 Sm2Co7 Gd2Co7 Tb2Co7 DY2Co 7 Ho2Co7 Er2Co7 Y2Co7 LasCol9 CesCot9 PrsCol9 NdsCol9 LaCo5 CeCo5 PrCo5 NdCo5 SmCo5 GdCo5 TbCos. 2.17 I. 15. 23. 2.1 6.8 1.4-2. 2. 24 15. 7. 23.9 6. 12 1.17 I. 28 15.23. 24 15.8-8. 6.97r 3L0r 7.9r 0.17 1. 23.4 1.3-5. 3. 2.9 TmCo6 YCo5 Symmetry rh rh rh rh rh rh rh rh rh rh rh rh rh hex hex hex hex hex rh rh rh rh rh rh rh rh rh rh hex hex hex hex hex hex hex hex hex hex hex hex /~ 0. 14. 16.17 1. 14 1.1 5. 24. 2.2 HoCos.5 0.23-25 15.2 3. 27 15. 29 24.I DyCos.45-5. 21 20.7 6.0 9. 5.3 5. 9 1.3 6. 2. 26.7-7.12-14.17 !.0-6. 23. 10 1.9-10. 24.J. 2 11.5 7. 23.3 5. 23. 24. 6 1.4 4.9-4.5r 13Ar 9. 6 1.0 1.1 2.2-1.4 9. 15. 18.24. 4 1.26 15.H.7-1.8 1. 4 1.6 3. 4 I. 22 15. 3. 23-25. 14.2-2.5 ErCos. 21 20. 27 15. 24 15.17r 2. 16. Ir 2. 2 I.1 1.4-2.17 I.46-2.8 0. 2.3 3.6 3.5-11. 5. 25 15. 3.2 Tc 78 330-349 387-396 611-612 506 450 418 389-401 370 345 362 301 490 50 574 609 713 767-775 717 640 647 623-670 639 616 293 690 714 840 737 912 910 1020 1008-1020 980 966 1000-1066 986-1123 1020 977-997 Tcomp References I. 2. 7 I.17 1.7.9 10. 24. 5-26. unpublished 7. 31. Yakinthos and Mentzafos (1975) 10.31 30.4-10. 24. 21.2-27.2. 20.2. Givord and Lemaire (1971) 13.5 1290 rroom temperature value.6 1160-1200 11.32 30. 27. Velge and Buschow (1968) 16.2. 25. (1976) Buschow and Velge (1976) . (1971) Wallace and Swearingen (1973) Ermolenko et al.33 30.7 1180-1195 7-8.8-7.32 30.2 1180-1185 27. Buschow (1972) 12. 26.RARE EARTH TABLE COMPOUNDS A. 28.31 30.31.5-31 1150-1183 20. Koen et al.32 34. Buschow. (1969) 15. 32.(1973a) 9.6 1192-1200 26.3-13.7 1173-1183 9. Lemaire (1966a) 3.1-23. Buschow et al.32 30. 33.) 387 Compound Ce2Cot7 Pr2Col7 Nd2Col7 Sm2Col7 Gd2Co17 Tb2Col7 Symmetry rh rh rh rh rh rh hex hex hex hex hex hex hex cub Crystal structure Th2Zn~7 Th2Znl7 Th2Zn1? Th2Znl7 Th2Znl7 Th2Zn17 Th2Nil7 Th2Nil7 Th2Nil7 Th2Nil7 Th2Nil7 Th2Nil7 Th2Nil7 NaZnl3 Magnetic ~ Tc Ycomp structure References 30.2. 31 30.31. 19.5-14.33 30.2.2.2. Buschow (1970) 2.7. Buschow (1973c) 17. (1975) Nesbitt et al.3c (cont. (1976) James et al. 12.18. Narasimhan et al.31 11 12.31 30.2.8 1167-1200 20. Schweizer and Yakinthos (1969) 5. 23. Figiel et al. (1972) 6.12.31. 30.7 1190-1200 13. 22. 34. (1973) Ray and Strnat (1975) Heidemann et al. (1966) Deryag/n and Kudrevatykh (1975) Miller et al. (1968) Kren et al. (1962) Buschow and Fast (1967) Buschow (1966) Strnat et al.4-27. Strnat and Ray (1970) 18.8 1160-1200 30.2. 1. 31. Georges et al.2. (1976) 14.31-33 .31.15. 29.2.1 1074-1083 31-32.4 1209-1240 8. 22 DY2CoI7 Ho2Col7 Er2COl7 Tm2Col7 Yb2Cot7 Lu2Col7 Y2Col7 LaCol3 24.5-10. Bloch and Chaiss6 (1969) 4.3 1152-1188 5. Narasimhan et al. Burzo (1972) 8. (1962) Lemaire (1966b) Wallace et al. (1975) 11.31. (1969) Ray et al. 70-2. 1.52-2.0 21-21.18. 18.34 24.1-6.3.2-4 I.66-3.18. 7 13. 16.6 4. 16.6-15 5. 5. 19.59 2.2 !. 18 24.5.8 DY6Fe23 Ho6Feq3 Er6Fe23 Tm6Fe23 280 265-280 205 105-120 FF Yb6Fe23 Lu6Fe23 Y6Fe23 Ce2Fel~ Pr2Fel7 Nd2Fet7 C Sm2Fel7 Gd2Fei~ Tb2Fel7 Dy2Fe17 Ho2Fel7 FF . 17 24.6 3.8 3.J. 26 24.18.3. 25 24. 18 24.5 28.2 18.I.5. 5.3d R a r e e a r t h iron c o m p o u n d s Crystal structure MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 PuNi 3 PuNi3 PuNi3 PuNi3 PuNi3 PuNi3 PuNi3 PuNi3 Th6Mn23 Th6Mn23 Th6Mrt23 Th6Mn23 Th6Mn23 Th6Mn23 ThsMn23 Th6Mn23 Th6Mn23 Th6Mn23 Th6Mu23 Th2Zn17 Th2Zn17 Th2Znl7 Th2Zn17 Th2Nit7 Th2Ni17 Th2Ni17 Th2Nil7 Magnetic structure Compound CeFe2 SmFeq GdFe2 TbFe2 DyFe2 HoFe 2 ErFe2 TmFe2 YbFe 2 LuFe2 YFe2 SmFe3 GdFe3 TbFe3 DyFe3 HoFe3 ErFe 3 TmFe3 YFe3 Nd6Fe23 Sm6Fe23 Gd6Fe23 Tb6Fe23 Symmetry cub cub cub cub cub cub cub cub cub cub cub rh rh rh rh rh rh rh rh cub cub cub cub cub cub cub cub cub cub cub rh rh rh rh hex hex hex hex /z 2.H.0 14. 29.18.6 30.3 14.18 24. 17. 29.38-2.3. 29 24.5 1.49 Tc 221-240 676-700 785-810 696-711 633-638 597-614 590-595 566-610 558-610 535-554 650-651 728-733 648-655 600-612 565-580 550-555 535-539 490-539 429 468-659 574 424-545 501-560 493-495 475 480 471-491 478-484 220-270 283 327 385-420 460-485 408 363-380 325 Tcomp References I. 24. 28-31.1 4. 16.17 16.99 2.75 3.67-4. 21. 14 13.0-5.3 2.5-7 16. 22 16.8-15. 22 16.78-3. 29. 36 24.8. 35.5-7 I.20. 10 I.6-1.21.18 16. 10 24.2.6.6 30.8-30.97 2. 23. 29.18. 10. 1.0 32 43. 18.2.7.85 2.68-5.26 24.2-4. BUSCHOW T A B L E A.2-3. 30 24. 10. 16.8 4.7-9 I.10. 22.26 24. C 15.3-7. ll 12.31 5.75-5.4-17.1.18 24.1. 19 16.27 24.5 17-18.7.8-3.7. 6.388 K.50-2.5 1.21 16. 24.8-2. 10 FF FF FF 480-490 255-248 31 615-621 595-626 544-550 383-405 222-250 FF FF FF. 16. 17 1. 3.5.26.18. 29.9-7.29.1.8 I. 18 .6 5. 10.7 1. 1.67 4.33. 36 24.8 2.1 14.8-47.8 15. 3. 5.9 37. 10.16. 18. 24. (1966) Givord and Lemaire (1972) Givord and Lemaire (1974a) Weik et al. 29.30 24. 2. (1964) Deryagin et al.RARE EARTH COMPOUNDS 389 T A B L E A. 6. (1973a) Van der Goot and Buschow (1970) Simmons et al.0-34. (1976) Buschow and Van der Goot (1969b) Gubbens and Buschow (1973) Elemans and Buschow. (1962) Hoffer and Salmans (1968) Buschow and Van Wieringen (1970) Strnat et al.29. 39 24. 28. 39. 14. 31.31. 41. 28.3d (cont. t8. (1975) Wallace and Skrabek (1964) Dublon et al.37. 20. 3. 35.unpublished Salmans et al. (1977) Ray (1968) Kirchmayr (1969) Nesbitt et al. 298. 8. 25. 36. unpublished Elemans and Buschow (1974) Burzo (1975) . 10. 15. (1979) Buschow (1971b) Buschow. 6. 38. 37.40 24. 29. 32. 27. (1973) Davis et al. 30 Er2FeI7 Yb2Fel7 Tm2Fet7 Lu2Fel7 hex hex hex hex hex Th2Nil7 Th2Nil7 Th2Nil7 Th2Ni17 Th2Ni17 Y2Fel7 1.2-18 25. 19. (1977) James et al. (1971) Will and Bargonth (1971) McMasters and Gschneidner (1964) Cannon et al. 34.5. 7. Buschow and Van Stapele (1971) Miskinis et al. 33. 17. (1972) Meyer et al.29. (1975) Givord et al.31. 33. 31. (1968) Oestereicher and Pitts (1973) Narasimhan et al. 4. 16.) Crystal structure Magnetic /z 16.29.5. 30.38 39. 11.5-332 21. (1974) Buschow (1971c) Steiner and Hrubec (1975) Steiner et al. (1971) Burzo and Givord (1970) Burzo (1971) Clark and Belson (1973) Barbara et al.5-314 280 276 33. 22. 40. 41.7 264-270 30.8-34.6 Tc Compound Symmetry Tcomv structure C C C F References 24. 12. 23. (19770 Moreau et al. 13.7 302. 26. 39. 5. 36. 9. hex hex cub cub cub hex hex hex hex cub cub cub cub cub cub cub cub cub cub cub tetr tetr tetr tetr tetr tetr tetr tetr Mggn2 MgZn2 MgCu2 MgCu2 MgCtl2 Mggn2 MgZn2 MgZn2 MgZn2 MgCu2 Th6Mn23 ThsMn23 Th6Mn23 Th6Mn23 Th6Mn23 Th6Mn2~ Th6Mn23 Th6Mn23 Th6Mn23 Th6Mn23 ThMnt2 ThMn12 ThMn12 ThMn.2 378 475-486 13.35 8.13 12. 2.3 10.8-13.72-7.16. 3.3. 6 4:6 12.3. (1979) Kirchmayr (1967) De Savage et al. 11.23 5. 9.15 -90.3. 12.30 ~ (0. 3. 15 12.6 8-17.3. 18. 3.15 12.04 10.13 12.9-9. 2.3. 3 4. 3.0 439 -90 49-54.15. 17. 5.J.3.9 8. 6. 15. 15 16. 15. 13 10.4 455 25 49. 9. 8. 15.6 4. 6 4.18 10 40 C F AF 5. 8 6. 11.2 7. 15 12. 7 4.44 X = 0. 6. 15 12. B U S C H O W T A B L E A.56 2.8.0 Tc (44$) TN Magnetic structure References I.86 10. 6.5 9.1 0p -80 -90 45 20 . 8.6 415 30. 9. 13 10. (1977) Wang and Gilfrich (1966) Kirchmayr and Lihl (1967) Deportes and Givord (1976) .91 20 5.83 10.3. 2 I. 14.71 x 10 -3 emu/mole j( = 1.6 7. 15 17.6-10.390 K.6 416 85 3. (1965) Barnes and Lunde (1975) Wang and Holden (1965) Delapaime et ai.13 12. 3 4.13 12.4-16. 4. 14. 7.2 486 -196 -25 -398 -65 X--3.3.2 434 -20-30 45.04 15. 15.13 12. (1965) Buschow (1977) Deportes et al.8 378 8. 13 14.7x 10-3emu/g 10.8 443 -5 49.92) 4.3 11.9 9. 15. (1963) Buschow and Sherwood (1977b) Corliss and Hastings (1964) Felcher et al. 16. 11 12. 3.8 8. 5. 3. 5. 8 10. 6 12.28x 10-3 emu/mole 60 9. 13.47 I 1.H. 13.7 10. 11.5 461-468 -360 44. !i.2 9. (1964) Oesterreicher (1971) Kirchmayr (1969) McMasters and Gschneidner (1964) Nesbitt et al. 135 II0 110 95 87 120 FF C C C C C Teslyuk et al.3 12.15. 3.3e Rare earth manganese compounds Crystal Compound Symmetry structure PrMn2 NdMn2 GdMn2 TbMn2 DyMn2 HoMn2 ErMn2 TmMn2 LuMn2 YMn2 Nd6Mn23 Sm6Mn23 Gd6Mn23 Tb6Mn23 Dy6Mn23 Ho~Mn23 Er6Mn23 Tm6Mn23 Lu6Mn23 Y6Mn23 NdMnt2 GdMn12 TbMnl2 DyMnl2 HoMn12 ErMnl2 TmMnl2 YMn12 1.2 ThMni2 ThMnj2 ThMnl2 ThMnt2 izef r 2. 2. 8 8. I 75 10. 14 6.006× 10-3 cm3/mole X = 0.5 19.05 10. II. 4 6.2 3.35 134-173 10. 14 11.073 × 10-3 cm3/mole ~. 2 I.15 10.30 x 10-3 cm3/mole 24-29. I 1 I I.6 72 A"= 0.16 55 10.92 33 7.3 2.4-10.8 3.4 12 5.80 9. 2 I.98 7. 10-12 13. 5 3.7 I.18 x 10-3 cm3/mole cub cub cub cub hex hex hex hex orh orb orh hex hel hex hex hex hex hex hex hex hex orh MgCu2 MgCu2 MgCu2 MgCu2 MgZn2 MgZn2 MgZn2 MgZn2 Fe3C Fe3C Fe3C ThTFe3 ThTFe3 ThTFe3 ThTFe3 Th7Fe3 Th7Fe3 ThTFe3 Th7Fe3 ThTFe3 Th7Fe 3 ThTFe3 X = 0.7 28 6.6 9. 2 I.5 15 X = 0.5 -3-3 5.09 x 10-3 cm3/mole 7. 20 142 cub cub cub cub cub cub cub cub cub CsOl CsCI CsCI CsCI CsCI CsC1 CsC1 IdgCu2 MgCu2 7. 2 3.8. 8 8. 7 I. 7. 8 9.38 10. 2 1.5 100 35 6. 4 8.6 7.43 58 no C-W 7.6 2-8 6.92-8. 2 3.55 7.7 115 6.33 x 10-3 cm3/mole X = 0. 2 I. 7 I.55 41 10.52× 10 3 cm3/mole 73 X = 0. 2 I.4 -4 5.7 6. 4 3. 7 I. 4 3.65 × 10-3 cm3/mole 7. rhodium and palladium Crystal structure Magnetic structure Compound Gd3Ru DY3Ru Y3Ru Gd73Ru27 DY73Ru27 Y73Ru27 Gd2Ru DY2Ru Y2Ru LaRu2 CeRtl2 PrRu 2 NdRu2 GdRu2 DyRu2 ErRu2 YRu2 Gd3Rh Dy3Rh Y3Rh LaTRh3 CeTRh3 PrTRh3 NdTRh3 SmTRh3 Gd7Rh3 Tb7Rh3 DY7Rh3 Ho7Rh3 ErTRh3 Y7Rh3 GdsRh3 YsRh3 Gd3Rh2 Y3Rh2 Gd4Rh3 GdRh TbRh DyRh HoRh ErRh TmRh YRh LaRh2 CeRh2 Symmetry /tett 8.6 18 X = 5. 7 I.45-6. 5 3.3-10. 5 2.2 4.40 x 10-3 cm3/mole 8. 7 8.05 150 10.3-7.9 10.RARE EARTH COMPOUNDS 391 TABLE A. = 0.1 =7 3. II I1.9 38-40 28-35 83 8 X = 0.8 8.15 16.3f Compounds of rare earths with ruthenium. 2 I.9 98 X=0. 2 3. 8 8.90 X~ -0. 8 8.6 X = 0.30 34 9. 2.39 37 3. I I I I. 2 I.7 8. 7.88 × 10-3 cm3/mole . 8 8.21 × 0p 105 8 10-3 cm3/mole /t Tc TN References I. 7 6.95 48 10.7 6.8 8.31 13 3.22 26 X = 0. 11.44 x 10-3 cm3/mole Pauli paramagnetic 2.72 x 10-3 cm3/mole 0. 8 8. 21.85 7.34 49 no C-W behaviour no C-W behaviour 7. 24 23.8 22 10. 22 23.6-7.9 10.17 6.392 K. 22 9.2 6. 8 8. 31 30. 24 -6 X = 0.87 10. 31 30.31 29 3.5 15 7 8.1 8.©fr 0p 7.2 33 no C-W behaviour 8.754× 10-3 cm3/mole 7.63 65.7 0.50 7. 7.18 Compound PrRh 2 NdRh2 SmRh2 EuRh2 GdRh2 TbRh2 DyP. 31 30.3 11. 31 30. 7. 7 I. 22 I.5 30. 22 26. 28 29.012 × 10-3 cm3/mole 53 X = 0. 22.0-11.09 .38 39-44 10. 17 6. 24 23.5 x 10-3 nine/mole 2. 8 8. 22 1. 27.9 7.6 Tc 8 7 20 73 39 27 16 7 TN Magnetic structure References 17. 17.46 4. 31 4.1 7. 7 6.) p.0 -12 10. 25 1.6-11. 31 30.7 265 10.h2 HoRh2 ErP. 7 6.5 X = 0.3 10 . 29 26.42 335 63. 17 18.8 333-335 6.7 7.2-8. 17 19. 27 25.17 17.31 30.3f (cont. 22.31 40-46 10.5 rh rh rh rh rh rh rh Pu3Pd4 Pu3Pd4 Pu3Pd4 Pu3Pd4 Pu3Pd4 Pu3Pd4 PusPd 4 20 14 12 .48 31-63 9. 7.46 3.17 8 no CoW behaviour 8. 8 8. 2. 7 6.5 16 10.6 2 8.h 2 YbRh2 YRh2 OdRh3 YRh3 GdRh5 YRh5 Gd5Pd2 TbsPd2 DYsPd2 Ho5Pd2 Er5Pd2 TmsPd2 LaTPd3 CeTPd3 PrTPd3 Nd7Pd3 SmTPd3 Sm3Pd2 Gd3Pd2 Dy3Pd2 Ho3Pd2 Eu2Pd SmPd EuPd GdPd DyPd HoPd Gd4Pd5 Dy4Pd5 Ho4Pd5 Pr3Pd4 Nd3Pd4 Sm3Pd4 Gd3Pd4 Tb3Pd~ Dy3Pd4 Ho3Pd4 Symmetry cub cub cub cub cub cub cub cub cub cub cub hex hex hex hex cub cub cub cub cub hex hex hex hex hex tetr tetr tetr orb orh orh cub cub P.5 10.2 0 8.6 4. 24 23.77 17 7.11 10.4 -6 10. 24 23. 8 25.8 39. 22 26. 25 28. 20 6. 17 17.22 1.J.4 20 8 2 10. 22 26. 22 1.95 no C-W 75-80 30-35 20-23 6.17 17.287 × 10-3 ¢m3/mole 38 X = 0. 17 6.2 t.5 38 22. B U S C H O W TABLE Crystal structure MgCu2 MgCu2 MgCu2 MgCn2 MgCo2 MgCn2 MgCu2 MgCn2 MgCu2 MgCu2 MgCu2 CeNi3 CeNi3 CaCu5 CaCe5 DysPcl2 DysPd2 DysPd2 DysPd2 DysPd2 ThTFe3 Th7Fe3 Th7Fe3 ThTFe3 ThTFe3 U3Si2 U3Si2 U3Si2 CrB CrB CrB CsCI CsCI A.H. 20 6. 22 26.39 30 3. 22.4 -2 3.5 29 10. 33.61 1-3 10. 27. 36.3 10. 4.3 0 X = -0. 36.4-3. 36. 36. 24. 36 37. (1977b) Crystal structure not k n o w n W i c k m a n et al.073 x 10-3 emu/mole 20. 33 32.40-9. 19.03 1. 6. 31. (1959) G h a s s e m and R a m a n (1973) L o e b i c h a n d R a u b (1975) Olcese (1973) L o e b i c h a n d R a u b (1976b) D o r m a n n a n d B u s c h o w (1976) C h a m a r d . 18.4-3.71 7. 32.3-10. 38 37.69 -7-0 3. 35. 26. 17.0-8. 21.20 34. 37.RARE EARTH COMPOUNDS T A B L E A.05 7. 8. (1972) Harris et al. (1972) T a m m i n g a (1973) Singh a n d R a m a n (1965) Crangle and R o s s (1964) B a u m i n g e r et al. Crystal s t r u c t u r e not k n o w n L o e b i c h a n d R a u b (1976a) C o m p t o n a n d Matthias (1959) Shaltiel et al. (1975e) Dwight et al. 25. 38 34. 36.3-9.) /t Tc TN Magnetic structure References 30. (1977a) Jordan a n d L o e b i c h (1975) L o e b i c h a n d R a u b (1973b) Harris a n d L o n g w o r t h (1971) L o n g w o r t h and Harris (1973) Pierre a n d Siaud (1968) P a l e n z o n a a n d Iandelli (1974) Y a k i n t h o s et al.50 -5 .B o i s (1974) B u s c h o w et al.38 0-4 9. 22 Compound Symmetry Er3Pd4 Tm3Pd 4 SmPd 2 EuPd 2 GdPd 2 DyPd 2 HoPd 2 /te~ 9. 36. 36. 34. unpublished Berkowitz et ai.5 0.5-3 9. 38. 14. 36. 16.135 x 10-3 emu/mole no C-W behaviour 3. 25 33. 38 37.B o i s et al. 36.075 x 10-3 emu/mole X = -0. (1964) L o e b i c h and R a u b (1973a) Fornasini a n d P a l e n z o n a (1974) Y a k i n t h o s et al.1-10. 38 34.0-2.5 2. AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu~ AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 AuCu3 X = -0. 38 34. 36. 3. 12. 35. (1974a) Dwight (1964) Buschow. 36 27. 25. 28. (1965) C h a m a r d .5 -1 4. 22 32. 38 11. 38 34. 5.39 7. 38 34.W behaviour 80 . 36.12 6 3 rh rh cub LaPd3 CePd3 PrPd3 NdPd3 SmPd3 EuPd3 GdPd3 TbPd3 DyPd3 HoPd3 ErPd3 TmPd3 YbPd3 LUPd3 YPd3 cub cub cub cub cub cub cub cub cub cub cub cub cub cub cub 1.51 0-2 9. I0. 7. 22 32. 38 25. 15. 2. 38 37. 31 30. 38 37. (1973) H u t c h e n s et al. 31 32. 36.3f Crystal structure Pu3Pd4 Pu3Pd4 MgCu 2 393 (cont. 22.5 0 7. (1971) . 29. 9. (1968) Harris a n d R a y n o r (1965b) G a r d n e r et al. 23. 36.8 8.3 0p -4 -2 no C .1 no C-W behaviour no C-W behaviour 8. 36 37.1 10. (1964) B o z o r t h et al. (1971) G a r d n e r et al. 13. 30. 38 37. 27. 1. 57 -26-5 3.43 0 1.67 6-13. 2 2.3 6.60 0 1.5 230 3.33-2. 6 14. 2 1. 2 I. 3 3.4) 6.12 10. 10.60-1. 2 1. iridium and platinum Crystal structure MgCu2 MgZn2 MgZn2 MgZn2 MgZn2 MgZn2 MgZn2 MgZn2 MgZn2 ThTFe3 ThTFe3 Th7Fe3 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCH2 ThTFe3 ThTFe3 Th7Fe3 ThTFe3 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 2.13 10.7 7. 2 8. 2.3 emu/mole 2. 10.9 1.32 + 34 X = 0. 2 4. 2 I.2 (0. 13 10. BUSCHOW T A B L E A. 2.029 × 10-3 cm3/mole 2. 3 9. 11.35 3.53 3.3 Tc TN References I. 3 3.9 7.H. 5 10. 2 1.7 6. 15-17 28 23 35 66 34 15 9 3 Pauli paramagnetic . 2 I.060 × 10-3 emu/mole X = 0.60-2. 2 9.655 x I0.J.15.19 6 7.9 105 8.13.98 36-46. 14 10.28-6. 2 7.5 0.394 K. 8 7. 3 3.10-8. 2 7. 10. 2 4. 3 3.5 3. 8 9.3g Compound of rare earths with osmium. 6 3.7 7.1 2.11 4-10 0.40 1. 2 7. 2 3.7 X = 0.46 Magnetic structure Compound CeOs2 PrOs2 NdOs2 SmOs2 GdOs2 TbOs2 DyOs2 HoOs2 ErOs2 LaTlr3 Ce7lr3 Pr71r3 Lalr2 CeIr2 Prlr2 Ndlr2 Smlr2 Eulr2 Gd/r2 TbIr2 Dylr2 Holr2 ErIr2 Tmlr2 Yblr2 YIr2 La7Pt3 CelPt3 Pr7Pt3 NdTPt3 LaPt2 CePt2 PrPt2 NdPt2 SmPt2 EuPt2 GdPt 2 Symmetry cub hex hex hex hex hex hex hex hex hex hex hex cub cub cub cub cub cub cub cub cub cub cub cub cub cub hex hex hex hex cub cub cub cub cub cub cub /ten 0p /t 0 1.5 6.8 6. 3 3.0 1.1 6.6 .1 1. 2 9. 2 1.0135 x 10-3 cm3/mole 16 12 37 (70) 88 43 23 12 3 I ~0 F F Pauli paramagnetic 33 23 55 X = -0.3 0.0 5. 6 4. 2 I. 3 4. 5 4.40 30-32 6. 4.50 0p 17 6. (1977) Arnold a n d N e r e s o n (1969) N e r e s o n a n d Arnold (1970) N a r a s i m h a n et al.94 17 diamagnetic 4. 10.88 ] 7. 18 15.RARE EARTH COMPOUNDS T A B L E A. (1973) Taylor et al. 13. 19 9. (1964) Buschow. 21 9. (1968) Wallace and Vlasov (1967) W i c k m a n et al.5-22 13.13 10.2 AF AF 18 12.60 9. 17. 15.00647x 10-3 cm3/mole X = 0. V i j a y a r a g h a v a n et al. 18 15. 21. (1973b) G s c h n e i d n e r (1961) Bozorth et al. 21 9. (1959) Olcese (1973) C o m p t o n and Matthias (1959) Shaltiel et al. 10.08 7 6. 11. 7. 8. (1968) Harris et al.61 10. 6. 14. 20 19.65-8. cub cub cub cub cub cub cub cub cub cub hex hex hex hex t~e~ 9.8 20.298x 10-3 emu/mole 2. 16. (1977b) G r o v e r et al.40-7.13 10. 2. (1976) D o r m a n n et al. 5.13 10.26-7. unpublished Elliot (1964) Felcher a n d K o e h l e r (1963) M c M a s t e r s and G s c l m e i d n e r (1964) Crangle a n d R o s s (1964) J o s e p h et al. 21 9.84 -22 9. 20.58 10.) ~t Tc 16-26 14-25 9-19 3-15 TN Magnetic structure References 10. 10. (1972) .13 9.48 X = 0.34 2 7. 15. 19. 3. 6 15.3g Crystal structure MgCu2 MgCu2 MgCu2 MgCu2 MgCu2 MgCu 2 MgCu2 MgCu2 AuCu3 AuCu3 CaCu5 CaCu5 CaCu5 CaCu5 395 (cont. 21 Compound Symmetry TbPt2 DyPt2 HoPt2 ErPt2 YPt2 LaPt3 CePt3 PrPt3 TbPt3 DyPt3 LaPt5 CePt5 PrPt5 NdPt5 1. 10.67-7.92 -108 3. 19. 18 15. 9. 18. 10. 85 7.8 9.0 10. Details pertaining to the structure type listed in columns 3 are given in table A. Values for the paramagnetic Curie temperatures (0v) Curie temperatures (To) and N6el temperatures (TN) are given in K.1 I 1.50-8.3 -10 1.6-10. I-3 I. 3 3.3x 10-3 cm3/mol¢ Pauli paramagnetic . 1 1. Cu. I 24 35 1.396 K. 2 1.48-8. Pd. In.6 15-17 53-70 7.86 25-27 . Oesterreicher (1973b) 2. I 1. Usually only one reference has been chosen out of the collection o f references available.I.38-7. 3 1. 1 I.8 0p /z Tc TN References 1.9 I0.73 3. T A B L E A. 5 5.8 25 55-90 7.72 12 Pauli paramagnetic 1. 5 1. 1 I.~= 0. 2 I. Ga) Crystal Compound Symmetry structure l'rNiAI NdNiAI GdNiAI TbNiAI DyNiAI HoNiAI ErNiAl TmNiAI LuNiAI PrCuAl NdCuAI GdCuAI TbCuAI DyCuAI HoCuA] ErCuAI TmCuAI YbCuAI LuCuA! YCuAI GdNiln GdPdln YPdln YbNiGa GdCuSn GdAuSn hex hex hex hex hex hex hex hex hex hex hex hex hex hex hex hex hex hex hex hex hex hex hex hex hex FezP FezP Fe2P Fe2P FeqP Fe2P Fe2P Fe2P Fe2P Fe2P Fe2P Fe2P Fe2P Fe2P Fe2P Fe2P Fe2P F¢2P Fe2P Fe2P Fe2P Fn2P Fe2P In2Cu ln2Cn /Zef r 3.0-11. I 1. 0p. B U S C H O W T A B L E S A. 2 8. 1. 3 3.5 .7 36 1. I.38.4a-e Magnetic properties of ternary intermetaUic compounds o f rare earth metals.2 1. 1 1. Buschow (1975b) 4.27 17 -8 4.90 10. Oesterreicher (1977b) . B = AI. I I.01 67-90 42 7.I 10.H. 3 4. Klaasse et al.~The values given for X of Pauli paramagnetic compounds are room temperature values and not values attained at 4.8 × 10-3 cm3/mole 80 83 103 102 X = 1.2 10.2 I. 3 3. Since in most cases the values o f ~. lower and higher limits have been listed.41 52 29 8. Tc and Tn are reported.0 7. (1976) 5.2 K since these latter may depend strongly on the amount of localized moment impurities present in the samples.82 39-47 11-12 7.4 x 10 -3 cm3/mole 0 -32 2. The second reference pertains to the literature in which the values of/te~.7.J. The values of the effective moments (l~e~) and saturation moments (~) are expressed in Bohr magnetons per formula unit. 4 5.42 61-70 45-52 7. ~.71 13 no C-W X = 13. I.10 5 1. To and TS reported by different authors in literature are dissimilar. Leon and Wallace (1970) 3.I1 4. 0p. 1 1.6 4.39-7.2 I 1.1-10.6 4.66 35 13 8.59 23 3 7.25-~8.~. I. I. The references comprise two groups separated by semicolons. The first reference pertains to literature of the crystal structure and lattice constants.4a Compounds of the type RAB (A = Ni.8-9. 2 I.84 8.I-0 7. ~. 1 1. 2 I.40 15-16 . I.4 I.01 57-65 30 7. 4b C o m p o u n d s o f t h e t y p e RA2B2 ( A = Cu.0 8.3 2.9 8. 57 37 38 365 6.1 t3.7 8.10 3.7 -0.8 8. B = G e .2 2.60 6.0 -4.5 -43.5 2.17 10.8 4.6 2.0 33 47.02 3.5.2 5.12 6.34 1.7 14.8 -39.5 15.41 -2.9 . F c .5 4.1 1.7 7.8 8.3 3.89 X ~ 3 × 10-3 cm3/mole .7 6.5 2.i 1. I0 .7 7.96 9.I 2.8 X ~ 5 x 10-3 cmS/mole X ~ 2 x 10-3 cm3/mole 668 693 713 723 738 820 753 820 825 790 605 665 683 13.5 3.8 -3.RARE EARTH COMPOUNDS 397 TABLE A. C o .74 2.5 5.6 7. 1.8 8.8 8. 1.27 10. 1.9 -8.7 7.0 (15) -2 0.6 10.5 4.00 2.5 7.5. Si) Crystal structure ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCreSi2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 Compound LaCo2Ge2 CeCo2Ge2 VrCo2Ge~ NdCo2Ge2 SmCo2Ge2 GdCo2Oe2 TbCo2Ge2 DyCo2Ge2 HoCo2Ge ErCo2Ge2 TmCo2Ge2 LuCo2Ge YCo2G¢2 LaFe2Si2 PrFe2Si2 NdFe2Si2 SmF¢2Si2 GdFe2Si2 TbFe2Si2 DYFe2Si2 HoFe2Si2 ErFe2Si2 YFe2Si2 CeFe2Ge2 PrFe2Ge2 NdFe2Ge2 GdFe2Ge2 TbFe2Ge2 ErFe2Ge2 LaMn2Ge2 CeMn2Ge2 PrMn2Ge2 NdMn2Ge2 GdMn2Ge2 TbMn2Ge2 DyMn2Ge2 HoMn2Ge2 ErMn2Ge2 CeAu2Si2 PrAu2Si2 NdAu2Si2 SmAu2Si2 EIIAu2Si 2 GdAu2Si2 TbAu2Si2 DYAu2Si2 HoAu2Si2 ErAtl2Si2 YAu2S[2 PrCu2Si2 EuCtI2Si2 Symmetry tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr ~te~ 0p /t Tc TN References 1.5 5.1 I.5 14 13 II 7. 1.2 -6.6 3.7 7.9 1. I.9 -4.90 6.8 8.14.7 8.7 6.5 4.2 5.50 5.7 7.6 0. I.53 no C-W behaviour 2.2 2.2.5 5.38 %60 5.6 6:6 6.9 10.8 40.5 6.7 7 5.8 7.0 10.00 306 316 334 334 3.7 7.6 -2. 1.8 8.6 9.9 14.5 -5.1 I.0 3. A u .7 7.5 -43.7 7.3 28 40 30 14.8 8.63 6.6 15.151.8 -9. 1.8 8.50 6.87 3.5 8 !i 6.1 2.8 8.8 8.3 3. M n .2 4.7 -32. 2.!07 3.) ~ Tc TN (12) (10) 16 11 379 References 4. (1975) 8.0 186. 12 4. 2 l. (1973) Felner et al. 9. McCall et ai. 3 1.0 172.3 183. 2 1.06 4. 2.33 0p . 3.28 9. 11. 7. 3 1.4c C o m p o u n d s of the type RA4Bs (A = Fe.3 165. I 1 4.10 -12 3. 6. (1979) T A B L E A. 2 I. 2 1. 13 Compound GdCu2Si2 TbCu2Si2 PrCu2Ge2 GdCu2Ge2 CeMn2Si2 CeAg2Si2 Symmetry tetr tetr tetr tetr tetr tetr ~ett 7. (1975) Pinto and Shaked (1973) Rieger and Parth6 (1969) S a n k a r et al. 2 i. 10.3 184.J.398 K. 2. 2 I. 2 1.1 4.7 8. B = AI) Crystal Symmetry structure tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr CeMn4AIs CeMn4Als CeMn4Als CeMn4Als CeMn4Als CeMn4AI s CeMn4Als CeMn4Als CeMn4AI s CeMn4AI s CeMn4Als CeMn4AI s CeMn4AI s CeMu4AIs CeMn4AI s CeMn4AI s CeMn4AI s CeMn4AIs Compound /.4 159. B u s c h o w et al.55 330 -20 1.teff 0p # Tc TN 135.0 2.2 1. 4 LaFe4AIs CeFe4AIs PrFe4AIs NdFe4AIs SmFe4AI8 GdFe4Als TbFe4Als DyFe4AIs HoFe4AIs ErFe4AIs TmFe4Als YbFe4AIs LuFe4Als YFe4AIs GdMn4AI s YMn4AI s YbCr4AIs CeCu4AI s 4. B U S C H O W T A B L E A. 11 12.6 197. Felner (1975) Oesterreicher (1976) B a u m i n g e r et al. 4.7 2. 13. (1976) N a r a s i m h a n et al. u n p u b l i s h e d 1.4b Crystal structure ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si2 ThCr2Si 2 ThCr2Si2 (cont. 2 1. 2 1. (1977) 4.9 4. (1976) Malik et al. Bargouth et al.7 142 References 1. (1978) S a m p a t h k u m a r a n et al. 2 1. (1974a) Oesterreicher (1977) Siek et al. B u s c h o w . Mn. 2 1. 9 4.3 .4 I.10 X = 6 x 10-3 cm3/mole -220 .H. (1976b) 2. 12. 2 1. 5. 2 1. Van der K r a a n a n d B u s c h o w (1977) B u s c h o w and V a n der K r a a n (1978) . 2 9. 2 I.9 I. B = Ag. Felner (1977) T A B L E A. 2 1. 2 2.4 0p #- Tc TN 7 7 9 16.9 12 4.39 7.0 9. 1 I. Au.8 6.08 12.5 20 8. 3 1. Ni) Crystal structure MgCu4Sn MgCu4Sn MgCu4Sn MgCu4Sn MgCu4Sn MgCu4Sn MgCu4Sn MgCu4Sn MgCu4Sn MgCu4Sn MgCu4Sn MgCu4Sn MgCu4Sn 399 Compound NdCu4Ag " SmCu4Ag GdCu4Ag TbCu4Ag DyCu4Ag HoCu4Ag GdAu4Ni TbAu4Ni l)yAu4Ni HoAuaNi ErAu4Ni TmAu4Ni YbAu4Ni Symmetry cub cub cub cub cub cub cub cub cub cub cub cub cub #en 3. 2 5. 1 I. I I. 2 I.B4 YRh4B4 Symmetry tetr tetr tetr tetr tetr tetr tetr tetr tetr tetr P-err 0p p. M o n c t o n et al.. (1977) 3.6 11.62 1 7.65 9. T a k e s h i t a et al. V a n den Berg and Matthias (1977) 2.3 9.33 22 5. 2 2. Tc TN References I. 2 I.8 12. 1 I.4e C o m p o u n d s o f the t y p e RRh4B + Crystal structure YRh4B4 YRh4B4 YRh4B4 YRh4B4 YRh4B4 YRh4B4 YRh4B4 YRh4B4 YRh4B4 YRh4B4 Compound NdRh4B4 SrnRh4B4 GdRh4B4 TbRh4B4 DyRh4B4 HoRh4B4 ErRh4B4 TmRh4B4 LuRh.62 1. I 9.5 References I.03 6.4 11. 2 2.5 5 5. 2 1.86 9.4 4 6.4d C o m p o u n d s of t h e t y p e RA4B (A = Cu.14 25 22 38 28 23 14 24 1. 2. I I. 2 2.56 0. Matthias et al. 2 2.0 8.RARE EARTH COMPOUNDS T A B L E A. (1976) 2. 2 -9.38 9.91 8. 2 1.9 10. (1977) .0 . I 2. 2 I. I 4 5. 2 2.0 no C-W behaviour -7. R. Day. M. Rev... E. 1969b. N. Stat.. P. 1961. and N.X. 1976. Nereson. Solid State Comm.E. Ofer. and J. Soy. Clark and N. 4. 1968a. Rev.R. J. 1975. Chem. Atnji. 34.. suppl. K.400 K. I. 585. B. Phys. Phys. Banks. 1976. (a) 22. 3 (The Institute of Physics. J. Rossignol. D. Conf. J.. 1969a.G. 55A. Sadikov.. Baenziger. B 10.. B. Graebner and H. Phys. Mag. K. Dariei. Purwins and E.J. . Phys.St. C1-1126.N. S.N. Pauthenet. Morin. P. Atnji.K.H. Phys. Rossignol and J. (a) 41. Aleonard. Physica 86-88B. 1976. Rev. Barbara. 1048-1063. Stat. 1969. de Phys. BUSCHOW References Abbundi. U. B 13. Barbara. Sci. Rossignol... 1977a. Atoji. 83. M. Ross and M. R. 77. 51. B. Aifieri. M. and M. Koon. 219..P. Bauminger. Conf. 389. and M. Phys. Phys.A. 32. Purwins and E. Darack. 51.P.F. B 7. 3380.A. B~cle and E. K. Rev. Phys. Siaud. Savitskii. M.. Markova. J. Z. G. Atoji. Bowden and R. Lebenbaum. 222-223. E. Atzmony.. Chem. Crystallogr.. Phys.F. G. Dublon. 4364. E. J. 1975b. Ott. Phys. M. D. Kanematsu. 1972c. Atoji. U.. B. Ofer. C. F 5. 1968. Phys. 4006. I. Phys. Paccard. J. Rare Earth and Actinides. $0. 1053. Japan 23. Phys. 197. J. Andres. 57.P. 1495. 57. I936. K. J. 4041. Furrer) (Plenum Press. Bunbury. Appl. Phys. Barbara.H. C.St. I. Bernstein. AIP Conf. I. 1254. Liithi and H.X. M.C. Atzmony. Physica 86-88B. J. Int. V. Sol. 39..A. 17. Phys. M.P. 238. 37.P. Sherwood. 1964. J. R. 48. Gatlingburg (Tenn. Phys. Rev. Ott. B. Chem. M. 1525. Phys.D. K. Proc.A. in Crystal field effects in metals and alloys (ed. 1977b. 2716... B 11. A. Williams. R. 1779. P. Siaud. 1361-1373.T. B 14. Maita. Rev. Kanematsu and T. Ohoyama..L. 321. Atoji. Maita and S. 1979. J. G. 1973b. Arif. Atzmony. 267. 1967. Appl.) June 1976. Dariel and G. Arif. Andres..C.. S. 51. Rossignol and J. Barbara.J. M. Proc. Alekseev. Pierre and D. Bunbury. 158. Chem. 1084.K. Gignoux. J. Appl. J. M. 507. Andres.R.R. Barbara. 1975a. Atzmony.. 1968b. Acta. Sigalas and D. 35. J. N.C. G. M~F. M. J. L247. 48. Abrahams. J. J. D. Nereson and C. Lett. Moriarty. K. Dariel. AIP Conf. H. M.F. B. 851.H. 2407. C1-299. J.R.P. Barbara. 1972. N.H. Boucherle. Atzmony.. C. Phys. A. B. U. Phys. S. Andres. 1970. 1974. S. Phys. digest no.H.P. J.. 452. 1974. B. P. N. J. Phys. Arif. Proc. Sehweizer. 24. 599. Schweizer. Wong. Barbara. P. Bauminger. Banks and K.J. B.. Barbara. Phys. 1975b. Nguyen and E. Chem.. Solid State Comm.R. Chem. and M. J. H. Soc. pp. 1975c. M. B 6. 32. Y. Barbara. Schmitt. U.. Morin. Siaud. Akulov. New York).. V. E. 3713. 553.K. C. 14.S. McCausland.. P 6. Acad... 605611.. 1976. Atzmony. Walker. J. Darack and J. Givord and R. 1976. B. J. Boucherle. B~cle. Phys. Arnold. Arnold.M. Darack. F $. D. Walker. Sol. Bucher. Proc. 10th Rare Earth Research Conf.X. 1972. 560. 2060-2067. New York). and E. Chem. J. 1069.P.. Solids 25. B~cle. Dariel. 46. Nguyen and E. Barbara.J. Chem. Lemaire and D. Wernick and H. Phys. Chistyakov. Atoji. 1971b. J. C. in Crystal field effects in metals and alloys (ed. Rossignol and J. M. 1971c. Low Temp. Aleonard. 1975. 1972a. Lemaire and R. A. Lett. 100. 1971a. Olson.. J. 1975. 1975. Phys. 1967..W. 3877.K.E. B. Schmitt. 1. Dariel. $2. Chem.H. M. 1977a. E. J. Lebenbaum.. Phys.K.C. Nowik and S. Pierre and D. Lemaire. Nowik and S. Barbara. Bucher. 1972. G. S.. 57. 1977. U. 4220.. Andres. Chem.P. de Phys. I. Phys.P. Rev.S. 1966. (Paris) 274. McCausland. vol.. B~cle. Alfieri.J. K. Bucher. Wang. 17. Givord. Schmidt and S. J. Schmidt. Phys. Phys. Andres. Puffer) (Plenum Press. R.. H. D.F. J. E. E. Phys. London) pp. M. Solid State 18. Walker. 1976.. 948. Terekhova and O. F. 1977b. S.F. 1973a. on Neutron Scattering. Chem. 1973. Arif. R. 1972b. Phys. Boucherle. 1671. B.F. 2402. Atoji.G. 6433. Proc. 3882.T. P..L. U. Rossignol.H.G. Purwins and E. 9. B. Barbara. D.HJ. J. J. Lebenbaum. 41. E. Appl. (a) 17. Castellano and P.R. 1974a. 1977. Froindlich... 881.C. Crystallogr. Berndt. 1977e. (Paris) 2/011.L. Schweizer. Ofer and R. 201.. J.M. D. Nowik.. IEEE Trans. /Ms-Nielsen and E.M. 1976. Soy. D. 1975. D. Torgeson. 2724. J. 19. and K. B 9. Chem. B~cle. R.L. 1977d. 1971. Bucher. Burzo. B 6. 1976. 97.. 1977.J. 1977f. Paccard. J.R. J.O. Phys. Kadomtseva and R. Ofer and D. 366. B.. D.J. Phys. Acad. Phys. 127. Harper. Phys. 1970. 1978. 1972. Phys.. Rossignol. G..H. Belov. F.E. Lander. Reddy. Bruzzone. 1974b. 660-663. Phys.. Grill. University of Grenoble. Rev. K. R. 1977. Phys. Barnes and R. Angew.. Phys. G. Bioch. Beckman. H... Rev. Bauminger. F. I.H. Matthias. 155. Reese. Voiron and G. B 13. 759761. M. 1974). I. F. Borsa. and G. Phys. Schmidt.G. 631. Rowland. 49. C.. 1975. 1968. Miedema. So. 1679. 5. I. 1973. B 2. Givord. B~cle. Sol. 1972.H. Birgenau. Rev. H. and A. Barbara. 16. AIP Conf. . Belakhovsky. Cooper. Suhl.. Buschow.. Bloch and J. Fornasini and F. Burzo. E. A. J. J. Novik. 3. Bucher. D. Acta. T.H. Mayer.J. Felner. E.J. 1376-1387. 35. 855-863. A. N. M. 543-544. Bruzzone. D. 1973.. MAG-10. I. Froindlich. I. and B.. F.. 401 Bloch.M. D. B 6.M. 1968. 23. 1976. 1977c. R. Merlo. Laforest. D. J. Bargouth. J.. Bauminger. Lemaire. Edwards. E. Dernier. Aitken. 1964. Felner and D. Rev. Brouha. Levron. F 5. Phys. Giraud. A. Besnus.S.T. 1972. B. T. Buschow and A. Rev. New York).G. Ofer and M. Brouha. Co. Rossignol and M. W. B. Felner. Holtzberg and S. C. 231. Solid State Comm. Proc. Nelson. A. 1975. J. Hull. 1973. J. 295.. Yanovsky. Lemaire and D.S.. Rossignol and E..R. Shaltiel. 191. Barbara. 20. Physica 86-88B. (Paris) 268. 1971. D. Bfihrer. J. Berkowitz.R. Wallace. Narasimhan.P. Chaiss6. G. Z. 32. 235. R. 1973. 6. Phys. S. J. Davidov. M. 2648. Proc. 939. D. S. 13.C. Stat. 44. R.G. Solid State Comm. 182. R. 1963. E. D. C. C. Kouvei and G.R. Rend.V. Phys. 24. Davis. 19. Bunbury and A. and T. Solid State Comm. Acad. Purwins and E. E. Appl. Moscow. 1813. I. 248. Lander.. Phys. M. 1970. 1970.G. and F. Brun. B 11.. H. 1974a. 13. 183. and R. Mat. I. ICM-73 TOM V (Nauka Publ. Parisot. and F. Brun. R. S. and R. E..440. Voiron.. Sol. Naz. Bowden..L. M.G. Phys. Walker. 1595. Mag. J. Physica 86-88B.O. Ray.Z. Less-Common Met.W. LessCommon Met.P. Bloch. Phys. 465. Felcher and J..D.N. Buschow. Bartholin. Methfessel.S. de Phys. Lin.F. 5007-5020.R. Butera. 1967. Atti. 1977. Barnes. 115. Rev. M. Ruggiero. Guimfirfies and ILE. 1979-1988.J. Pierre and D. M. D.F. Sol. 217-218. Brouha.. Burzo. 25. Snijder.. Rev. G. 1955. 161-170.. Phys. Solid State Comm. G. 1157. Rev.K. C6-61. 215.S. Physica 86-88B. 1159-1161. M. 1959. Uehara. T. J. Zvezdin. 574. Burzo. 359.K. I. Walker. M.K. Thome and D. G.H. Maita. Bloch. J. Olcese. 840. E. B. K.St. Burzo. 2882-2887. P. 1973. 177. 129. Levitin. A. A.F. 37.. M. Craig and R. Bauminger. 8.P. Acad.H. E. D. Godet. Shaltiel. 569. J. Bauer and J. Ups.K. Mag. Phys. Appl. J. E. G6nin. R. Lemaire.A. G. Fulton and A. Less-Common Met. Lemaire. 1217. 1976. Shimizu and J. Furrer) (Plenum Press. Int. Florence. Bozorth. W.P. Siaud and J. W.. unpublished results cited in Buschow (1977d).RARE EARTH COMPOUNDS Barbara. J. Bucher. Felner. Barnes. 1967. Will and K. J. Price. 1975. G.O. R.F.O.M. 1030. 1975. Davidov.P. Bloembergen.. C. Solid State Comm. Brun..P. Stat. M. B~cle. 33.H. Burzo. 86. R. Purwins and E. and K.P. Rev. Phys. D.A.E.. and J. 1974b. Buschow. Walker. 483. E.O. K. F. Barbara. Novik. E.S. 1967.. Thesis. Schieber.. Bucher. Borsa. C 1.R.J. H.A. P. Physica 86-88B. Phys. Malta. E. Phys. 1974. J. Beille. E. Phys. 1969. 15. S. B.J. in Crystal field effects in metals and alloys (ed. Kouvel. 13. M.F. 1976. Mag. F 6. Corenzwit and D. J. Physica 86--88B. Lunde. Sc. C. J. Lander and R. Phys. I. 1969b. 1978.H. Buschow.J.W. Oxford).H. K. Phys.J.S. Buschow. 11. 3910.F.402 K. 24. van der Goot. K.J. 1970.. J.S. 19. 1971b. J. Buschow.J.H. Less-Common Met. Sol. de Wijn and A. J. 515-522. Ursu. 5. Buschow. Phys.H. 122-126.M. 593.. K. Crystallogr. 1976. van Diepen. Star. van der Kraan. Buschow.. BUSCHOW Buschow. 1977c. Urzu and J. J. K.H. 1977d. and J. De Wijn. J. 1571. van der Goot. Less-Common Met.H. 1967. 61. and A. 173. 13. K.Hj. Phys. K. Sherwood. 1969. Burzo. Z. 1976.J. 1976. van der Goot. K. CNRS p.. Sol. Acta.. Buschow. Sherwood. Phys.J. 1974. 1973b. Fast.H.W. 11-17. 32. Physica 86-88B. 1971. and C. I. Buschow. . K.S. 1970. 1971a.Int.K. K. Buschow. K. K. 117.H. 309-311.S. suppl.J.J. van Diepen..H. Phys. F 4.H. 33. E.H.. J.J.J. 421. K. Buschow. Phys. Solid State Comm.S. Buschow. 44. 1977b. Sol. and R.M. and A. Physica 85B. Fast. and A.A.J. 50.H.H. van Vucht. Sol. Phys.. Star. Solid State Comm. and I. and W. Phys. Chem..J. and R.F.H.J.H.H.J.J. Buschow. Buschow. and J. van Stapele. J. Buschow. Less-Common Met.H. J. Matkovich) (SpringerVerlag.. Buschow. 1977. Helv.F.W. 137. CI. 1974. 1977a. K. A. K. van den Hoogenhof. 4085. Less-Common Met. 1246-1255. Philips Res. J.H. K. J. 1965a. J. H. and J.J.HJ. Buschow. Stat. K. van Wieringen.J. Less-Common Met. J. Stat. Phys.. 79. 1976b. Sol. Phys. and A.J. 1967.H. K.HJ. 40. 9. 101-112.H. 204. Buschow. K. J. J. 1966. Reports Prog. IEEE Trans. 1967.H. Phys.H. 43. Appl. 59. K.H. Burzo. 33. J. 55. 1970. G. 199-210. K. Less-Common Met. 171. 131.3.J.H. 452. 329.J. 50. 185. 1978.J.J. 51. Buschow. Buschow. 21. 29A. 1974. 301-306. K. 48. J.J. van der Goot.H. Less-Common Met. 42. 4666.J. Less-Common Met. 35. Oppelt. 1972. van der Goot. 921.J.. 9.. (b) 51. K. Buschow. and A. 22.. 79. Les elements de terres rare. J.H.H. K145. Phys.H. Buschow. K. K.J. 1967. 1966. Stat. Star. B27.L and R. 42. van der Goot. K. 1965b. 57. and L. Phys. K. 1972.J.J. Appl. 4643. Buschow. K. 20. Sol. Z. K.. Andresen and A. K.. Buschow.H. Less-Common Met. K. 1969a.C. Buschow. K.J. in Boron and refractory borides (ed. 311-312. Phys.J. K. I. and J. Less-Common Met. 309. 609-612.F. Chem.N.. 8. J. 2289. 1975b. 26.H..J.J. Buschow. Creijghton. K. K. and J. Schlapbach.J. Chem. Solid State Comm. Buschow. Sol. Laforest. 309.J. 1971. 12.. Stat. Star. and J. Fast. 825-829. Fast and A. 672-674. J. 21.F. Buschow. 16. 3433-3437. van Diepen and H. Solid State Comm.H. (b) 65... Phys. 45. Appl. K. 1977b. A.H. Buschow. Buschow. Mag. K. 233. and A. 1976a. J.463. 1972. Maeland) (Pergamon Press. Phys. Phys.H. 209.. K.P. N.J.. 165. 1978. E. J. Phys.H. and R. Buschow. F.H. 1978.H.. Buschow. Less-Common Met. 231-239. Buschow. Buschow. Less-Common Met.J.. Schinkel. Busch.F. Less-Common Met. Busehow. Phys. 1968. van Steenw~k.H. 51. K.J.H. Less-Common Metals. E. and A.. Rep. and A. 715. 19. 25. (a) 7. Magn.J. 39. MAG-13. Buschow. Stat. Buschow. Buschow. 18.S.J. Buschow. Fast.L. Buschow. 1031. Buschow. J. Lazard and M. K.J. Berlin). J.P.H. 29. 1969a. 1973c. Ciorascu. Burzo. K. Buschow. 49. Sol.M. K. 1480. Phys.H.J. 1971a. 1968.J. Buschow. 1973a. Buschow. K. Buschow.H.C. and W. E. 1170. 1966. 1975a.H. and F.N. Burzo. Acta 51. K.F. Chem. 1971c. Chem.J. Buschow. 21. 31.S. 24. Less-Common Metals 8. Phys. Phys. Sherwood.J.J. 18. K. K. 1977a.M. K. Buschow. 1971b. Lett. 467. in Hydrides for energy storage (ed. Velge.H.H.J. Pierre. and J.. Solid State Comm.J.K.J.H.H. 1977e.C.H. J. K. Less-Common Met.J. Sol.H. Phys.H. J. J. Buschow. 1972. 239. V.. Buschow. Buschow. Less-Common Met. D.J.J.J.J. Appl. Rev.. Phys. 881.H. Buschow. 84. B 8. C.. H.J. Proc. K.266 (1975). H. A. Matthias. 1974. 1972.L. Chamard-Bois. H. Int. Solid State Comm. 1974. Rev. AIME 233. Lett. van Daal. Rev. H. van Diepen and H.P. Kochler and E. Coles. C. Proc. WoUan.K. Phys.H. F 2... 1959.C. de Jong. Campagna and G. Dormann. J. 1975. . 42. 145. Campbell. J. 9748. Chazalviel. Wollan. Phys.. Phys. Cryogenics. Chiotti. C. and P. H. J. R.F. J. Brouha. Carfagna. and G. 1972.H.W. K.. Phys. J. Miedema. 1971b. Chem. 1970. 789. 1975b. 1961. Proc. 1963. Phys. 19. 1974b.H.. Buschow. J. Phys. Appl. 77. C1-1136-1138. Am.. Cole. Phil.C. 1974.H. A.J. Pierre..H. 1970. Taylor. 32. Rev. Purwins. Buschow. K. A. 161.O. Chao. Hsu.C.W. 7. Phys. and K. on Valence Instabilities.A. 1968) 105115.W. University of Grenoble CNRS AO no.D.E. M. A. 2730. van Diepen and H.B. Appl. W. Elemans. Buschow. G.. J. G. M. Biesterbos and A. B.M.J. Buschow. Buschow.J. A. K. Phys.J. 50. F. L.O. 1969b. 24. 1972. Phys.J. K. van Laar. 1517.W.J. van Laar and J. LN. P. Less-Common Met. Chao. van Diepen and H. Co. Cooper.. J. van der Goot and J.J. Holden and A.W. D.W.L.RARE EARTH COMPOUNDS Buschow. H.M. Stat. 335. R.G. 1975c. Thiei. H. 49. Sol.J.J. Phys. R.L.D. Buschow.. M. K. B. J.. 1978. Proc. 1510.H. Knorr. van Mal and A. B 3. Phys.Y. Cannon. 37. Trans. and I. Phys. C. Parks) (Plenum Press.R. Fis. Phys. A. Hall.J. 12. Phys.. Rev. L47. 1964a. and D. Griffith. 1976.J.J. and A. W. May 1975. Solid State Comm. 1972. J. 1975d. Phys.. Coles. van Aken.L. Acta. K. J. Crystallogr. 39. J.L. De Wijn.H.N. 433-436.M.J. Appl. de Wijn.HJ. 257. and B.J. Luo and P. K. 39. J. Wallace. 845. M.H. L. Rochester (ed. 1975a..T. 1971a. Solid State Comm. 1966. 903. 7th Rare Earth Research Conf. 1965. 1973b. Flouquet. 1973a. B.T. E. v a n Vucht and W. J. A 136. K.. 5. Sol. 240. 1964b.M. Cable. Atti Lincei Rend.J. F 5.C. 1975f.H.P. Solid State Comm. Conf. Nat. 37. Phys. 383. 20812084. 12. Rizzuto and G. Olcese. (b) 49. Res.W. K. Cooper. J. Mat..K. 1971.H. 1974a. 25. Birkhan. Tournier. Chatterjee.R. Sol.H. 1352. J. 4315. B6. 1966. Wertheim and P.S. J. F. B 11.. J. A.. Buschow. 5134. Thesis. Bull.R. 1977b. 1662. Lambe and N. Buschow. 651.S. Buschow.HJ. and W.J.C. 5. Langereis. van den Hoogenhof. Miedema. de Wijn. Belson. and E. Compton. Laurance. Koehler and E.. Mat. 34 1971-1973. van Steenwijk and R.. Eibschtitz and K.B. J. J.R. J. Palleau. Furrer..R.R. Oicese.R. Huiskamp. 1968. Moscow.A. 16. 1964.R. de Phys. J. Mag. V. J. 417. Thiel. Cal. Clark. J. Buschow.F. J. F 4. M. Duwez. Phys. 261.. Solid State Comm.H. A. Cohen.. 1978. Schmidt. 1975e. B. Cock. Soc. Perreault. 1976a. K. 1625. 15.H.. W. Walker and A. Phys. Phys. 5259. J. Less-Common Met. de Wijn. 786.H. 24.G. 19. 27. 261.E. Rev. Colombo. Appl. 253. Sherwood and K. K.. G.k and R. 1971. van Daal.H. Zandbergen and B. Sci.J. Physica 91B. M.. 1977a. Huiskamp. Phys.T. Callen.Th. and H.C. F. R.J.W. Buschow. Peyrard and R. Bull.M. K.C. T. K. New York 1977). Proc. W. J. 4609. J. Chao. 1974. Campagna.. Duwez. J. K. 403 Cable. Phys. K.W. ICM73 TOM IV (Nauka Publ. 1972. 1976b. 35. (Coronado... L-461. Mason. 1973) p.. van Diepen and H. 725. (b) 50. H. 35. 1974. Phys.J. Roeland.A. 9. Phys.J. 42.C. Buschow.. Nguyen Van Nhung and J. 423-426. Soc. R. 163.J. H.J. Keradac. Stat. 79. 1962. Buschow. Wertheim. F. Less-Common Met.C. Appi. F. Buschow. van Steenw~. J. Buschow. Appl. Chouteau. Duwez. 213.H.. K..H. J.E. Miedema. 46. Appl. Buschow. J. LeFever. I.L. K. J.H.. Chao. Brouha..H. Luo and P. Oppelt and E. J.N. P. de Phys. 12. 1271.J. de Wijn. van Diepen and H. 1963..Brouha and C. 1971.J. Cailen. K. 2631. 647. Buschow. Buschow. Soc. 1625-1636. Buyers. Phys. R. 41. T.M.W.W. 15. 213.B. M. Coldea. West. Maranzana and P. Pop. Less-Common Met. Chamard-Bois. Robertson and H. Solid State Comm. W. D.B.. Dirks.W. K.J.M. Appl. Olijhoek and A. 1977. Devine.. (1975). D. Rettori. Nottingham. Solid State Comm. Davidov. 1973. Dormann. A. K. M. H. Debray.H. Devine. K1518. C. 1973. 4gA. Solid State Comm. E.H. E. Mat. Orbach. Debray.J.J.M. B. Stat. D. C5-171. Deenadas. Sougi and D. J.. Callen. J. P. 11. 2. Star. J.F. K. 1970.'I962a. James. R. D.B. Phys. J. 4009. and D. 29 (1974). Orbach. 45A.H. H. 1977. Hastings. Stat. 13. (b) 64.W.. 23.. 1977. D. A. Givord. Mat. 50. Gignoux. Lemaire and H. A. Meriel. L. Mag. Stat. Deportes. 4829. W. 12. G. Givord. K129. Phys..H. van Diepen and K. Methfessel. Phys. Rev. Ryba. Chem. 1964. Phys. K. Phys. A. D. .. Kudrevatykh.. 56. Phys. Brown and M. A.P. 1977. Herr.J. de Phys.G. Depoi'tes. BUSCHOW DeGennes.W. Appi. B.F. Methfessel. Cyrot. Sakurai. 1975. Chem. Phys. 1974. 1979.M. 220. E. E. Domngang. Mat. 1974. Baberschke and R. Atzmony and D. Dormann. Buschow. P. Less-Common Met. Phys. de Wijn. MAG-12. J. 1974. Craig and W.A. H. J. 1069. Crecelius. and J. (a) 30. P. Physica 86-88B. Phys. Phys. and U. 1973.. 1973.S. 1973. Sougi. J.E. 1973. M.N. pp. 1965. A. 40. J. (B) 7. (b) 77. 763. Mag. D. D. Huck and K. D. 47-54. 524. 14. Dormann. Taylor. B..W. Chock.H. H. Debray. DeGennes. M. 789. Davidov. G. Phys. Cyrot. Dormann. 57. and J. C.. M. Bashkov. (Carefree.H. Deryagin. Phys. Phys. Proc. D. 1962b.J. E. Debray. A. Tarasov.. D. H.K. Rev. 510. Mag. J. D. Maletta. K. Dixon. Czjzek and H. Nagai. R. D6portes.W.B. C. Lett. Phys. E. 30. 1662-1667. Thompson. Deportes. 1976. 1973a. Bozorth. De Savage. 1976. Buschow. Stat. 37. 22. Sol.. 1970a. Buschow. Givord and M. de Wijn. 19. 69. 1971. 759. Schweizer and F. J. Corliss.E. Appl.M. Debray. 1973c. B 9. Phys. Creijghton. Mag..A. D. 1976a. Wallace. Dublon. Wortmann and S.F. Sol. 1975.J.A. Conf. J. J. J. 141. 1987. Phys. and M. 621-625. D. 992-993. Ross.G. van Diepen. Dariel. 4. 1967. J. 1977. L71.E. M. K. Rettori. 1979. Rev. 47. A. Delapalme.. H. B 1029. Chock and R.H. B. and J. and K.J. 1976.. Solid State Comm. de Wijn. Radium. 36. B 27.H. J.M. Locher and K.P. 1973b. C. Sol. 1977. Kudrevatykh. Y. de Wijn. Lebenbaum. Sol. 2156-2159. Ulyanov. Solid State Comm. Phys.W. Orbach. Mag. Buschow. Sougi and P. Buschow. Appl. van Diepen and K. 1973. IEEE Trans. R. 40..M. 1964. Maple. J...W. M. Dormann.404 K.H.J. S. Schaafhausen and K. J. Sol. 45A. 2129-2133. 630. Debray. J. (a) 23. F. Rev.A. and D. Phys. Mag. Atzmony. Davidov. Davis. D. and N. Solid State Comm.M.. Barabanova. Wortmann and S. 1974. Deportes. Int. W. 1885. 21.R. Fink.V. D. Stat.. Sol. E. M. Physica 86-88B.. J. 19. Phys. Baberschke. G. Phys. A.M.R. Phys. van Diepen and K. 133. Phys. Coll.. Tasset. and M. de Wijn. Crangle. Dunlop. Buschow. 4.L.M. J. Lett. A. Givord. 163.. D. 941-943. Phys. and A. Hardman and W. Buschow. Phys. and J. 370. Deryagin..V. F 7. J.M. J.H. J. L... 75. J.. 161. Schmidt. F 7.M. Buschow. Hastings. Lavagna. Buschow. 1964.K. Appl.J. 177. 11. 1783-1786. Mag. R.J. 1000. Chem. Phys. Phys.. Phys. 12.P. 713. Rettori.J. A. Proc. 1976b. R. Issa.J. 1977b. unpublished results cited in Debray et al. Arizona) 439-448. Debray.. Phys.J. Int. and K. R. K.J. Crangle..M. Phys. F. (b) 76.. Sol. Chelkowski. J.. C. E. Rev. 1051. 845. J. Lemaire. Andreev and E. L. 1979. Lavagna. J. Ray. C 7. Phys. D. Buschow and A. 40. van Diepen and K..R. Lett.B. Radium. Phys. 1976. Hauk. R. 1968. V. Wang and E. Wallace and E. J. Chem. R.. Maki. 1970b. 1974. 7.. CNRS 126. Rettori andE. Givord. 4325. Huck and K. J.W.K. 253. Meriel.J. Buschow. Sol. de Phys. Dormann.J. Orbach and M. Z. Debray. Gignoux and F.H.N. 23. 197-199.. Buschow. 161. 1972. 58. R. F 3.H. Day and J. 10th Rare Earth Research Conf. Corliss. 240. 1976. (a) 30. J. Stat.J. and M.H. 1977a.B. 35. 1853. Rev. K.H. G. Sougi. Davidov. Buschow. J. Lett. Conner and J. 1975. and K.. Rev. K125. Ferron. 245. Chem. Phys.R. 133. Met. F. Merlo.L. Crystallogr. Smith and I. AIME. Ermolenko. Felcher. A. Koehler and R.. 5. Phys. (a) 36. 1st suppl. Dormann. Sol. 669. 12. A. E. Atti. Downey. 127. 1518. Gignoux. II. Int. Gignoux. G.R.E. 44. Givord. Sol. D. 1973. J. 2. 43.L. 1965. 162. (McGraw-Hill. G.. Phys. Rev. Edwards. K.. 1975. and F. J. J. 23. D. 1976b. Buschow. Solid State Comm. J. Solid State Comm.. 1001. 1976a. Moon. 1964. Gignoux. R. and R. 877. J. F. Chem. Phys. M. 1005.E. R. 8. Phys. F 2. M.H. A. 1964. New York). Gignoux. Inorg. 275283. Sayetat. Gignoux. C 9. Phys. Phys. Phys. Ghassem.. C 8. A. D. Physica 91B. J.R. Atzmony. Line. H.A. 824-838.T.. Givord. 1968. W.. 1975. Gardner. A. J. Felner. Penfold and I. Fuess. Naslain and P.K. 1974. Solid State Comm. 1972. B 5. C1-1139. 1962. 1975. 75. Gignoux.M. 1974) 231..P. 1976. 1974. 1976. J. T. Paccard. 3.B. Givord and A. Z. J. R. Givord. 1443. Harris. 860. Gignoux. Downey and R. Stat. 247. Irkhin. Maita.. F. 1975. . 32.G. A. Gignoux. Olszewski. F 9.C. Solid State Comm.V.C. I. Felcher. Wallace. Gignoux. CNRS p. Givord. Schweizer.J. L292.. E. Kroupp. J. J. J.W. A. 1970. 1063. D. 1965. Lehman and S. A. Stat. 1979. 171. Science 160. L. B.E. 1974. 3878. Fornasini. Lemaire and D. D. H.H. Solid State Chem. Rozenferd. Phys. Phys. Kelarev. Eckrich.HJ. Mueller. Z. J. Trans. R. H. F 7.M. 1970. Knot. Z. Phys. Mercurio. R. 131. Rev.A. D. R. Phys. J.RARE EARTH COMPOUNDS Dublon. B23. A. Aeta Cryst. E. Eagles. A. Farrell... and H. Corenzwit. Felner. I.M.A.S.. Acad.499. Dariel and U. in Magnetic properties of rare earth metals (ed.. 1491.P. J. Furrer. 405 Fisk.. D.H.. I. A. Phys. M. J. 1966. A. Geballe. 1967. J. Soc. M. Koehler. 1961. Friedel. J. Star. 763.S.E. New York).. C 4.B. Oppelt and K. 1976. Tchernev. A.C. 357. Chem. 1975. F. 1974. J. J. Paccard and D..R. Ferron. Ganapathy. 325S. Constitution of binary alloys.. 1971. 50. 1972. 2075.W. D and R. 1977a. H. Figiel. Taylor and B. 38. Edwards. J.R. Cooper and E. R. Proc. R. Mag. Soy.P. J..J. (a) 24.P.. 267.. Z. Appl. 891.E. 267. Eckrich.S. J. 415-419.. J. S. 1975. 36. Del Moral. A. Buschow. Buschow.J. G..F. Phys. Naz.H. Etourneau. K. Moon. Schieber. Sol.. 1970. F.P. 1976. Raman. Rev. 1973. Coles. Harris. Metallkde 64. 836. and L. Hagenmuller. 1968. 1977b. 36. A. A. 34A. D. Georges. D. Phys. Mag. Phys. M.V. ICM-73 TOM I (Nauka Publ. E.N. Vokhmyanin..L.A. 1064.M. R.. Oppelt and K. L.I. D. E. 51A. Watson. 19.. Downey and H.V. W. Mag. New York).H. Schweizer. Lemaire. Lemaire. 262-264... Perrier de la Bathie and F. T.W. Bartel. 1965... 197. Paris. 1963. Rev. J. Lett. Sol. I. 885. D. 37. Co. Phys. Phys. 1977. 1971.. K.R. 1977. Acta. Appl. Elliot. 1968. Elemans. D. Ermolenko. Les elements des terres rares. 1971. 5. 2000. G. C. 333. Atzmony. and W. 172. Mat..A. 391. D. 157. Solid State Comm. Dwight. Solid State Comm. G. M. Phys. Yakinthos. 0a) 76. Rc. 75.P.. Less-Common Met. Grill and M. Lemaire. 21. Conner. Fornasini.J.F. Purwins. Freeman. 371. 1823. A. V. and A. Oppelt. Phys. Solids 36.. Andres. in Rare earth research III (ed. B21. D. L. Phys. Fisk. W. 21. Schweizer and J. unpublished results cited in Stewart and Coles (1974). Dormann. Koehler and R.E. de Phys. J..J. Palenzona. Freeman. Givord. B14. Kugimiya. 105. A. JETP 42. Gregory and J. Corliss and J. 14. Sidorov. Hastings. Dormann and K.M. Pirogov and A.C.P. J. Garnder. and F. Givord and R. J. ANL Report 6868.. Phys. Penfold.H. Dwight. Phys.. Accad. Conner. Moscow. Dariel and U. Felner. J. Yu. W. 18. 1967. Rozhda. R. Phys. 1979. 77. Dublon.J. Dwight. Appl. R. Givord.P. Givord and J. Eyring) (Gordon and Breach. Pauthenet. Matthias. 1976. and W. Mayer. Sci.P.L. 1977. Elliot) (Plenum Press. K. 261.E. Z. 1972. Less-Common Met. Elliot. 1976.E. Forsyth. J. 5. 2058.P. 16. Furrer. Dwight.M.. and A. J. Steinfink and D. 1978. 1965b. K151. Mag. 1974.J. Harris. MAG-10.E. 1962. N.D. Gorlich. and R. Phys. 379. A. Hansen.M. 1977. 31. Phys. Lem~ire. Gupta. 1973. and K. and E. Lemaire. Lee. C.C. 6. Givord. 1972. Lett. and J. Henry. U. and R. C6-617-620.S. and A.. J.. Phys. Buschow.M. 921-927.Z.P. Lemaire. 387. and R. 2653. Z. E. 387.Phys.. D. Sol.J. Less-Common Met. Givord.. P. Met.R. B 22.. 1973. Laforest. P. Solid State Comm. K. AppL Phys.. 492-496. Wallace. Herbst. 1969. D. R.V. J. Hendy.. 40A.L. Appl. 2198-2207. CI. Less-Common Metals 9. Stat. 201. 1976. Rev. A. Mat. D.J. van der Kraan and K. in Crystal field effects in metals and alloys (ed. Harris. J. Gubbens.J. Greedan.K.HJ. Gubbens.M. E.J. 1976. P. 26. Gomes. 1971. K.S. J. Physica 86-88B. 34. Phys. B 10. Solid State Comm. 341-346. Hacker. 1974.C. BUSCHOW Gubbens. Soc. Givord. Phys. Taylor. F. Buschow. 1977.K.. Harris. S. 35. Guim~tr~es. Schranb. Vijayaraghavan. Richter and K. Grover.. Z.J. 7.C. Glausinger.P. 1965. J.J. 40.L. I.H. D. Givord. 923. Sol. 1961. 3739.S. J. Trans. V.H.V. 1974. 60-66. Havinga. New York). I. Solid State Comm. 114. 31.. Dormann and K. W. A. R. de Phys.J. Hillenbrand. P. M. 6.406 K. Longworth.S. 1976.R.C. L.J. Heinrich. Kiibler. J. 1972. and M. 1979.M. Physica 86-88B.R. Sci. D. 1973.. Proc. 11. and D. van der Kraan and K. A. LessCommon Met.W. Moon. J. Stat. A. LessCommon Met. J. 474.J. Phys. Stat. Goebei.E..J. 151. Buschow. 1974. 281. LessCommon Met. Hacker. 1974. I. E. Gardner and R. 1974) pp. Phys. J. H. Phys. J. B. Solid State Comm. 331. Buschow. Narasimhan and W. . Givord and R. 1975. K.H.M. F 4. and A..C. P. 13. Phys. 1454. Guim~rfies. Buschow. Acad. W. St.E. Ph. and J. A. Halstead. (Paris) 274. 1974b. Buschow. New York). Mag. Buschow. K. 8. de Phys. Gualtieri. and R.J. ICM-73 TOM V (Nauka Publ. van der Kraan and K. 1979. Hasegawa. Moscow.M. J.E. Damsma and M.J. 1971. F. Co. Proc.U.. Schweizer and F. Gubbens.E.H. 567-569. A. (b) 61. 269.C. P.M. 21. Sol(a) Gignoux.J. Tasset. Lemaire.r~es.H. 885-892. Dormann and K. K101.M. Chem. and G. 1975. Harris. Gignoux.C. Solids 37. Solid State Comm. Furrer) (Plenum Press. W.H. Phys. 109 (1974). B.. SOc. 1958..C. J. and R. Moscow. F. Bunbury. 1973. 81. 30A. IcM73 TOM III. 668-669. Givord. Givord.W. Hill.. Freeman.A. D. 1166-1169. 270. J. A.H. Hacker. Buschow. Lemaire and P. Heidemann.K. I. New York). G. 1970. 1973. Halstead. 19. W. Sol. J. and G.V. Harmon. Am. Proc. (Paris) B 274. 621. 199. Solid State Chem. 31-34. Machado da Silva. 23.. van Daal. J. Haszko.V.H. 1978. P. Molho (1980).M. Guim~.. 368.F. Buschow. Co. T.. Phys. R. Gross. F 3. 219.R. 9.M.. Knott. J. 1961. F 4. C. R. 13. A. Givord. Gubbens. 367-372. 101. 7. 1971. 1972. Gupta and M. 1976. J.M. Latka. de Phys. 9. Tomala. (b) 70. Phys. A. and G. 107. J.. Abood and K.J. (a) 9. Phys. Kmiec. Lemaire. Rare earth alloys (Van Nostrand. and K. 44. Sc. (Nauka Publ. P. Liu. 1977.R..M. D. LessCommon Met. AIME 221.. Manchester. and J. 1971.M. and A.. 9. J. 2008. van Apeldoorn. Phys. Givord. F 5. D. Lett.E. Koehler and R. H. Bull. 1975.H.H.C.. E.. Givord. C2-656. 1968. van Loef and K. Sol. 1974). A. Meyer. 1974. 1974. ICM 1979). Rev. 50.. Acad. Hrynkiewicz. Havinga. H. 1974a. 1979. Rao. 425. F. Mansey and G. R. and V. and M. Buschow. Gupta and R. Solid State Comm. 263. 1965a. Thesis. Buschow. IEEE Trans. J. Raynor.P. Gubbens. J.R. 21-24. AIP Conf. D. Harris.R. I. A. A. Solid State Comm. Raynor. T. Murani and K.E.J.H. Shah. K. Phys. van Maaren.S. Gschneidner. 1977. Constitution of binary alloys (McGraw-Hill. 601.A. Shepard. Suppl. • 1973. Chem.. Szytula and K. 45.A. Wilhelm. W. H. Stat.A.N. J.J. Raynor. 1972. D.H. Phys.H. Buschow and H.H.H. E. (Proc. 50. 124.R.. Chim. L. Wernick. Lett.H. 1977. Physica 91B. Rep. 9. 244. 1974. J. 129. Z. 310. AIP-Conf. Atti. Klaasse. A...H. 7th Rare Earth Conf. 4525-4533. 18.E. 293..A. J. 11. R. 1962.V.T. A. Bak. D. 1971. Palenzona. J. A. Dormann. Acad. Lincei Rend. 1955. Hungsberg. Phys. LessCommon Met. W. Kissel. B 8. Nazi. S. KronmOUer. Ohashi and H. P. 84.. Wallace and K. Rev.S. A. Phys. . Methfessel. 2283. A. J. Ja¢carino. LessCommon Met. C. F.J. H. LessCommon Met.R. Classe Sci. Lebenbaum.T. 15. B. 1967.M. Naz. M.M. Ihrig. New York). Dwight. Chem. Mat... J. 39. 251. 35. 1975. Japan 26.C.R. Kasuya.H. 7. K. Stevens. and A. Phys. A. landelli. Croat. 1975. Vigren. A. Greedan. 16e Congr. 29. 1968. Sol(b) 54. Bieyendaal and F. E. Palenzona. N. Solid State Chem. J. Dunlap and M. 1969a. Walker. 1974. James.. lhrig. Klein. H. ?dig. 55.V. and A. M.E.. Angew.. 34. 2151. W. H.R.E. Proc. 1966. Menth and R. Palenzona. 1968. 62. Hilzinger. J. landeUi. 1974. Chim. Jaccarino. V.M.J.E.R. 1967. 1965. K. de Boer and P. W.417. Sci. E. 1972.. Proc.. and A. Hutchens. H. 1973. Fis. B 7. Mat. Rao. IL 255. Kimball.R. LessCommon Met. Jordan. Perkins. Rozenfei'd.C. W. 42..S. Soc. 153. landelli. Houmann. 1969. H. 1. Pure. R. 273. J. Phys. Kirchmayr.E. H. Z. Moscow. Rev. 593. Methfessel.W. LessCommon Met. LessCommon Met. Craig. Kalvius. J.A. 3. 1960.G. Rev. Phys. Hutchens. A.E. Phys. Chem. B 5.D. Lett. A. G. 1975. 1969b. 1974) pp. lhrig. 564.. landelli.V. 819-823. 45. W. 227. A. Coronado. Kanematsu. Z. Paris 255. Walker. Solid State 16. 12.S. 1967. W. and L. 12. H. H. 1974. McGuire. G. 896.G. 407 Irkhin.C. Lihl. Rev. Craig. J. G.E. Furrer) (Plenum Press.A.R. 493. IEEE Trans. Craig and V. 184. 2006. 385. Phys.H. Kiibler and S. Miura. Rao. 1878. A. 1973. 2429. Buschow and D.. Int. Kaneko.D. Anorg. Z. Sol. Sterkenburg. 16.. Accad. Wallace. Itai. Iandelli. Suhl and J. An. Solid State Phys.R. cited in: W. Gambino and T. R. T.E. 1973.. 1973. p. and A. 27. N. 337.. 1970. Nevitt. Deryagin. Lyons. A. James. Kond.. Acad.S. Wallace. R. Gschneidner and R. landelli. 197I. Hutchings. 1964. Ferro. and A..D.J. 50. and W. 1979. Wallace. J.G.G. P. J. Kaplan. Appl. 165.R.S. Phys. Phys. New York).A. de Boer. and L. 381-383.A. T. Phys. B. Phys. and H.U. Sov. J. R. 1972. Wallace and R.. A. Bertaut. Hardmann. 221. Kirchmayr. and V. and O. Shibata.E. Mattens. 330. 29. R.S. Hirst. 1975. Phys. 18. Cal. AFML-TR-66-366.R. 259. Lincei Rend. Umezaki and T. Yu. Methfessel. Phys. V. J. Peter... Joseph. 9. Theor. Saimans.U. J . Yamauchi. landelli. Mat.H. Z. J. and E. Kazakov. Banks. Kaplan.R. R. 5. Reactor Inst. Palenzona.. 1960. Alfieri and E. Matthias. Keem and J. Kirchmayr. 1976. 333. Prog. Palenzona. A.V. 1964.T. de Chatel. T. Physica 20B. B 24. J. Appl.W. and D.P. Hutchens. H. 2691. Phys. S. K.P. Reymer. 1976. Nat. Kawano. Purwins and E. Phys.P. Buis and J. 1976b. S. 1969. Proc. H. 463. 1976a..W. Yelon. 561. Wallace. H. and S. Phys. MAG-2. J. Solid State 16. Co.L. Phys. Kristallogr. 1954. and K. T. Nal 37. Solid State Comm. (Ky6to) 16. Loebich. 152-160.T. Phys. in Crystal field effects in metals and alloys (ed. A. 1956. Sci. Iandelli. N. and R. B 12. C. and S. V. W. 1965. and A. and F. J. H. Soy. landelli. 221. Rare earth intermetallics (Academic Press. 99. Lemaire and F.. Kyoto Univ.. 1966.. M. Gschneidner. J. K. 1964.. Stat. Rev. Phys. Kudrevatykh.. Iandeili. Pans 1957. 1972. Hoffer. Phys. Appl. 1977. Holtzherg. 1293. Gazz. C 7. 2072. ICM-73 TOM V (Nauka Pubi.RARE EARTH COMPOUNDS Hilscher.L. 28. Proc. A..F. Jefferson. 15. 370. 40. Rev. 170. Fis. 1963. R. R . USAF report. C. B 24. Kirchmayr. Rev. Palenzona. Sankar. Klaasse. J. Phys.. LessCommon Met. J.E. Franse.H. G. and W.M. J. F. Inoue. Z. Phys. 3132. Gubbens. 47. Phys.. Lethuillier. 599. Atzmony. Cobalt 39. 50. P. Berthet-Columnas. 309.E. 1970.. Lemaire. Paris 265.E. Wallace. Longworth. Chaussy. 1976. G. and J. 1966. Schweizer. and E. Phys. 1968.B. Meixner. 1973. 45. Acad. 175-185. Wallace and R. Matthias. Raub. (Paris) B 264. J. Z. LessCommon Met. Vijayaraghavan. Pure and Appl. 223. Philips Res. Knorr and W. Less-Common Met. Raub. Lethuillier. Wallace. 2733..P. LessCommon Met. 1973.L. 41.B. R. J. Markiv.S. 1017.R. Chaussy. Drexel. 40.K. Appl. 258.E.P. 695. Percheron-Guegan. Mansey. C.. Chem.C. S. Mahoney. 22. Phys. B 8. M. 186..R. Ukr.E. Pauthenet and J.. Cryst. Binder and B. 23.. 239. Mat. 14. Paccard. Rao and R. 46. J. Krypiakevich. Harris. 1813. Phys. 20. Solid State Comm. J. Loebich. 1966b. Lemaire. 311. Metallkde 56. 329.. E.. Gladyshevskii. H. J. Phys. Loebich. 42. 1968a.V. Raub. Evdokimenko and E. 1. 1974. Bull.. Physica 86-88B. S.V. 1976. 1979. 9. LessCommon Met. Sci. Met. B. Leask and W. Koen. 123: Lethuillier. 10. Schweizer and F. Lethuillier. 1965. Sov. and J. K6ster.. and A. Rev. and E. and D. 186. S.J. BUSCHOW Liu. Z. and V. Acad.H. Wallace.G. K. 1976a. 1968.E. M. D. Suppl. Harris. J. 2. 34. Miner. M. Levy. 33.G. 1976a. J. Mullen. 2968. Craig. Proc. 1960. Allg. Longworth. no. Takeshita and W. Phys. 1977. Raub. 1964. 85... Lott. Pauthenet. 1242. University of California. R.. 141. 1976. Phys. Soviet Phys. F.R. LessCommon Met. Quezel-Ambrunaz and A. Paccard and R. Leon. 1. Kren. V. LessCommon Met. T. Levy. E. Solid State Comm. Anorg. 1976b. Lethuillier.H. . E.. J.K. P. Post. Sci. S. Raynor and I. Solid State Comm. Bronger.H. LessCommon Met. J.. K. van der Kraan and K. Rev. Lueken. Dopovidi Akad. Maita.M.. and I. G. and V. 16.S. 1969. R. 1961. J. 676-79.E.V. Bucher and J.. P. Tasset.E. AIP Conf. 1967~ C. 37. B. 104-112. Loebich. R. Maranzana. and S. R. F. 1968b. P 35. Klimker. W. 11i. 330-331. R. Rev. R. P. Malik. O.408 K.J. Wallace. B. Ripmeester. Pierre. Proc. Arlinghaus and W. 63. Lemaire.J. Lett..I. 83. 3962. P. Rev. F. and P. Tasset. Bull. Lemaire. Corenzwit and W. Klessen and W. Cobalt 32. J. 1969. 112. 1975. 30A. Cryst.. Markiv. 1967. A. Chem. P. Lea.M. 9. 105. W. LaPlaca. J.. 1521. C. Inorg. • Malik. LessCommon. 85. J. J. and I. Phys.E. Malik.. B 10. Acad. S. 113. Paccard and R. Loewenhaupt. 1964. J. 87. Soc. 1381. Wolf. K. G. Hfifner. Kuzma. Harris. Cryst.I. RSR 1964.K. 1973. 1969. Phys. Less-Common Met. Cristallogr. and M. Cobalt 33. S¢i. and E. Luijpen. Krypiakevich. and J. and W. Fr. S. Rev. Lfithi. Andres.. Acta. P. Rev. 31. and W. Chiotti. 1970. B 13. Moscow. 479. 1973.. ICM-73. 1966a.K. LessCommon Met. Mader. Co.. Obermyer. Wallace. Lethuillier. Buschow. Lemaire. Lemaire. and W. M. Bl131. Zachariasen. 1974. TOM IV (Nauka Publ. 18.G.L. M. 25.H. 355. Chem. R. 1975. Chem. 1967.I. Schweizer and F. 1975.. D. 30.H. J. 46. 1974. 1967.J. B 1280. Sankar. Phys. O. Chem. Thesis. J..R. de Phys.. J.J. Martin. 1971. Dariel and U. Kuijpers. 5. 1974. AIP Conf.R.H. 7.. Evdokimenko. R. B 13. G. Solids 23. M. 1976b. B. G.V. Phys.R. de Phys. J. 36. J. Gaug and R. and E. 218. Phys. Rev. R. J. Nauk. S. 1974) pp. 479-483. R. 1973b. J. M. K. J. Proc. 201. 1702. V. R. Rev. Raub. 7. 49.M. Res. 1977b. Skolozdra. 132. Loebich. M. Loewenhaupt. Lett. 12. M. Lemaire. 1958. Phys.. Rev. 733. 1977a. Paris 270. Pauthenet. Phys. Malik. Benz.C.A. 1973. Meier. 1971. Less-Common Met. 1962. J. I. Phys. Rosen. O.I. Percheron.P. and D. and E. 1969. J. Appi. 1970. C. 46. 970. Kuzm~/. B 16. K..R. 209.B. 1973a. LaForest. LaForest. O. 97-101. Mader.J. D. O. E.U. 26392648.K. 89. 1070.T. 329. P. Loebich. S. J. Paccard. Maple.G. 1969. P. 90. Repts. J. H. M. unpublished results cited in Morin and de Combarieu. 2818.. Craig.J. Proc. Appl. Phys. J.S. Appl.V. Arnold. W.S..V. J.S. Bergner and W. and K. Calphad 1. Morin.M. 1967. Williams. J. 39. 40A. S.H. de Phys. Baenziger. W. 1975. Furrer) (Plenum Press. Shah.V. Simmons. New York). Olsen and G.. 978. 156. Cryst. Narasimhan. Rev. 1963. M.. Crystallogr. E.B. Gordon.. Morin. Appl.J. 1968. Narasimhan.. Phys. J. 1973b. Less-Common Met.M. and E. Wallace. 729. P. 2067. Schmitt. 11. A. LaForest. J.L. 1336. Pierre and D. V. AIP Conf. Chiu. Rev. State Sol.R.L. MAG-10. T. Phys.. K. 65A. 1975. J. Barz.A. J. 425-432. Sherwood.T. Y. F 6. 13. T. K.S. LaForest. de Boer. Shirane and W. J. Eckert. 1964. 1973. Boom and F. Miedema. Ohashi and K.. Gschneidner. Drexel. 4575. J. 4724. 1966. 840. 32 Suppl. 353. 381-382. A. P. P. Muraoka.R. E. Stat.M. Meyer. C1-1133.B.H. Williams. J.L. J. J. 409 1973. 46. D. 32. C1 670-671. 4957.. IEEE Trans. Pierre and D. Burzo and D..A.. Chem. F. Moriarty.A.. Nereson.L. Appi. Corenzwit. A.R. McHenry. Solid State Comm.A. 108L Narasimhan. de Combarieu. Wernick and R.S. Appl. 1968. J. E. Appl.RARE EARTH COMPOUNDS Matthias. 44.C. 1972. LaForest and J.D. J. Miller. R..N. Lett. Butera. and W. 44. Int.. Sci.A. J.. Rev. 34. A. Acta. 53. 4932. 1965. G. J.J.R.T. Pierre. Rodrigues. C. 193.P. 37. K.A. O.S. McWhan. Matthias. R.A. (a) 17.. Science 159. B 9. Nesbitt. Butera and R. 283. K. Lett. Moriariu. 1971. 1974a. J. J.J. C. Wernick. Nesbitt.O. Murani. Nereson. C6-615..V. G. 1399. . Japan 42. and G. 10. Phys. Capponi.U. Arnold. J. 1976. Pierre and D. 36. 1973a. 1974b.. 1977. Appl. Schmitt. Burzo and D. K. Knorr and W. P.L Narasimhan. 1975. 669.E. U. J. Schmitt. 1970.M. P.. 1975. Rossat-Mignod.. Moreau. Phys. O. 74.L. Wallace and R. K..V. (Paris) 277.H.. Phys. Farrel. Phys. Phys.E.S.S. Malta. Nereson.W.U. B. B.. R.S. Physique 38. New York). Moncton. A. 13. 46. Milhouse. 25. Moon. Arnold. Schmitt and D.T. Thomlison. 879-882. 1962. E. P. 1966. Conf. /kiP Conf. Barb. Morin. K. 265. 1973. 1977. 37 Suppl. 4605. Michel. Phys.D. M. 1972.S. IEEE Trans. Boom and F. J. Lett. 311-314. D. Butera and R.G. Kaneko. Nakamura. de Boer.E. Nereson.R. K. C. J. Craig. T. Corfu.. H. B. Morin. 2958. Pierre and J.E. Mueiler. Silbernagel and J. N. D'Silva and H. 1449. L. Nuclear Mettallurg. H. Barb. Morin. Wallace. Phys. J. E. Acad. P. K.J.R. C. Less-Common Met. E. Srour.. and K. J. Phys. Gschneidner. O'Keefe and W. J. 93. M. 1974.. Geballe. 1973.C. Morin.S. Andres. J. Miskinis. R.P. Solid State Comm. Butera. Y. R. J. Olson and G. 32 C1-1124. Walker.. Phys. Series X. 1971. HartmannBoutron and J. J. 530. J. 21. 41. 19. 1978a. Phys. 1674-1678. Narasimhan. Acad. N. Proc. J. N. Nguyen Van Nhung. Solid State Comm. 1976..H. 1977. 1977. J. Soc. 975-978.S. Buschow. Knorr and K.. J. 1976. Humphreys. Appl. Kancizaki. 1978b. Morin. J. 37. 17. N. 1976a. and J. Hull and J.C. Rao and R. McMasters. Solid State Comm. 1970. 23. 13. R. van den Berg and H. Ryba. 687. Taylor. Silvardiere. D. Wernick and R. Miura. 44. 1975.M. Phys. J. Moriariu. 10. Miedema. James. 1976. V. Stewart and K. Nguyen Than-Trang.. Libowitz. P. Pierre..E. (a) 24.P. W. Shiga and Y. M. Purwins and E.J. 1164. W. Koehler and J.. Pierre. Solid State Comm.H. J.341.E. Metal hydrides (Academic Press. de Phys. 479-482. 1968. A. Appl. B. B 5. Craig. J. Phys. M6ssbauer Spectroscopy. 1977. D. Blackledge and G.H.A.S. Solid State Chem. 1972.. Pierre and J. de Phys. Sol.G. Sherwood. 33. 1977. 1971. Acta. Morin. 4727. 1965. de Phys. C.R. Nguyen Van Nhung. Phys. E. in Crystal fields in metals and alloys (ed.C. 1006. McCall.J. M. Phys. 1347. Michel.. R. H. Sc. Rao. J. 8.V. Proc.L. 39.E. K. N. 611-616. Givord. Gros.. 1963. Barlet and J. 1976b.A. Corenzwit. and A. de Phys. Narasimhan.V. 707. Morin. Chaussy. MAG-12. J. 537540. M.L Narasimhan and R.67. P. J. McMasters.. A. Phys. Nat. Phys. T.M.S. A.L. 48. Sol. F 3. G. (b) 51. A handbook of lattice spacings and structures of metals and alloys (Pergamon Press.J. 1975. K205. Palenzona. G. EPS Conf. 1. M6ssbauer. Sol. Pierre. 48.R. Sci. 1025. 1970. V. Schweizer and J. A. Achard. H. Buschow. J. 379. Furrer. Sci. Merkel and K. Naz. 5174. E. 1129. J. Mat. Gorochov and J. Phys.. Acad. 7. 1971. C.. H:. Iandelli. and A. 1963a. A. R. Siaud. Pierre. 131. Kirchmayr. S. I. J..L.W. C.H. Olson. Sol. 16. Pierre. (Paris) 271.. D. Sol. A 26. 8th Rare Earth Research Conf.. Dunlap. (a) 39. 55.L. (a) 34.. Phys. Stat.T. Proc. Kovturn. Mag. H. Phys. Yu. 9..G. Palenzona. Less-Common Met. 285-286.. Naz. J. (Paris) (B) 265. Physica 80B.. 44. Sol. B 15. Yu. Pierre. Pierre. J. BUSCHOW Sci. Phys. A. 465.W. 287.. S. H. Appl.. Rev. Pokrzywnicki. E. G.. Oesterreicher. . Sol. Nowik.. H.S. Buschow. de Phys. 1972.A. 1968. Oxford). Atti. Phys. 1972. The crystal chemistry and physics of metals and alloys (Wiley Interscience. Coll. Chem. H. Phys. Rossignol and A. Perkins. Mat. Sci. Fiz. I. Oesterreicher. Primavesi. Stalinski. Wertheim. Acad. F. Oesterreicher.. 63. J. A. OIcese.J.. 1967. J. S. Olcese. 5570-5574. 1963b. B 13. 1977.. Atti. 1967. J. Gerboc and T. Phys. K 11. 2350. J. 723. H. J. A. 1973. 1977. M.L. 10. Niculescu. p.. Phys. Fiz. 3261. 4698. (Paris) 260. Nereson. Percheron. C-l.P.7. Pauthenet. 1974. Oesterreicher. 8th Rare Earth Research Conf. pp. H. Lett. and R.R. G. Phys.D.. Atti. J. Phys. Dormann and K. Olcese. Sci. 71. Less-Common Met. 43. Proc. Appl. 33. 43. Int. 81. and P. Less-Common Met. B.J.L. Lincei Rend. 1973. Phys. Pinto. Phys. H. 24. Phys. and S. 490. I. Phys. 30. 32. Perkins. Phys. Oesterreicher. Stat. (b) 65. Acad. 1965. J.J. 1976. Kupriyanov and V.C. Acad. 1973b. 1271. 1972. Fiz.R. 1974. R. Oesterreicher. Soy. 195. Ostrovskii. C. 35.. Taylor. Wahl.R.. Lincei Rend. Pokrzywnicki and B.. and S. Paccard. 38. 1979. Walker. Appl. 34.J. Lett. Nagel.J. A33. Buschow. Nat. D.E. Oliver.J. M. Pop and M.T.H. Phys. C 9. J. G. Purwins. Stat... and K. Percheron.. Mag. Sci. H. 1971. Nevada. Pearson. 2739. F. Poldy. W. Naz.S. Parviainen.H. Oppelt. Misroch. 477. 642. 1972.B. Oesterreicher. Shaked. J.. Star. 7. Int. LessCommon Met. 1977.. G. Washo. (a) 37. and K. 701.H. Sci. Naz. 1977. Str~issler. 1963c. Oppeit. 1977b. F. J.C. K. 1977a. 403. 1. C. 1973a. 1969. A. C. A. J. 1973. Less-Common Met. A. Rev. du CNRS 157. R.410 K. V. 823. G. 1169. Phys.G. Phys. Palenzona. J. 1972. West.. Mat. Petrich. Pitts. A. Oesterreicher. 1973. and S. B1056. Solid State Comm. E. J. W. Phys. H. 143.B. A. 1967. 553. Less-Common Met.F. Sol. G. 34. Appl. Stat. F. (Proc. Appl.. Buschow. Reno. 1968. Acad. (b) 53. S. K73. A. Acad. Reno. Stat. Phys.K. Lincei Rend. 225.. 1967. Nat. and R. Pauthenet. J. 44. Acad. O. B 7. F 2. 1970. 165. J.R. Arnold and N. Jaakkola. and B. JETP 41.A. 290. H. 663. Parker and M. Paccard.F. 1963d. Star. and E. 12. Atti. Olcese. and K. Nevada. Paderno. Less-Common Met. and H. Mat. 1967. 37. Paris 264. Phys. Phys. 1958. J. Pettifor. Sci. 761.. Rosenberg.H. Acad. Lethuillier. Nowik. Acad. 8.L. (Paris) 266. 1973. 1973. 121. 1966. 1975. Abstr. New York). and H. C. 55-57. Stat. Lagnier. Oppeit. Pierre. 24. 275-282. Yakinthos. Rev... Barbara. Cohen and K. Parth~. Lincei Rend. OIcese. Oppelt. ICM 1979). Nat. Buschow. 23. D. and R.H. J. Fiz. Orehotsky. 1020. Pearson. 701. Paderno. L212-L215. 34.N.. Sci. 1972. C.M. 1976.. Mag. 1976. Nikitin.J. 1968.L. (Paris) C 277. Campagna and G. 1976.R.R. 1980. Oesterreicher. Phys. J.K. and R. J. Vasilkovskii.A. J. Phys. Nat. K75. Phys.. A. Acad. Rev. Sol. 1978.R. Sol. B. 1483. 3. 34. Sci.L. J. and H. J. Mat. 1975. de Combarieu and R.G. Pitts. and R. R.P. 34. Hoffer. 1968. Wallace. Internat. Phys. 1975. Schweizer. 1561. J. Givord and R. Z. 11.H. and B. B. K. 254. Rosenblum and E. KI01. Savitsky. MAG-11. New York). 70A. Rieger. J. 1. 42. O. S. Shunk. 1317. Dariel. Phys.P. 420.684-692. 35.J.M. G.. Sol.P.S.J. and C. Phys. Crystallogr. Cobalt. Ross. A. K.J. LessCommon Met. C 9. 1976.S. 180. 1968.E. 1970. Ray. and J. 1969. J. Ray. Shirley. L. 1975.C. Japan 21.. D. Rev. C 9.J. 1972. Bierman. 1975. T. 1967. Phys. E. Shoemaker. 1964. Gambino. Stat. 1966.A. 1973.. L. Shaffer and C. and F. 96... 1965. R. CNRS no... 444. Sekizawa. W. 2207.. 1968. Chem. 1973. A. Sol.K. unpublished resulted quoted in Ray and Silvadiere. Sch~ifer. 1976. R.. 19. Sekizawa. 279.. W. Atzmony and M. and V. Acta. Acad. K.R. Sales. and W. Sankar. D. Leciejewics. and I. Sankar. Phys. 37. 1976a. Rev. J. 1954. P. S. Acta.. V.E. W. Phys. Coronado. p. James. Wohlleben. Ruggiero. Metal.H.J. 473-484. D.W. F.. Shiryayeva and V. Berlin). M. W. Toxen and R. Lett. 1976. Solid State Comm. Sigalas. Rao and R. Tech. L.C.W.. J. 1969.R. Elschner and K.J. F 5. Phys. Will and K. Pauling. Ray. Silvadiere.274. 28. J. Japan 21.. Sill.K. S. Ya. Atti. Marsh. A. Crystallogr. Phys. E.E. Phys.V. Constitution of binary alloys. Grant. Co.D.A. Buschow.F.R. 1060.. 1964. New York). AIP Conf.T. Sampathkumaran. Kristallstrukturen zweikomponentiger Phasen (Springer-Verlag.G. 1429.U. 239. 169. Kimball. Wallace. F. pp. 2nd suppl.I. 30. Shenoy. Phys. 10.M. Solid State Comm.H. Phys. 35. Rev. V. Garret. H. Sekizawa. J. L. Johnson. SOc. J. Phys. E. 28-35. 1973-1973.J. D. V. Phys. and A. W.J. Sci. Metailoved 39. 1979. Smith. Wallace. Tharp and Q. S. H. Wernick and V.B.K.G. Appl. Terekhova. Mat. A. SchSfer. 1964.U.R.K. J.. 1975. J. Mass.G. 1118.K. AIME 245. Buschow. Coil. Strnat. Percheron and J. M.. and K. 1240. 1969. Phys. Jaccarino. Yakinthos.. 1976.J. J. Sadagopan. Klimker.. W. 4. SchMer. E. D.M. 1963. W. Mag. Gupta and V. Lett. 363. 1968. 1049.S.G.. 637. L. 99. Harris.. Siek. Chem.. J.J.E.. Olcese and G. Rev. 1994. Proc. $. Japan 21.A. AIP Conf.A. Phys. 236. 1356. (McGraw-Hill. 1976. Phys.. 34. Proc. Soc.RARE EARTH COMPOUNDS Radhakrishna. Simmons. 35. B. W. J.. 1966b. 1968. Phys. 7th Rare Earth Research Conf. Fiz. V. Appl.M. Rao.. J. 1053-1057. Moreau. J. K. Rosen. Lemaire. Ray.. 1846.S. Monatsh. Schubert. G. V~ayaraghavan. 435. 14. 1966a. H. 1975. 1971. Proc. and K. 940. Bonino. University of Grenoble.F. 1976. 1978. B. J. A. J. 1975. Phys. Shaltiel. P. S. Smith. Phys. 24. Chem. Parth~. Wernick. Salmans.I. Yasukochi.K. AIP Conf. G. Mag. Matthias. Obermyer.J. Yasukochi. G. 1967. Buschow. Phys.K. 170. Soc. Furrer) (Plenum Press.H. U. G. A. Fedro. IEEE Trans.. AFML-CF-68-159. M. Phys. J. Moscow). 1974. Fedro. 1973. Nat. Sankar. 513. Scrabek. G. Rept. 1964. Harmer and J. W. Schweizer. 22. J.. S.E. 41.E. Metallography of rare earth metals (Nauka Publ. 1036. Buschow. K.. Sanchez. Ruderman. and J. 1964.P. Ewring and L.K. J. 1137. Appl. 1297. 1976b. 14711474. Yasukochi.U. 1977. Strnat and G. Kalvius. Trans. Will and K.R. .L.J.D. 1952. G. Singh. Schmidt. Lincei Rend. Malik. Dunlap.G.C.E. (a) 29. J. Sherwood. AJ. Prindeville. J. K. Thesis.C. Fiz. Williams and J. Sekizawa. 216.. Mag. Will and K. and J. Paris-Grenoble.E. G. Shenoy. J. B. and E.H. A. Cal. Shur. 356. Giessen and N. Davison. 37. Proc. 75-82. 411 Sch~er. Kittel.S. B 11. Less-Common Met.M.. 978.. A. A. Chem. Snow and A. Raman. Sill. A. Ray. 64. S.C.S. 100. L657-L661. and K. 1977. and K. Frederick and H. Malik. Maykov.C. Friedt. Lett.G. Rao and W. and D. J. in Crystal field effects in metals and alloys (ed. S.R. Mat. Phys. Sol. J.J. Livet. Segal. Achard. Appl. S. Szytula and J. 15. Sill.F.H. F. Appl. and P. TOM V (Nauka Publ. Phys.A. L55.J. Janneck and K. Stearns.J.. 230. C 2237. 29. Kawano.J. Harris and W. University of Amsterdam. Lindgard. Phys. 1975.I. (a) 31. 93. Buschow.H. M6ssbauer Effect. Gardner. Ann. 4383. 1979.E.H. KJ. Conf. 490. F. Phys. F. Soc. and B. 1977.I. Buschow. Tamminga. 853. Phys. and R. I. Christopher. S. Hoffer. U. Rev. K. Sol. Schmidt. P.J.M. Sugaki and Y. Frankevich. 1974.H. 1970c.H. Takeshita. and W. J.. Crystallogr. see also Fisk et al. 94. 24. Buschow.J. Prof. Buschow. Buschow. J. Nat.P. J. 1973. 23. 137-151.J. van Daal. 151-157. Phys. K. Ostertag and J. 3833-3840. and B. Appl.L.J. F6. 1970a. 246.F.. CNRS pp.M..J. Strnat.. B. Olcese. van Apeldoorn. and K. 2704. Sol. Steiner W. 7. B 19. Prof. Phys. K. and P. MAG-7. K. Adv.S. 43. K. 1970b. Ukr.M.C. Nauk. Z. 1970. pp. 21. Stat. van Daal. Dopovidi Akad. IEEE Trans. Matthias. 2091-2096. Gubbens and K. Hrubec. Phys.. 1977. 1974. B. Mydlarz. Sol. (a) 3. Stalinski. 1977. Tsuchida. M. 34. A. Phys. 9. Teslyuk.. K.E.J.. P. 1976. and B. Tomala. Phys. AIP-Conf.. Soc. Japan 39.B. J. van der Kraan. 458. A. A.C. 205. and K. Rep. J. Fink and H. C.M.. Chem.R. (a) 35. B. Adv. van Daal. Ray. Buschow. and K. J.N. van Daal. W. 37.E.I. 1971. Gubbens.M. van der Velden. Stalinski.M. R. Sol.Soviet Phys. Phys. and P. R. Steiner W. (b) 82. A. J. Y. Wallace. Benson.. Stat..J. J. 14.. Umezaki.J. G. 1975. 1976. Iliew and T. Strnat. S. Phys. 1977. Rev. Furrer and A. Buschow. J. A. 1969. Aust. U. and J. Buschow.F. Phys.C. 1975. 1977. van den Broek. 226. Gubbens and K. Phys.K. K157.H. van der Kraan. 1974.C.J.495-501. 1968. 1963.. 1974.. (a) 31.M. 1977.. Buschow. 1976.I.E. Lett. and W. J. Terekhova. van Diepen. van der Kraan. 551. S. Sol. 1974) p. 87.H. P. Moscow. (b) 82.S. Phys. 1953.P. 1973. Stat.M.H.A. 449. 1971. 165-174. Sol. and H.. 489-493. B. J. H.412 K. R.N. Rev.H. Gubbens and K.H. Rev. A.K. 209. Shibata. H. 4081. Met. van Aken and K. J. 701. Szpunar.E. A. IEEE Trans. Boekarest. 24. Co. B.B.J. 349. Stat.. M.. H. Ray. Steiner W. 1125. Acta.R.. Phys.H. Phys. Taylor.J. 1967. 1979.. B 8. H. Czjzek. 143-153. V. and K. Yu. Ortbauer. and K. Chem.T. Less-Common Met. 857. van Daal.. Olson. G. Taylor. Sol. Thesis. G. J. E. 68t. J. Costa and G. Tannous.H. Millhouse. . Metallkde 61. Phys.J. 1970. Strnat. Prof.M. Belakhovsky. Star. 113. A65. Streever. 18.M. van den Berg. and H. 4. Stewart A. J. 1974. Kripyakevich. P. Stat. Kyoto Univ. 1977.W. 9. Sci. Sol. LessCommon Met. D. Solid State Comm.R.H. Russ.J. Soc. 1966. Achiwa and T. 217. Prof.H.H. Phys. 1965. 74. Stalinski. 408. El-Attar and W.A.M. Lindgard.C. 1964. 1961.H. Physica 86-88B. Phys.M. Stearns. A. 1975. Weihs. P. A 165. 1966. 31A.. 27. Acad.R. and K. 1938. and K. and S. Tsuchida. A. Steiner W. van der Kraan. 107-109.. Les elements des terres rares. 16.M. and J. (1971). and A. B. Krypiakevich and D.. 7. Stewart A. M. 121. 1976. Phys. J. T. Phys. 469. 41. Less-Common Met. Stevens K. Phys. 45. Planck and G. Phys. 1977. 1974. Tellenbach. RSK 1039.H. Ray and M. T. H.J. 1975. Malik. 340-343. Phys. A.H. G. Torchinowa. Phys. Prof. 1973. Haferl. 103. Szpunar. (a) 42. 1. 372.J.. Magi 2. J. van der Goot. Phys.. Szpunar. suppl. Krypyakevich. Pokrzywnicki. I. Sperlich. Sol. Stat. Stoner. D.. G. 1336.. 3811. BUSCHOW Taylor. 551. 1975. (b) 57.J. II. 1966. Solid State Comm. 1971. Stat. Taylor. Cryst. Buschow. and P. Swift. Phys. Nakamura. Frankevich and R. 22.J. A. Wallace. 12. Reactor Inst. Sol. 1976.A. J. 1967.B. Coles. 383. 739. Teslyuk. and K. Stat. 461-470. B 4. 1974. 1252-1253. AlP Conf. P. W. KIIg-K123. Lett. C6-469-472. Storm. C 8.J. ICM-73. Proc.C. J.N. 2053. 701. Wallace.H. Kozarzewski. N.J.E.H. M. van der Kraan. Zijlstra. Phys. T. H. A.M. Prof. Busfhow. Phys. 49A. de Phys. Lett. F 5.S. Buschow. Roy. Hoffer and A. Czopnik. Solid State Comm. Kuprianov. JETP 38. 1964.O. 1965. Velge. 35. Star. J. 1684.. Buschow. de Wijn and K. Mat. Phys. H. New York) p. van Stapele.H.K. Solid State Comm. 22. Chem. Soc. J. S. C. Chem. Phys. Lchmann and K. R. Phys. and J.. 1977a.. Rupp. Malik and V. and J. V.E. Walker.F. LeFever.J. Mat. Hullinger. H. and M. J. J. 1969. G.M. 1975a. F. and Y. Hirst. Soc. G. Wickman. Wallace. pp. 203. 1973. Wang. Walline. Vonsovskii.J.E. de Phys. 1966..L. Wallace. Phys. Wang. 6. van Steenwijk. 19. Magn. Vorres) (Gordon and Breach. 1974. Fischer. 91.H. 1969. 6. Rare earth intermetallics (Academic Press. 1717-1720. Will. 686.J. 1086. AIME 218. J. Buschow. 39. Thiel and K. Rao.E. Weimann.H. Acad. Trans.J.W. Crystallogr. F. 1962. Williams. K.V. Buschow. Swearingen. Appl. 476-481. B. J. III. J. Mag.. Sol. Phys. Purwins.A. Winterberger. Bloch. A. 137.. 3285. Phys. 1974.R. Williams and A. 589. 1964. 1967. T. M.E. A.M. Vlasov.H.G. J. Soc. Marathe.. W. Sol. 319. 1964. P.E. J. Kondens Materia 13. Jaccarino and J.. Wallace. J. (b) 48.H.P. J. M.M. Less-Common Met.J. Paris 274. J. G. A. 1971. W. A.A. 949-952. Pierre. V. van Steenwijk. W.Thesis.H.M.J. G. University of Leiden. Monatshefte fiir Chemie 102.Th. Wang. Geller. 1-3. Volkmann and H. Int..J.E. Wernick. 1125-1129.H. 871. Buschow. Voiron. 604.J. Bargouth and K. Nesbitt and R. 1977b. 431-441. 1-37. R. H.J. New York). Appl. Solid State Chem. Watson. J. H.W.. G. M. 3. 21. Mag.W.H. H. 41. Y. 98. W. Jr. de Wijn.R. 1967.. Miedema.H.J. and S. and D.Th. Elschner.J. Solid State Chem. Buschow and H. 141.N. J. Thiel and K. 8. 189. R. Voiron. 342-344.E. 1971. 8. 6.H. Proc. Buschow. Buschow.R. W. Mag.. Wernick. R. Belakhovsky and J. J. H.. 131. 28.J. J. Elschner and K.E. Chem.H. Phys.H. S.H..W.. Nikitin and V. 1973.H. J. Wernick.A. 151-154. see also the quotation in Joseph et al.H.E. J. J. New York). AIME 233. and B.. and B. H. Chamard-Bois. van Mai.J. Phys. Inorg. Wagner. van Vucht. Rare earth research. Rep. Buschow. 10.C. and M. Bargouth. Wallace. Proc.L. M. Buschow. F. Vijayaraghavan. van Diepen. Kovtum. V. H~ilg and E. and Tech. Weik. J.F. Gossard.H. 51. 185. Chem. Magnetism (Wiley. and J. W. 731-736.H. A. Wertheim. L. van Diepen. H. 1967. II.U. R. Will. Phys. 705. 29.M. Aoyagi. E. Sherwood. G. 11. Phys. (ed. J. 46. Wilhelm. W. 20. Wallace. and W. Buschow.H. van Vucht. 1965. H. 1974. Philips Res.N. Rev. Met.C. Met. Hillenbrand. H.B. de Wijn and K.T. Wallace.J. 1975b. Ostrovskii. 604. Mag. J.A.E. 1455-1461.G. J. 4th rare earth conf. 1972. Stoll... 1968. Z.J. Trans. 413 Chem. 32.H. R. Buschow and A. 866. B. Williams.J.J. Less-Common Met. Vasilkovskii. Wallace.J. 1971. Thiel and K. 1968. and K. 607.. Phys. Wallace. A. P..J.H. Sherwood and C. Buschow. W. Chem. van Steenwijk. and E. 510514. Holden. 1968.H. Less-Common Metals. and W. and L. Huiskamp. Bopp. Hopkins. 271. 3489. Phys. Sci. 1976. R. Jr. 1960.A. W. Rev. 29.E. 1964. G. Wallace. H. 1972. Skrabek. 1973.E. 1973.J.. A 13$.J.K.R. 1969. 87.O.. V.. G. 1971.C. Rev. 1971. Soy.C.O.K. Walsh. 37-38. Walline.J. Cooper.V. W. Buschow. 65. Landor and F. 26a. New York). F. Phys. 181.C. K. M. suppl. Frankel) (Academic Press. Buschow and R.E. Solids 29. F.RARE EARTH COMPOUNDS van Diepen. Physica 7911. Acta. van Steenwijk. Wernick.H... 42. E. de Wijn and K. Mag.J. Chem. 1967. 1971.M. AIP Conf.J.H.H. Freeman and R. H.D. 1965. N.S. J. 5. R. 3. LeFever. . 1975. Naturforsch. 1968. and K. 1977. 1964.E. Physica B86-88.. Sol. and K.C. Schmidt and L. Stat. Rare Earth Sci. Phys. J.H. J. 39. Bargouth. Japan 17. J. P. LeFever. Phys. 33. F. Physica 7911. B-l. Weimann.J. and M. 89..Th.. 696. in Hypertine interactions (eds. Prog. 185. R. 1968. S. 407. Gilfrich. 1972. W. Buschow. K.P. Phys.H. Int.. Will. (1972). Rev. Phys.. 2216.. 1973. Will.W. 5259~ van Diepen. Longinotti. Wernick.. Yakinthos. 1972. Phillips. . B. H. J. 50A. and N. Japan 21. 1977a. Yakinthos. 207. Yakinthos. 1957. 989. J. K. Soc. J. Yakinthos. 63. 1977. Watanahe. T.J. 1965. New York). Yakinthos.K. J. Rentzeperis. Phys. J. Stat. BUSCHOW Yakinthos. Phys. Kripyakevitch. 68.K. L123. Anagnostopoulos and P. 10. Lett.S. Rev. 1975..P.K. 1979. Solid State Comm. 51. J. Yaguchi. 195.E. Yashiro...F. J. T. Stat. Phys. E. Yakinthos. Phys. Y. Phys. Phys. 436. Phys. K. V. Physica 86-88B. 1977a. Phys. Sol. 747. Less-Common Met. Yakinthos. 39. 893. Stat. SOL (b) 82 349. J. Mentzafos. (h) 64. E.E.. Yosida. Yakinthos.H. Phys. M. Soy. Chem.P. J. 1977b. Roudeaut. Wun. (a) 39. and J. Zarechnyuk. F. Phys. 1977b. and E. 12.E. 113. 9. 1969.K. 1963. Stat. and P. and D. J. O..K. Ikonomou. (b) 50. J.. Wybourne. 7.. (a) 40. 1978. Crystallogr. Yakinthos. SOl. 37A. and D.G. J.. Hamaguchi and H. Sol. Japan 40. Wohlfarth. Wood. Phys. Sol. J. phys.. 1974. Stat. 1976. 485.K. Phys. C 2. Sol. Rev. 106. J. 643.I. Wohlfarth.414 K.K. SOc. Rossat Mignod.K. Paccard. Phys. 1966. KI05. 357. Gamari-Seale and J. J. 1971. Laforest. Phys. Spectroscopic properties of rare earths (Interscience. 1974..J. 1928. KISI.. Lett. and P..405. 1972. J. Wohlfarth © North-Holland Publishing Company.chapter 5 ACTINIDE ELEMENTS AND COMPOUNDS W.P. Vol. 1980 415 . 1 Edited by E. TRZEBIATOWSKI Institute for Low Temperature and Structure Research Polish Academy of Sciences Wroctaw Poland Ferromagnetic Materials. . . . . . . . . 431 3. . .5. . . . . .2. 419 1. . . . . . . . 423 3. . . . . . . . . . . . . . . . . . Survey of magnetic properties . . . . . . . . . . . . . . 417 1. . . . . . . . . . . . Final remarks . . . . . . . . . . . . . . . . . . . . . .2. . Intermetallic compounds . . . . .2. . . Electronic structure of actinides . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3. . . . . . . . . .2. Solid solutions . . 429 3. . .2. .4. . . . . . . . . . . . .2. . . . . . 425 3. . . Compounds . . . . . 425 3. . . . . .8. . . . . . . . . . . . . . . . . .2. . . . . . . 427 3.1. Magnetic properties of elements . . .1. . . . . Ternary compounds . Hydrides . . . . 443 References . Pnictides . . . .1. .2. . . . . . . . . . Elements . . .1.2. . . Magnetic properties of compounds . . . . . .6. . . . . . . . . . . . . . . . 418 1. .4. . . . . . . .2. . . . . . . . . 433 3. . . . 444 416 . . . . . . . . . . . . . 417 1. . . . . . . . . . . . 422 2. . . . . . . . . . . . . . . . . . 422 2. . . . . . . . . . . . .3. . . . . 421 2. . . . . . . Chalcogenides . . . . . . . . . . . . . . . . . . . . 425 3. . . . . 433 3. 439 3. . . . . . . . . . . . . . . . . . Magnetic ordering in elements and compounds . . . . . . . . . . .or intermetallic compounds . . . . . C o m p o u n d s with IVA and I l i a group elements . . . . . . . . . . . . Preparation of metals and compounds . . . .2. . . . . . .7. . . 443 Monographs and review articles on magnetic properties of actinide elements and semi. . 425 3. . . . Characteristic features of 5f electrons in the solid state . . . . . . . . .2. . . . Comparison of crystal structures of lanthanide elements and compounds with those of actinides . . .CONTENTS I. . . . for example. The 5f electrons of the light actinides are delocalized and their bands significantly overlap their neighbours. But in the solid state the elements and their compounds differ in some particular features from the lanthanides. The Seaborg concept concerning the existence of a homologous family of the 5f elements has been once more directly confirmed by X-ray photoelectron spectroscopy of solids which identified the 5f band. extensive theoretical calculations have been given. plutonium and others. elements and compounds is very large. there exist distinct differences in the behaviour and properties of the 5f electrons in comparison to the 4f electrons. Its half-widths diminish continuously from uranium to 417 . The density of states and the Fermi surface have been calculated. according to its physical properties like the high melting point of the typical metallic fee lattice. especially in the case of the lighter elements. However.I. uranium. In spite of the fact that the band structure of actinide metals is complex. Thorium atoms. y-U. Electronic structure of actinides The electronic structure of the actinides allows appreciable analogies to be drawn with that of the lanthanides. in UO2 (Veal and Lam 1974). I. Freeman 1979. concentrating naturally on the simpler allotropic forms such as a-Th. Koeling 1979). because they include fissionable isotopes useful for energy production and because they offer the possibility of producing new transuranium elements either as byproducts of reactor processes or through nuclear reactions by means of accelerators.I. Introduction The interest in the physical properties of actinides. These elements are far less well-known than others. Therefore thorium. do not contain the first 5f electron. The calculated hybridized 5f-bandwidth is narrower than the d-bandwidths in the transition metals. The electronic structure of the actinide atoms (table 1) is quite similar to that of the lanthanides. so that some details about their crystal and electronic structures will precede the description of their magnetic properties. particularly for thorium. hybridizing strongly with the 6d and 7s band. or y-Np (Freeman and Koeling 1974. 8-Pu. in contrast to cerium. behaves rather as a transition d-metal. These metals show no magnetic moments and their magnetic susceptibilities are practically independent of temperature.418 W. the smaller are the interactions of their electrons so that the 5f electrons gradually occupy localized states and magnetic moments appear (Hill 1970a. 2 Es 10 11 2 6 . *An excellent review on the electronic structure of actinides and on their physical properties is given in the book " T h e Actinides". The conditions for the appearance of magnetism in metallic actinide systems have been recently discussed by de Novion (1979). curium and the following metals show distinctly localized 5f states. Koeling 1977). A. T R Z E B I A T O W S K I TABLE ! Electronicst~ctureoftheactinides Ra Ac 10 2 6 ! 2 Th 10 2 6 2 2 Pa 10 2 2 6 1 2 U 10 3 2 6 1 2 Np 10 5 2 6 2 Pu 10 6 2 6 2 Am 10 7 2 6 2 Cm 10 7 2 6 l 2 Bk l0 8 2 6 1 2 Cf 10 10 2 6 . The larger the mutual separation of the magnetically active actinide atoms or ions in the lattice. In contrast to the lighter actinide metals. With increasing atomic number the 5f band becomes more and more narrow and finally these electrons behave as those of the 4f family. Characteristic features of 5f electrons in the solid state Metals of the first half of the actinide family exhibit. they recall the d-transition metals. b). eds. Such an electronic structure explains very often the physical properties of the actinide metals and compounds with increasing atomic number*. (Academic Press. The 5f electrons are also much more strongly influenced by the crystal field than the 4f electrons in the case of the lanthanides. 1. Uranium and plutonium are the metals to which most attention has been paid.J. . but great difficulties arise in the theoretical considerations because of their complex crystalline structures. N e w York). Freeman and Koeling 1974. Jr. F r e e m a n and J.2. Darby. These 5f states must also be considered as itinerant in contrast to the lanthanides which form narrow isolated bands of a localized character. as mentioned above. 1974. 2 2 No 10 14 2 6 Lr 10 14 2 6 1 2 5d 5f 6s 6p 6d 7s 10 2 6 2 S e q u e n c e of lanthanide e l e m e n t s La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu americium metal (Kmetko and Hill 1970. Fm l0 12 2 6 . a predominant itinerant character. This is a consequence of the more spatially extended nature of the 5f wave functions and their natural overlap.B. These circumstances arise even for the electronic states of uranium if their compounds are being considered. 2 Md 10 13 2 6 . and for compounds by Suski (1979). 2 . ACTINIDE ELEMENTS AND COMPOUNDS 419 1. and s bands overlap. within the subgroup (2) f. Attention will be paid here to the intermetallic or semimetallic compounds because they offer numerous examples of magnetic order. UZn12. CuAI2.occurring in the typical transition metal structures. The plot of atomic volumes against the atomic number of elements shows . They occur partly also among the lanthanide compounds. PbFCI. The heavier actinide metals have again simpler crystal structures. There is a particular interest in the compounds of uranium and plutonium with small interatomic An-An distances and refractory properties. The subgroup (1) contains no f-electrons. ThB4. AIB2. and within the subgroup (3) the localized character of the f-electrons prevails. Np.g. The first two representatives of this family. The crystal structure of actinide metals is often much more complicated./3-W. U. Np and Pu offer at least three allotropic modifications. U3Si2. often of an unconventional type. Comparison of crystal structures of lanthanide elements and compounds with those of actinides The crystal structure within the lanthanide family is characteristic of metallic lattice types like fcc. (3) Am and b e y o n d .3. PullSe9. UBI2. A large number of new types of crystal structure has been identified among the actinide compounds such as Th3P4. UA1. ThTFe3. The only exception is a-Sm which is rhombohedral. and double hexagonal unit cells (dhcp) such as occur among the lanthanides (table 2) are common. Pu2C3. CrB. Mn203. AuCu3. and the example of plutonium existing in as many as 6 allotropic modifications is quite unique. The latter is orthorhombic and isostructural with a-U (Ellinger and Zachariasen 1974). carbides. bcc and hcp. Pu . An interesting relationship also exists between the structure of a representative element of the 4f. nitrides and others. UHg3. Th2ZnmT. The number of allotropic modifications do not usually exceed three unless a high static pressure is involved. Laves phases and other types. oxides. namely actinium and thorium. The crystal structure of the compounds generally depends on the kind of bonding forces and on the ratio of the components.having numerous and often uncommon crystal lattice types. but already a-Pa has a tetragonal unit cell and each of the three elements U. From this point of view the actinide metals are divided into three subgroups: (1) Ac and T h . (2) Pa.with the crystal structures corresponding to those of the lanthanides. PuAg3. which occur especially at higher temperatures. PuNi3.and 5f-family. e. show the typical fcc metallic structure. suitable as reactor fuels. U3S5 and others. Certainly it is the f-band which influences the crystal structure. The hexagonal close packed (hcp) a-phases of numerous lanthanide metals occuring at normal temperatures mostly have their unit cells doubled along the c axis. The fcc lattice of a-Ce transforms into a'-Ce under a pressure of 56kb. These compounds often belong to common lattice types such as NaC1. U3Si. Cu2Sb. Pu3Co. PuAI3. Th6Mn23. d. 497 5.331 5.822 (B = 101.463 (B = 92.887 *After T a u b e (1974).768 face-centered A2 tetragonal 4.-U a-Np B-Np y-Np a-Pu /3-Pu 3.420 W. The heavier transuranium elements again approach the atomic volumes of the M-elements (Julien et al.139 5.44 body-centered 641 95 A2 double11.929 3.743 3.859 10.6 3 and 70). 1.069 hexagonal 986 900(7) 860(?) 98 99 Aj AI A3 At 6.887 3. The intermediate plot represents the actinide elements.284 3.11 3. As evident from fig. some interesting differences for the 3d-transition.34 3.0843 4.637 3.636 3.8537 10.416 4.241 1079 hexagonal 1175 96 AI double11.183 9.525 6. This also indicates the intermediate character of the 5f electrons as being responsible for this behaviour.335 hexagonal 1340 97 A1 double- 11.81 2.25 b 1400 3.52 6.897 3. which at the beginning follows closely the curve of the 4f-elements and then lies between the curves of 3d and 4f elements.79 °) 10..039 3.8695 (805~ 4. the lanthanide and the actinide elements. 1972).159 4.-Pu 8-Pu 8'-Pu e-Pu a-Am /~-Am a-Cm /]-Cm a-Bk /3-Bk a-Cf B-Cf Es system AI AI A2 tetragonal AI rhombic tetragonal A2 rhombic tetragonal A2 monoclinic a 5.997 5.652 4.241 5.388 10.9548 5.894 3.723 4.763 3.963 7.988 5.663 4.162 1170 668 772 278 577 115 185 310 458 480 1132 93 637 94* simple monoclinic body-centered ortorhombic 4.4680 4. the 4f-elements have the highest values of atomic volume with the very well known two maxima for europium and ytterbium ( Z . TRZEBIATOWSKI TABLE 2 Crystal structure of actinide metals Melting point °C 1050 1690 1560 Lattice constants Type Atomic number 89 90 91 92 Transformation temperatures °C Element Ac a-Th /3-Th a-Pa /3-Pa a-U B-U 3. . curium. PH3) may also be carried out (Baskin 1966). A common method of the production of uranium compounds consists in preparing fine uranium metal powder obtained by the hydrogenation of massive metal into UH3 at 250°C. in contrast to the other metals which. Atomic volumes of 3d. and finally by reaction with the other nonmetallic component (Trzebiatowski et al. The transuranium metals are a-emitters and because of their activity and toxicity glove-boxes must be used. berkelium and californium as metals or as compounds have only rarely been studied. 1967a. Preparation of metals and compounds The actinide elements are reactive metals and therefore their production must be carried out in a high vacuum or neutral gas atmosphere of the highest purity. neptunium and plutonium compounds. with the exception of plutonium. are available only on the gram or microgram scale. Because the heavier transuranium elements are accessible only in very small quantities. Compounds with a lower content of the second component may be obtained by thermal dissociation. as in the case of pnictides or chalcogenides. Under these circumstances it is not surprising that the solid state investigations of the actinides were mostly performed on thorium.io-_ Fig. actinium still awaits its turn. Protactinium. 1.b). Thorium and uranium are produced in large quantities mostly by calcium or magnesium reduction.ACTINIDE ELEMENTS AND COMPOUNDS VOLUME (cm3) / ~ 421 20 10 TRANSITION METALS I I I I I I L I - ACTINtDES LANTHANIDES TRANSITION f METALS [ Ac Th Pa U Lo Ce Pr Nd Y Zr Nb Mo Lu Hf To W Np Prn Tc Re Pu Sm Ru Os Am Eu Rh Ir Cm Od Pd Pt Bk Tb AO Au -'4"---~-. like curium-242 exhibit also strong self-heating effects which make precise physical measurements difficult. and especially on uranium. 4f and 5f elements (after Julien et aL 1972). magnetic and other physical measurements have so far been rather rare. then by decomposition of the hydride by vacuum dissociation. The direct reaction of the metal hydride with the other elements (Naoumidis and Stocker 1967) or the reaction of metal with the gaseous nonmetallic hydride (e. .4. Isotopes with shorter half-life periods.g. 1. Spirlet (1979) and Calestani et al. thorium dioxide or metallic tantalum. producing the actinide phosphide or telluride simultaneously by volatilizing the zinc (Lovell et al. TRZEBIATOWSKI A volatile process may be applied which consists in heating the actinide metal with a suitable compound like Zn3P2 or ZnTe.8 x 10-~ emu/g for americium metal. Bridgman and others. 2. Recrystallization of the substance just below its melting point may produce single crystals. Much larger values were observed for Cm. (1979). This method uses the reactive gaseous substances like chlorine. Other microscale preparation methods of transuranic compounds have been given recently by Damien et al. 1971). 2. the magnetic susceptibilities are known only for a certain number of the actinides from thorium up to californium inclusively. Henkie and Klamut (1977). (1979). alumina.g. Their room temperature values range from +0. (1972). During the last 10 years a large number of contributions about the magnetic and electric properties of actinide compounds was published. Slow crystallizing of high melting compounds like US directly from the melts obtained by electric arc. which however necessitate the highest vacuum or a pure inert atmosphere and appropriate ceramics as crucible materials. Buhrer (1969).422 W. Survey of magnetic properties The magnetic behaviour of actinide elements and their compounds is especially interesting because they show a wide variety of often complex magnetic properties.(section 1. Wojakowski et al. However. neither the simple band theory nor the localized electron theory are able to explain them completely. (1972). . and the metal single crystals are obtained by the known methods of Czochralski.1). Crystallization of intermetallic compounds like uranium dipnictides. for example USb (Lander et al. so only a part of these can be cited in the following sections. electron beam or induction heating may also result in single crystals (Tillwick and du Plessis 1976a. especially applicable to the compounds of actinides with nonmetallic components. beryllia. Bk and Cf (Gmelin 1976). chalcogenides or phosphides (U3P9 from low melting and nonreacting metallic melts such as bismuth or antimony also give positive results.b). Sevastianov et al. However. For physical measurements single crystals are often required. Magnetic properties of elements The magnetic properties of actinide metals generally follow what is expected from their electronic structure . e. Examples are given by Henkie (1968). I. bromine or iodine as a transporting agent acting on the polycrystalline samples and depositing small single crystals on the other side of a transport tube placed in a furnace with a constant temperature gradient.412x I0 -~ emu/g for thorium to +2. consists of vapour transport processes. Another method. 1976). After Hill (1970a.8 ttB. The first magnetically ordered compound among the actinides was the ferromagnetic uranium hydride ~ .18/zB) or Cf ÷3 (10.1).~ = 8.25 . The susceptibilities of thorium. The first value agrees very well with that calculated for the f7 electronic structure. although among the homologous lanthanide metals a large number of ferro. and these formed a new family of magnetic materials similar to the hitherto well known lanthanides. Californium metal has a magnetic moment of 9. Contrary to these metals. so they may be consequences of spin fluctuation effects. although not so high as in the case of d-transition elements or compounds.8 ~B.~ for neptunium . although in the case of Am-metal it contains 3+ metallic ions with six f-electrons. yielding values of the magnetic moments P. Neptunium and americium behave similarly.6 K (Smith et al. One feature concerning these two groups of elements should be emphasised: The ordering temperatures of actinide compounds are commonly higher thah in the case of lanthanides. 8. Curium metal is especially interesting because it is the only actinide metal which is magnetically ordered (section 3. According to expectations the lighter metals like Th.2.6 .~ for uranium. This gives J = 0 and Van Vleck magnetism is responsible for the observed properties.and metamagnetics exist. especially for the lighter members of this family. Contrary to the elements there exist a large number of magnetically ordered substances among the compounds.22/~B) ions. but no ordering effects could be proved. The phase transformations of elements are evident on the susceptibility-temperature curves and a small maximum in the susceptibility at 10 K and a minimum at 40-50 K were detected in plutonium.U H 3 .b). identified by Trzebiatowski et al. Numerous other ordered uranium compounds such as chalcogenides and pnictides were discovered soon afterwards by the same authors (Trzebiatowski et al. respectively. 2. slightly lower than that calculated for both Cf 2* (10. 1978). Pa.2 and 8. also characteristic of Gd 3÷. berkelium and californium show a normal temperature dependence for the paramagnetic susceptibilities. (1952).0/za. Np and Pu show practically temperature independent Pauli paramagnetism. 1967).4-3.7 ILB. curium. uranium and the following metals increase slightly with temperature and some suppositions about low temperature transformations in uranium have been made. U.ACTINIDE ELEMENTS AND COMPOUNDS 423 The other metals are still not available in the necessary quantities. these critical minimal distances are 3.7-9. The localized magnetic moments occur if An-An distances are sufficiently large so as to diminish the overlap of the Lelectron bands. The data for berkelium metal is less certain and the homologous terbium ion Tb 3÷ has a moment of 9. 3. Magnetic properties of compounds The magnetic properties of metallic or semimetallic actinide compounds are very interesting and the individual magnetic character of these elements shows up more distinctly in the compounds than in the elementary state. It is interesting to remark that americium is unexpectedly superconducting with Tc = 0. as is evident from fig. UP. For example. If these values are exceeded. Among the actinide compounds the following classes may be distinguished according to their magnetic properties: (1) Without distinct magnetic moments and ordering. Isostructural compounds like US. the kind of magnetic order depending primarily on the second component. TABLE 3 Magnetic families of actinide compounds Crystal structure type NaCI UN UP UAs USb UBi NaCI Th3P4 Cu2Sb NaCI Th3P4 US USe UTe U3P4 U3As4 U3Sb4 U3Bi4 f UP2 UAs2 USb2 UBi2 af PuP PuAs PuSb Th3P4 Th3As4 Th3Sb4 Magnetic order af f f Weak magnetic Grunzweig-Genossar and Kuznietz (1968) and Grunzweig-Genossar et al. (1968) tried to explain the kind of order existing in cubic uranium monopnictides or chalcogenides by considering U +4 ions with f2 electrons and combining the Rudermann-Kittel-Kasuya-Yosida (RKKY) theory of exchange through the conduction band with a superexchange through the anions.2. Th3P4 is a semiconductor (Price and Warren 1965) but U3P4 is a metallic conductor (Henkie and Bazan 1971.424 W. (2) Paramagnetics obeying the Curie-Weiss law without established magnetic order. Therefore only substances of this kind are presented in detail.7). 1977). Identical magnetic order exists between members of the groups of compounds shown in the following table. By studying their solid solutions one may observe transitions between the different mechanisms of electrical conductivity (section 3. . (3) Ferromagnets or antiferromagnets. PuP often present different spin coupling. localized magnetic moments and possibly ordering effects may occur. TRZEBIATOWSKI and 3. Bazan et al. But neither the simple band theory nor the localized electron theory may be applied. The main interest in this context is focussed on ferromagnetics.40/~ for plutonium compounds. One observes that the Curie or N6el temperatures of isostruetural compounds show correlations with the interatomie distances of the actinide component. 2. The electrical transport in these actinide compounds is either semiconducting or metallic. r. Because magnetic research on transuranium compounds only started recently. oPuPI ~ UPbz ~'.A n distances (after Lain and Aldred 1974). oPuRhs Ol'U P'd i Ipl~- I . .4 An-An distance(A) l 4. 0.I~JS b ~. Neutron diffraction studies have shown that the propagating vector is q = (0.1... interesting new examples of magnetic materials are very probable in the future.J. 3. . / Nppd ~. Ferromagnets occur only rarely. 4. The dependence of magnetic transformation temperatures on the A n . curium and americium.L ~ " ~gO 50 0 32 ol-Ijr~ PuPtz I 3.½) and further research on its magnetic order has been undertaken.AI2/ >")'PUP ~'.2. Therefore the discussion is concerned mostly with the ordered uranium compounds and to a lesser extent with compounds of plutonium..2)/3-uranium hydride was identified as the first ferromagnetic actinide substance. Hydrides As already mentioned (section 2. p.1. 3.150 o 'O. /3-UD3 and a-UH3 are similar types of ferro- .8 Fig.ACTINIDE ELEMENTS AND COMPOUNDS 350 300 250 N6oC UsAs4 I I I | I I I I 425 UBi o/ / ~2o0 0 I-- USI~ / 7oNpSb US • NDAs/ •. 3. Magnetic ordering in elements and compounds Among the actinide compounds there now exist nearly 100 ferro..6 I ~ .. Compounds In the following sections the individual groups of compounds are reviewed taking into consideration the experimental and theoretical background. I I 4. 2.2.R USeXUs~U. Elements Fournier et al. 3. neptunium.L. This is the only actinide metal which is magnetically ordered.. [1977] identified curium as an antiferromagnetic with the N6el temperature of 52 K.and antiferromagnets. Thorium compounds do not belong to this class because the absence of the f-electrons excludes the appearance of magnetic moments.0 4. 426 W.-.l . e.q. q~ . . T R Z E B I A T O W S K I r~ t".... e~ [-. 1979). 1959) and for /3-UD3 (Abraham et al. U3Te~ seems to be ferromagnetic. Neutron diffraction research at 4. There exists a large magnetic anisotropy with an estimated anisotropy field of HA = 3000 kOe (Tillwick and du Plessis 1976a. USe2 seems to be metamagnetic and a critical field of 15-18 kOe is sufficient to induce ferromagnetic order (Suski et al. (1965). It may be mentioned here that the surface conditions may influence the magnetic order (Popielewicz 1976). 3. Finally. 1972) although there still exist some doubts. Heat capacity measurements on US and USe within fairly large temperature ranges were carried out by Westrum et al. Takahashi et al. containing f2 electrons with J = 4. U7Te12 may be regarded as ferromagnetic. In very low magnetic fields U~S3 behaves like a ferromagnet. Uranium dichalcogenides UCh2 do not exhibit a simple magnetic order within the investigated temperature range. The plutonium hydride was investigated by nuclear magnetic resonance (Cinader et al. especially on single crystals. 1972). as is also plutonium hydride Pull2÷.ACTINIDE ELEMENTS AND COMPOUNDS 427 magnets. 1960) were determined. 1976) (table 4). but in higher magnetic fields maxima occur on the magnetization-temperature curves. Chalcogenides The class of actinide chalcogenides yield several magnets (table 5) and especially the monochalcogenides with NaC1 structure. U2Se3 and U2Te3 exhibit complicated behaviour. 1976). It may be mentioned that the phase diagrams of these systems are very complex so that phase changes within the investigated temperature range may occur.7. representing below 178 K a simple ferromagnet.2 K has confirmed the magnetic order of uranium moments along the [111] axis (Wedgwood 1972) and a large rhombohedral distortion was established by Marples (1970). Flotow et al.b). (1971). but their magnetic ordering cannot be established without neutron diffraction experiments (Suski et al. The compounds USe and UTe exhibit ferromagnetic order. The magnetic form factor was determined on single crystals with polarized neutrons and it follows the model assuming the ground state of the U 4÷ ion to be 3H4 (Freeman et al. For example. Thermodynamic functions for /3-UH3 (Flotow et al. the refractory uranium monosulphide US (melting temperature 2460°C) was investigated in detail. Existing magnetic data on the orthorhombic uranium sesquichalcogenides U2Ch3 indicate that their magnetic behaviour is complex and more research. Galvanomagnetic (Kanter and Kazmierowicz 1964) as well as electric properties of US were determined. at least in high magnetic fields. . (1968).2. and U3Se~ shows more complicated properties (Suski et al. Magnetic and electronic properties of /3-UD3 have been recently reinvestigated (Ward et al. was accepted as a component of this metallic conducting compound. is necessary.2. The U 4÷ ion. which exist within the CaF2 type of lattice in a wider composition range 0 < x < 0. whereas NpS is antiferromagnetic and PuS is a temperature independent paramagnet. 1976). -' oo oo oo oo ¢D ~-~ O ~ II II II II II II II fl II fl O ¢D ..~. "='l= ¢~ O .=. TRZEBIATOWSIKI .428 W.. ~.~. i "O •~. or dipnictides (table 6).3. Sb. PuN. The Barkhausen effect was measured on U3As4 single crystals and the dynamics of the magnetization processes was discussed (Filka et al. 3. Trot and co-workers (1962. A theory of noncollinear ferromagnetism for U3Pn4 ferromagnetics was given by Przystawa and Praweczld (1972) and the number of valency electrons was calculated for Th3As4 and U3As4 from positron annihilation experiments by Rosenfeld et al. [110] and [111] has been measured between 2-230 K (Henkie and Bazan 1971) and its electrical behaviour below and in the vicinity of the Curie temperature may indicate a more complex magnetic structure (Henkie and Klamut 1977). (1974). Neptunium trichalcogenides NpSe3 and NpTe3 seem to belong to this class (Blaise et al. (1975). U3P4 and U3As4 show a large magnetocrystalline anisotropy (Buhrer 1969) along the [111] direction. Bi) of cubic symmetry with the Th3P4 type of lattice. 1964). 1977). 1974). Neutron diffraction data show that both U3P4 and U3As4 exhibit a collinear structure (Leciejewicz et al. identified by Trzebiatowski. The magnetization of U3As4 was measured in pulsed fields of 230 kOe (Ka~zer and Novotny 1977).7). 1976). 1977).monocompounds like US. The constants estimated by Bie|ow et al. but PuP is ferromagnetic. From heat capacities of U3As4 and U3Sb4 thermal functions up to 950 K were derived (Westrum et al.8 and 4. 6 7 × 106erg/cm 3 and an extraordinary value for K2 = . 1973). although for the monoclinic US3 or USe3 magnetic order has not been established by neutron diffraction. Among the transuranium chalcogenides ferromagnetism has rarely been detected so far. The electrical resistivity of single crystals of U3P4 and U3As4 along [100].2 K using magnetic fields up to 140 kOe.2. Pnictides Among the actinide pnictides antiferromagnetic coupling is represented by the uranium mono.2 . NpAs2 is ferromagnetic below 23 K and antiferromagnetic between 180-23 K with longitudinal wave modulation (Fournier et al. The magnetic constants of the U3Pn4 series depend on the An-An distances (fig. (1973) for U3P4 and U3As4 were about 1-1. 4 5 × 10Serglcm 3. . NpSb. As. Bazan et al (1977) have suggested that U3P4 is a compensated metal and the free electron Fermi surface has been constructed for this substance.3 . ThP. For the band calculation of A n . UTe3.see Davis (1974). giving anisotropy constants K~ = . and o t h e r s . Rhombohedral distortion for this kind of ferromagnet was provided by Przystawa (1970) and confirmed by Sampson et al. There exists an interesting and extensively investigated group of four ferromagnets within the U3Pn4 group (Pn = P.2.38 seems to have a ferromagnetic contribution below 20 K (Suski 1976). Magnetoresistivity measurements were carried out on U3P4 single crystals between 1. The parameters of magnetocrystalline anisotropy were also calculated by Zelen~ (1976).5 × 107 erg/cm 3. 3).ACTINIDE ELEMENTS AND COMPOUNDS 429 Further interesting results regarding US may be deduced from its solid solutions (section 3. _ _ - ®~ - _ <o e~ oo II II .430 W.4 ~ e. TRZEBIATOWSKI oo .i • "~ e4 e~ o ~ . Also NpB2 is ferromagnetic. Compounds with IVA and IIIA group elements To this group belong the carbides.1 I 4. silicides.19 < x < 0. 3. Magnetic moments and Curie temperatures of U3X4 compounds in dependence of An-An distances (after Lam and Aldred 1974). germanides. it is similar to the elements having small atomic volumes like hydrogen. which are temperature independent paramagnets. stannides and plumbides. Further.s9 seems to be antiferromagnetic between 220 and 310K (Ross et al. The only ferromagnets hitherto known among the carbides are NpCx and Np:C3 in contrast to U2C3 or Pu2C3.2. nitrogen and carbon.3 An-An distance{A) Fig. La. 1967).7 I // "" U. All these compounds possess structure types of lower symmetry than those of the analogous pnictide or ehalcogenide compounds. Some germanides like U3Ge4.P k'o a 2 = UsAs~ 201 ~15( I0( 3.Sb. An interesting ease of ferromagnetism occurs in the complex boride system containing uranium and lanthanide elements. NpC0. however. the stannides and plumbides. 1974).~ U~BX~l~\ I I U~Se~ 3. there is as yet no evidence regarding magnetic order in these compounds. The boride system Ux(Y.4. Both tin and lead are true metals as are their actinide compounds. Magnetic research on these compounds is rather scarce and more detailed investigations are awaited. Among the actinide compounds with IIIA elements the borides are the most characteristic. UGe2 and PuGe2 are again ferromagnetic. It was observed by nuclear magnetic resonance that only uranium atoms with coordination numbers equal to or smaller than four are magnetically active in this series. U~As 4 1 .ACTINIDE ELEMENTS AND COMPOUNDS I I I I I I 431 12 10_. Lu)1-~B4 is ferromagnetic for U~Lal-xB4 as example at 0. as well as borides or compounds with Ga.9 t I 4. 3.82 although the pure components are not magnetically ordered (Hill et al. because boron is the last nonmetallic element going from VI to III group elements. Examples of ferromagnetism in compounds with elements of the IIIA group . ~- U 304 - B u. In and T1 (table 7). TRZEBIATOWSKI .~ ~ ~ g .~.< m~ 8 0 .. . o ~ ~_~ ~ _'2 . ~n.~ __.~.< .o ~ il II ~ ~ II II ~ II II II ~ II II II II ~ ~ ~ ~ ~ • II II ~0 ..~.... . .432 W..¢V I eq D ~ ZZ~ Z . ~ ~. The uraniumnitride-telluride is the first ferromagnet among actinides whose magnetic moment lies at an angle of 2 0 . 3. . T1. It was stated that on single crystals within the temperature range 77-135 K the magnetoresistance is negative and anisotropic. In some analogous ternary neptunium and plutonium arsenide compounds with S.5 K) as established by Trainor et al. (1976). but U(Ga. Pb)3 are all antiferromagnets. In.Se or Te ferromagnetism also occurs and symptoms of itinerant magnetism were established by Blaise et al. like U P t or PuPt of the CrB lattice type (table 9).2. whereas the Curie temperature remains apparently constant (Huber et al.6. lntermetaUic compounds At present a limited number of actinide intermetallic materials is known to be ferromagnetic (table 9). 3. Interesting magnetic properties are exhibited by the compounds derived from the antiferromagnetic uranium sesquinitride U2N3 by the substitution of one nitrogen atom by a V. (1976). (1977). and also compounds containing platinum. Only UGa2 has been investigated in greater detail. Compounds like CrUS3. as stated by Leciejewicz et al. Detailed research on the magnetoresistance of UAsSe was carried out by Wojakowski et al. One may quote some examples belonging to the Laves phases of the MgCu2-type. besides the uranium component.2. Np. Am)Fe2 the contributions of both components .7 and FeU2S5 were identified as typical ferromagnets and the cobalt-uranium-selenide of variable composition is notable for its very high Curie temperature (700 < Tc< 1100).ACTINIDE ELEMENTS AND COMPOUNDS 433 occur in U2Ga3. so that often discrepancies in the numerical values of the magnetic and crystallographic data exist. CoUSe2. UGa2 and NpAi3. In certain cases like (U. Many of them have been only roughly investigated. with iron or nickel as the second component. 1975). U2N2Sb and U2N2Te appear to be ferromagnetically ordered. The results were compared with theoretical predictions of Yamada and Takada (1972. (1977). The example of U P t is interesting because the decrease of its interatomic distances through the application of 20 kbar pressure results in a decrease of the saturation moment of 90%. Pu. (1976) (see table 8). CrUSe3. The compounds of AnPnCh composition are mostly of the PbFCI type of crystal structure related to the anti-Fe2As type (Flahaut 1974). a transition d-metal has been discovered by Noel et al.5. A class of ternary ferromagnetics which occur in systems containing.5 ° with the xy plane. 1973). An interesting case is represented by NpSn3 because it is the first example of itinerant antiferromagnetism (TN = 9. Tetragonal compounds like U2N2Bi. PuPt perhaps exhibits ferromagnetic properties (Smith and Hill 1974). VUSe3. Ternary compounds There exist a large number of ternary compounds containing chalcogenide and pnictide atoms which exhibit ferromagnetic properties (table 8).or VI-group element. Also double chalcogenides and the unique compound UNC1 belong to this class of compounds. i" o= ¢1. '~ I Co ¢I i e.-i ~ e.'i ~ II " q ' .~ II " ~ .'il'.II "~ ~ ~i II II ~l II II II 'ql" ~ ~l II It II ~'.4 P 7 ~ II II ~l qil qi .~ II II " ~ I"~ "~ ~ ' ' ' II ~.i~x~ ~i II II ~ II II ~I II II II e . ¢J ¢I ..II e..>. ' i ~ ~1 II II I.434 W.i~ ~ ~ <. TRZEBIATOWSKI +1 el ~-... ~°< -- II II ~ ~ II ~ ~ II ~ ~ II ~ ~ ~ ~ ~ ~ ~ ~ ~'~ ~ ~. II ~ ~ II ~ ~ u II II ~ II II ~ II II ~ u II II II n iI II II II ii Ii ~ n iI ~ ii iI 0 0 ..ACTINIDE ELEMENTS AND COMPOUNDS 435 2 +I 0 g I ~E I < [. 436 W. °< ~ ~ II ~ ~ II "~ Ii ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ II II II II II II II II II II II II II II ~ II II ~ II II ~ 8 . TRZEBIATOWSKI I < [.. < [..ACTINIDE ELEMENTS AND COMPOUNDS 437 m 0 t~ " ~ ~ I . NNMN II II II II ~ 8 ~ ~ z ~ . . 22 3.2 15. 9.4 1I. 11. (1975) Harvey et al. 2. (1969) Smith and Hill (1974) Huber et al. 16 0.89 0. (1973) Chechernikov et al. F u r t h e r d i f f e r e n c e s b e t w e e n t h e s e f e r r o m a g n e t i c s e x i s t .30 8.4/za a t t h e a m e r i c i u m s i t e .428 7.25 a = 4.2 6.7 21 U: 0.3 2. 3.3-0. Fe: 0. 6.190 7. Np: 1. (1975a) 18.0 2. (1976) 20. T h e p r o p e r t i e s o f t h e i r o n c o m p o u n d s i n d i c a t e a n i n c r e a s i n g l o c a l i z a t i o n o f 5f e l e c t r o n s a s t h e a c t i n i d e c o m p o n e n t will b e h e a v i e r ( A l d r e d e t al. 1976).0 ( ~ ) ~:.3 2. (1974) 2~.9 22 0. Lam et al.76 c = 36.2 Pu:0. 7. 12 1. Aldred et al. UNi2 UCo55 NpFe 2 NpAI2 NpAI3 NpMn2 NpNi 2 NpOs 2 NpOs2-xRux NpRe 2 PuPt PuPt 2 PuFe 2 AmFe2 1. 1975).260 7.528 a = 4. 1 9 7 7 b ) . because with diminishing Np-Np distances deloc a l i z a t i o n o f t h e 5 f e l e c t r o n s o c c u r s ( A l d r e d e t al.772 c = 4. (1974) Aldred et al. 12 0. b e i n g a n t i p a r a l l e l t o t h e i r o n m o m e n t .06.5 18 28-32 7. AIdred (1975) Aldred et al.721 b = 10.633 7. 9.49 7.5 14 1. Dunlap et al.77 a = 3.5 Compound ThCo5 UPt UFe. 12 1. (1973) Ermolenko et al.410 7.35. 17.5 ( ~ ) Huber et al.12 56 20 .59 0.2 1I. Brodsky and Trainor (1977) Gal et al. Aldred et al. Laltice type ThNi5 CrB MgCu2 MgZn2 R3m MgCu2 MgCu2 AuCu3 MgCu2 MgCu2 MgCu2 MgCu2 MgZn2 CrB MgCu2 MgCu2 MgCu2 0 Magnetic moment (P-s) paramagnetic ordered 2. ~:1.1. 11.098 7. Curie temperature K 290 27 160 30 360 500 56. 1977).84 References 6 1.~.438 W. (1974) 21. (1973) 19. (1972) Matthias et al.785 4. (1977a) Derjagin and Andrejew (1976a) 15.816 b = 10. 5. so that an electron structure with p a r t i a l l y d e l o c a l i z e d 5 f e l e c t r o n s m a y b e a c c e p t e d ( L a n d e r e t ai. Brodsky et al. Mitchell and Lam (1974) Derjagin and Andrejew (1976b) 17.g. A m F e 2 is e s p e c i a l l y i n t e r e s t i n g b e c a u s e n e u t r o n d i f f r a c t i o n e x p e r i m e n t s i n d i c a t e a s m a l l m o m e n t o f 0. 4. (1978) to the ordered magnetic moment could be estimated. 10 Fe: 1. 14. b u t o n i n t r o d u c i n g r u t h e n i u m in s o l i d s o l u t i o n t h e ordering gradually vanishes. 4 5 7 13. (1975) Aldred et al.09 7.96 c = 8. 18 20 0. .4 14.5-8 47 19 6 600 350-400 6 170 45 2.06 c =8.~ a = 3.110 47 2.7 1.144 7. UFe2 exhibits small anisotropy and a small uranium moment. 13. 62.694 c = 4.47 1. (1970) Lander et al. 10.7 0. (1977) 16. N p A I 2 h a s l o c a l 5 f m o m e n t s a n d t h o s e o f N p O s 2 a r e o f r a t h e r i t i n e r a n t c h a r a c t e r ( A l d r e d e t al. e.230 7. N p O s 2 is f e r r o m a g n e t i c . TRZEBIATOWSKI TABLE 9 Ferromagnetic actinide intermetallics Lattice constant .1 8. 12.058 a =4. This system was further investigated by many authors by the study of magnetization. The same kind of magnetism has been intensively studied on the pure compound UAI2 (Brodsky and Trainor 1977. Further. being composed of a ferromagnet (US) and a weak paramagnet (ThS). which contain an antiferromagnetic component depending on composition. respectively. diamagnets. Fournier et al. which shows limited solubilities (up to about 30 at%) of the components belonging to the Laves phases type C15 and C32. The metallic system US-ThS was one of those investigated early (Chechernikov et al. Many types of magnetic order occur in these systems.43Th0. Most of the research was on systems containing monochalcogenides and pnictides of uranium or thorium. Because the Am 3÷ ion (f6:7F0) is nonmagnetic. 1976). temperature independent paramagnets. specific heat and neutron diffraction (Danan et al. Neutron diffraction studies of such systems lead to the construction of magnetic phase diagrams. because they may be composed of components exhibiting different physical properties such as ferromagnets. 3. 1979). Solid solutions Isotypic actinide compounds often form continuous solid solutions which are the interesting subjects of numerous investigations.2.7 ttB.5 (table 9). Examples of solid solutions which contain a ferromagnetic component are in table 10. exhibit ferromagnetic spin fluctuations as deduced by Trainor et al. The localized description is apparently in contradiction with the strong electronic specific heat and the band calculations which suggest a 5f-6d band crossing the Fermi level.7. and the course of TABLE 10 Some solid solutions of ferromagnetic actinide compounds NaCl-type Th3P4-type US-UP USe-ThSe U3P4-Th3P4 US-UAs UTe-ThTe U~P4-U3As4 US-ThS U3As4-Th3As4 USe-UP USe-UAs . antiferromagnets. The pseudobinary intermetallic system U~-xThxA12.ACTINIDE ELEMENTS AND COMPOUNDS 439 which amounts to 1. 1976). A ferromagnetic intermetallic compound of composition similar to the well known strong magnetic samarium compound SmCo~ has been identified as UCo5. 1968). Ferromagnetic coupling was established up to the critical composition U0. they may be metallic or semiconducting. The band model may therefore better describe the results of the physical measurements than the localized approach (section 3). (1976) from specific heat and electrical resistivity measurements.57S and conclusions were drawn about the electronic structure of these alloys. temperature and magnetic field intensity. only the Am 2+ configuration (f7:8S7/2) is likely to be responsible for this magnetic moment (Aidred et al. which may be understood as a modulation of the magnetic moment along the c-axis (Leciejewicz et al. 4. both from the magnetic measurements and from neutron diffraction measurements (Kuznietz et al. Within the binary system UAs-USe (Trzebiatowski et al.b. .. The system U P .2 0.5 kOe if containing more than 20 mol% US. TRZEBIATOWSKI the magnetization curves in uranium monopnictides.U S system (after Trzebiatowski and Palewski 1969). The ferromagnetic region of the U P . The solid solutions UAs-US. Neutron diffraction in zero magnetic field revealed antiferromagnetic order at 25 mol% US and complex magnetic structures at 25-34 mol% US. Mydlarz 1977). first investigated by Trzebiatowski and Palewski (1971) are ferromagnetic in magnetic fields below 9..B OS t3P 0.b) for 10 and 20 mol% USe.4 Fig. in uranium monosulphide and their mutual solid solutions was explained on this basis (Robinson and Erdfs 1973.440 W. 1975. 1967) the transition from the ferro. 1974). Suski et al. In higher magnetic fields the ferromagnetic region is extended and even at 8 mol% US one observes magnetic hysteresis (Mydlarz and Suski 1976. 1977). 1972). Metamagnetic behaviour was confirmed by Suski et al.U S e system extends up to 37 mol% USe. 1971. 1974. 4 shows typical behaviour. Lander et al. Within those compositions the longitudinal spin waves (LSW) structure occurs. Schinkel et al. I I I I t I t j-150~ lO0~"~ff o0 50 ~0.~-%c TN ~ r !00 5O 0=_. being enlarged by the application of high magnetic fields up to 320 kOe (Trzebiatowski et al. (1975a. 1971a. 1969a). Haessler and de Novion (1977) also disagreed with a localized model proposing an electronic structure which is influenced by strong localized spin fluctuations associated with 5f virtual bound states on the uranium atoms. Leciejewicz et al.6 0. Magnetic constants of the U P .U S (Trzebiatowski and Palewski 1969) whose schematic magnetic phase diagram is presented in fig.to the antiferromagnetic region is accompanied by the occurence 350 ~ I ' I ' I ' I J %25{ 20( 200 150 ~I00 ~f11. and ferromagnetism in fields of 80 kOe. the possibility of a change in the uranium electronic structure from 5f" to 5f"-j exists as it may occur in the UNis_xCu~ alloys (Daal et al. while solutions containing 33 mol% USe show the coexistence of anti. The Weiss constants and Curie temperatures vary nearly linearly with composition. A magnetic diagram (fig. N=5 in high rnognetic f ieicl. temperature curves by Palewski et al. . Within these the magnetic moment is cosinusoidally modulated with a periodicity of modulation IN as established by Leciejewicz et al. but preliminary measurements of their magnetization have been carried out (Markowski. 1975).' N=7 . private communication). In pulsed magnetic fields of more than 100 kOe metamagnetism was observed by B i d o w et al. 5. Samples containing more than 55 mol% USe are ferromagnetic in fields o f 50 kOe. on the magnetic behaviour of monocompounds and their solid solutions indicate a complicated band structure. Schematic magnetic phase diagram of the USe-UAs system (after Suski 1976a).~.b).67 O. In addition. The electrical and magnetic properties of U3P4-Th3P4 solid solutions offer the interesting example of a transition between a metallic and a semiconducting state (Trzebiatowski et al. (1972) for which sharp maxima occured. Interesting magnetic properties at 25 mol% USe were observed on the magnetization. being N-multiples (N = 7-11) of the chemical unit cell along one direction. . The model of Grunzweig-Genossar previously applied to the single monocompounds was also extended to solid solutions (Grunzweig-Genossar and Cahn 1973). .ACTINIDE ELEMENTS AND COMPOUNDS 441 of numerous magnetic structures of higher order.75 Fig. The continuous solid solutions of two ferromagnetic components U3P4 and U3As4 were investigated by Trzebiatowski and Misiuk (1970).~ U S el xASx 0. Theoretical considerations by Robinson (1973. " ~ . 1972). (1973). 1974) and Haessler et al. . They possess magnetic unit cells.. The preparation of U3As4-Th3As4 solid solutions causes some difficulties.÷-'" T [K] I I I 100 FERRO ! l ~N-11 .. . (1976)... after Obolenski and Troe (1977). (1971a. r IN-7 I I I I I I' I tA i ! iI x . 5) shows the extended ferromagnetic region in high magnetic fields (Suski 1976a). (1974) Raphael and de Novion (1969a) Raphael and de Novion (1969b) Smith and Hill (1974) Stalifiski et al. 19. (1966) Curry (1965) Fournier et al. 20. 18. 11 20. (1974b) Aldred et al. (1976) Trzebiatowski et al. 30. 16. 39. TRZEBIATOWSKI Further research on solid solutions of different components promises interesting results. 29. 16 10. 241 285.206 283 206 183 70 1I. Misiuk et al. TABLE 11 Antiferromagnetic actinide compounds and intermetallics Lattice type NaCI NaCi NaCI NaCI NaCI Mn203 Cu2Sb Cu2Sb Cu2Sb Cu2Sb TN K 52. 27 19 14. 55 122. (1973a) Harvey et al.5 27 52. 38. (1975) Misiuk et al. (1976) Lin and Kaufmann (1957) Marples et al. 42. 15.442 W. (1964) Ballestracci et al. 10. (1975) Murasik et al. 37 1 1 1 17 14 Compound PuN Pu3S4 UGa UGa~ UIn3 UTI3 UPb3 UPd4 UCu5 UMn2 NpPd3 NpSn3 NpCo2 Nplr2 NpPt NpB4 PuBe13 PuPd~ PuRh~ PuPt3 References 30 31 33 26 9 24 22 25 8. 90 32 30 15. 41 4. (1972a) Suski et al. 26. 40 18. (1963) Sternberk et al. 162 130 175 207 20 180 Lattice type NaCI Th3P4 rhombic AuCu3 AuCu3 AuCu~ AuCu3 AuCu3 AuBe5 MgCu2 AuCu3 T~ K 13 10 27 70 100 80. (1973) Lander et al. (1972a) 22. (1973b) Kuznietz et al. 12. (1974b) Nellis and Brodsky (1972) Nellis et al.5 11. 39 20. (1975a) AIIbutt et al. (1973) Misiuk et al. 0973) Gr~nvold et al. 39 40 40 39 24 13. 33.2 40 Compound UN UP UAs USb UBi U2N3 UPz UAs2 USb2 UBi2 UHg2 USe2 U~Te3(?) UOS UOSe UOTe NpP NpAs NpSb NpS NpAs2 1. 16 260 55 9. 5. References 20. 3. (1963) Boelsterli and Hulliger (1968) Brodsky and Friddle (1975) Brodsky and Bridget (1975) Buschow and Van Daal (1972) Counsell et ai. 41. 23. 36. 31. 28 AIB2 US2 Sb2S3 PbFCI PbFC1 PbFC1 NaCI NaCI NaCi NaC! CuzSb AuCu3 MgCu2 MgCu2 CrB ThB4 NaZnt~ AuCuj AuCu3 AuCu3 Aldred et al. 6. (1975) Suski et al. 1I. 2. 290 94. (1972b) Misiuk et al. 25. (1976) Trainor et al. 7. (1964) Trzebiatowski and Tro6 (1963) Trzebiatowskiand Tro6 (1964) Trzebiatowski and Zygmunt (1966) . 8. (1969b) Lam et al.5 15 7. 27. 35 36 5 6 33. 25. 34. 123 128 213. 13 106 55 72 160. 28. 17.5 24 6. 13. 29 38 3 2 32 31 7 29 28 15. 24. 30. 4. 37. (1961) Trzebiatowski et al. 21. (1972c) Murasik et al. (1968) Harvey et al. 14. 40 39. 40. (1974a) Aldred et al. 35. 32. 9. 96 203. (1974a) Murasik et al. Lindner. Wojakowski for their assistance in preparing the manuscript. Suski.173. Lander. I and II (A.. and A. Blank and R.or intermetallic compounds Trzebiatowski. eds. Inst. Tro~.) (Academic Press. Ser. 37.B. R. 1977). Wroclaw. on the electronic structure of the actinides. Suski and R.B. 1967. W. New York). actinide semi. (J. Aldred. Physica 86--88B. Fast. 4. No. Lam. New York). Final remarks As is evident from the preceding sections. W. The types of antiferromagnetic order have only rarely been determined so far. 1976.) (North-Holland. and W. W. Leipzig). Suski. Przystawa. in Physics and chemistry of the solid state. p. Suski. Prog. Magnetic ordering in the actinide intermetallics.. 41. Struktur und Eigenschaften magnetischer Festk6rper (VEB Deutscher Verlag fiir Grundstoffindustrie. D. vols. W. Freeman and J. PWN Wroclaw). Ossolifiskich. Conf. Mulak. IV. 1973. 621-634 (H. p. Conf.2. G. 1974. 1547. Suski. p. 1976. in plutonium and other actinides. Monographs and review articles on magnetic properties of actinide elements and semi.J. 41-98 (in polish.und antiferromagnetische Eigenschaften von Uranverbindungen in: Magnetismus. Darby. electronic structure and related properties. .) (Plenum. oh. de Phys. of Physics Conf. Magnetic and structural properties of actinide compounds. 1976. a new interesting class of magnetically ordered compounds. eds. and R. so that neutron diffraction in magnetic fields promise interesting results. D.J. in The magnetism in metals (J.or intermetallic c o m p o u n d s represent.A. Ferro. 1977. Brodsky. Int.. especially by alloying with a third c o m p o n e n t as well as by applying strong magnetic fields. 1978.. 2. R. Tro6 and A. Trzebiatowski. Acknowledgements The Author is much indebted to Messr. Antiferromagnetic order exists in numerous c o m p o u n d s which are collected in table 11. Proceedings 2nd International Conference on the Electronic Structure of the Actinides.ACTINIDE ELEMENTS AND COMPOUNDS 443 3. Magnetic properties of actinide compounds in: The actinides.) (Zaklad Narodowy irn. J. 3rd Int. eds. M.T. W. Tro6. Magnetism of actinides. Lam. Proc. Magnetic properties of actinides and their compounds. Amsterdam).. Recent investigations of the magnetic properties of some uranium compounds.J. eds. Tro6.. 1978.Magnetic properties of the actinide elements and their metallic compounds. W. Lopuszafiski and J. 11.H. Rep.Magnetic properties of the actinide systems. Jr. by comparison with the d-transition and the lanthanide families. 1979.8. The order may be influenced by different factors. Magn.. Moscow 1973. which m a y yield further insight into the specific behaviour and properties of 5f electrons in the solid state. All these c o m p o u n d s are therefore extremely useful for a wide variety of physical research.323-331. Phys. Suppl. vol. 1977. Dell. Lab. Tro6. 649. Dunlap and G. Eksp. Friddle. Phys. Phys. Brodsky. W. Charviilat. Fiz. AIP Conf. A. p. 353.. 511. Soc. in Plutonium and other actinides. T.J. Wojakowski. 1973. 1464. 86. Electr. eds. Mulak. Levitin. Hadari. Suski and R. Ellert.U..M. Dell. 18. Teor.R. 1973. Proc. Martin. Bertaut and R. A. Conf. Struct. A. Junkinson.W. D. 1966.B. Wroclaw.444 W. J. Damien and W. T. Stat. Rev. Lindner.R. Zh. eds. Fiz. 20. Dunlap and D. Blaise. Phys. R.R. 4. Bll. Brodsky. Lain. Shavishvili. E. A.) (NorthHolland..F.N. H. Phys..K. K. J. Sciences 3. W. Charvillat. Lam and G.) (Met.T. Solid State Commun. eds. Bridger. 1064. Phys.T. 635.. and A.M. Wojakowski. Pletushkin. Salmon and A. Wojakowski. Zamir and Z.E. 3766. Lain. U. 52.D. Phys. 1498. K. Mueller.Phys.J.M. Barykin.T. Pauthenet.) AIME. Trainor.E. in Proc.B. (J. C. Chechernikov.. in Pro¢. Dell and J. Z. A.B.. 1976. Martin. Conf. no. Sol. A. AIdred and C. B. D.H. Proc.. Zh. 143. Dunlap. J. Faraday Soc. Lam. 2nd Int. 1273. eds.H..S. 1976. Marcus. Mat.D. Aldred. 1975c. Slovyanskich and G. Rhyne. no 24. Phys. Ellert. C. and A.J. A. Nowik. in Transplutonium Elements (W. 27.D. Sol. Miiller and R. B. Preprint Int. Harvey. eds. TRZEBIATOWSKI References Abraham.M. Pietyushkin. Lander and M. Fournier.. C. eds. Wroclaw) p. Ansorge. 191. Teor. Struct. 17. 1977.J. J. Dunlap. Zygmunt. B.J. Wojakowski.I. A. Junkinson. W. Sol. Counseli. K31. Charvillat. 30. 2nd Int. D. 1960. AIdred.. Stat. T. BII. Actinides (Ossolineum. 1968. Electr..I.B. Benedict. Palewski. 13. 82. 664. 1975a.. E. Suppl. Faraday Soc. M. Cinader. A. Eksp. Rev.A. 469. 1193 (1965). Suski and R. 1976. Bielow. D.H. B. Mfiller and R. no. J. Chem. D. G.H.. No. Phys.W. AIME New York) pp. G. Boeisterli..F. Proc. BI0.M. Appl. Zh.D. J. 65-81. Bll. and R. Graham and J. J.. Rev. B.A. Menovsky.D. W.) (Ossolineum. Chem. 1968. Eksp.. A.F. in Compounds of interest in nuclear reactor technology.M. Dmitriewskij. Wroclaw) p.F. Rev. p.J. J. Yarembash and G.K. 1977.K.. 1964. I.T. Bazan. Zh. in Transplutonium Elements (W. 1169. Bg. J. Chem. M. 1972. Fields. D. 1972. 1169. H.J.. Wroclaw) p. 72 (1967). 2nd Int. Van Daal. 63.. Struct. M. R. Damien. Zygmunt.) p. A.F.F.W. Shenoy. 1976. W. 1975.. 91. A. (Pisma) 17. Darby. no 18. Actinides (J. J.. A.. Blaise.. Counsell. J.. Ballestracci. Wrodaw) p. Tro6. 1973. J. J.A. 80. (a) 12.) (Ossolineum. 1975b. P. P. 1967. C. Damien. Trainor.O.. Y.R. Mulak. Chiotti. Blank and R. Actinides. U.H. W. and H.) (AIME. Hulliger. V. New York) p.. Shavishvili. Mulak. C. G.M.P. Nowik. Lander. Cherchernikov.. Miner.D. 1977. Harvey and B. R.K. M. de Phys. A. Soc. P. Rev. 49.J. 1169.J.R.J. 30. 371. 62. A. 366. 1973. 921. . 1970. Conf. and R. Lain.R. D.P. 5. Fiz. A. Flotow and R. A. Troc. Brodsky. Calestani. in Proc. A.P. Baskin. Lindner.I. W.B. J. 1977.W. and F. Aldred. W. Electr. 431. AIIbutt. AIP Conf. Sevans. Mueller. Henkie and Z. A. New York) p. M. Suski and R. Phys.T. Solids 24. Spirlet and W. eds. Rev.J. Fiz.H. I. Trans. BI4.J.H. Suski. Eleetr. 487. Trans. D.J. 1978. Phys. Aldred. (R. Slovianskich. R.P. Aldred. 1974b. 1975. 1979. 1973. B.E. Proc. Dunlop. Charvillat. Amsterdam) p. Lett. Miiller. Bll. Lindner. 854. W. 475. Aldred. Teor. Lain. Rev. Salmon. R.I. J.. Teor. (J. Buhrer. W. Lain. Dunlap. 1974a. B.T.J. Am.J. 91B. Osborne. Soc. 271. 1963.. Struct. Aldred.T..D. Harvey and B. Proc. Bazan. D. eds. Aldred. Fournier. Pechennikov.W. G. 1011. Conf. 1966.T. Am.T. Popow. Physica 86-8811. Eksp. and N. Bazan. London. D. Blaise. Benedict. Miiller. 106. Aidred. 1975.M.. P. Cer.. Phys.D.H. de Novion and A. Actinides (J. 49.V. Radioanal. Soc. W.. Proc. R. Curry. N. 1736. M.P. J. D. Dunlap. A.) (Ossolineum. 437. 58.. 1968. Chechernikov. Brodsky. A. 2nd Int. Pawlowska. Salmon. Magnetism and magnetic materials (C. W. 357. High Magn. 1976. Lander. AIP Conf.T. 530. 555. A.. 81. M.C. 79. Siovyanskich. Phys. Buschow. Waber.. A. W.. 1969. AIP Conf. Neorg. M. 1.J. Less-Common. AlP Conf. J.B. in The actinides.R. J. B. 1970b. Freeman. A. Maple. B. voi.) (Ossolineum. 445 eds. J. M. D. 1971.R. 38.B. Blaise. Magnetism. 1974.. Faber Jr. (1974). C. M. Blaise. II (A. Ellert. Smith. Nucl.M. 991. J.. M. 1979. 4137. B. B13. 17. J. Phys.B. G.) (AIME. F. WohUeben. Suppl. Darby.B.D. Ermolenko.J. M. J.J. J.. Rev. Grunzweig-Genossar. C I0. 1970a. H. Sol. Blaise. Rev. Szklarz.N.. eds. Electr.G. 363. Chem.P. Suppl.. Appl. 4. Ofer. 109. Friedman. Cahn. Salmon.R. Phys. Mulak. Shut. Maple. J. F. 1976. Henkie. A. Zh. 2nd Int. Salmon. J. Conf.. Fournier. Maaren. Brodsky. Magnetism. 649.G. (1976b). Bazan.H. 30. 173. Iwanow.H. 1972. C. Osborne. 39.. Hill. Suppl. 1979. Zachariasen. 19. R. 504 (1975). (1971).H.. 1977. . 1955.. Kuznietz. H. Peterson. Thurman-Moe T.. Freeman.M. Phys. A. A. Physica 86-88B. Buschow. J.B. 1977. 1977. Henkie.T. 1974. Miner. vol. (1974). 1958. Mat. W. !. (1974). 1976. Phys. J. Phys. Dunlap. Phys. Struct.M. W..R. 1. J. Hulliger. Sklarz and J. Mag. Kuznietz. New York) p.W. 1708. L.E. 1968. 1973. and Mag. Chem. 880. W. Menovsky. VI. A.C. Lorenzelli.) (Academic Press. Lett.. Z. 4. Gruen. Solid State Chem. 589. R. Lohr. W. H. 3529. J. 58. Int. 65.H. Haire and J. Suski and R. (a) 5. A. 1979. J.M. B6. New York) p.B. Komarow.H. A. I.. 95.. D. W.H. 1968.M. eds. Physica 86-88B. Jr. 1169.M. 1968. Henkie. Conf. H.G. Suppl. 1972. and Mag. VIII auflage Transurane metalle (Springer Verlag.. Phys.E. Int.. A. A. 10. de Phys. Boston.A. 2139. Freeman and J. 1901.ACTINIDE ELEMENTS AND COMPOUNDS Daal. Perkal. de Phys. Harvey. Roczn. . A. Desclaux. 905. A. D. 23. A.J.H.M. de Phys. 348. G. 1975. Zh. Gal.. C. Andrejew. Z.. 1973a. C.V. J. M. New York) p. J. Stat.D. vol. S. Klamut.W. Z. Mueller.. 419. Mag.. Berlin). Chem. (H. Neilis. $5. Y. J. White.. Proc. Ya. 2. 1973. 1166.S. Gr¢nvold. (1959). 239. Hill. Inorg..R. J. P. J. Van Allen. J.. and G.W. D. eds. A. 32. 1968. Met. 2. Lander. d'Agliano E.L. VI. 30. 16. F. 124. Grunzweig-Genossar. Miiller.H.303.E. in The actinides: electronic structure and related properties (A.W. Int. C. G.. Haraidsen. Z. Hill. Awtorskie swidetelstwa no. A.. A. J. J.. H. J.H..B. 34. de Novion.G. M. Chem.H. J. M. Darby. 193. Cryst. Moscow.. Koeling. 562. in Plutonium and other actinides (W.L. Jullien. Phys. 446. 24. 52.. 1457 (1975). Mat. 84. Phys. 145. J. Galleani. Zentke. 29. Wohlleben. Filka.W. Waiters.. Proc.M.A. Rev. W. J. Freeman. p. . Markowski. Proc. D. 20. J.J. 4. Kalvius. de Phys. Grunzweig-Genossar.. in Plutonium and other actinides. Davidson..H. Neilis.G. 41. (1976).. Rev. M. 1901. Harvey. Brodsky. Tufte. R. E.H. D. 34. (1973). Fournier. Haessler. Fiotow.. C.H. H. (1968) J. 4. L Less Common Met. Giorgi A. 1973b.R. Phys. Fournier. A. Magn. (1974). Handbuch der Anorganischen Chemie. J. Wroctaw) p. Henry. J.D.L. Lindner.) (AIME.S. SIovianskich. de Phys. P. 1976. Moscow. .. D. 1977. Mahat. J. Damian. Davis. J. (J. no. Phys. 259. 42. 1168. no. G. Mag.L. Gmelin. H. Rev.. Andrejew. p. de Novion. Coqblin. 2117.. Damien. Huber. Osborne. 1974.J.B. 1979. Guerin. 1974. Danan. Earn. Hill. Aldred. Makarowa.K. Hadari. de Novion. B8. Henkie. D. M. 113. A. Met. Actinides. Eksp. 43.J.B. Am.231. 4. Flotow.R. K. Phys. H. Phys. Int. in Proc.J. J. Freeman. Dunlap. (Russ) 71. Dunlap.W. van. P. G. BeiUe. 9... W. XIX Ann. Z.J. B. W.. de Novion. 37. Conf. 1389. (1971). S. and R. A. Less-common. Chem. Troc. Phys. E. Lander.. F. M.H.H. Jr. J. (1977). Rev. Fizika Metaliow i Metallowed. 1. Teor. 773. B. AIP Conf. 51. 37. Nucl.J.D. Huber. Derjagin. Abraham. Giorgi. Bauminger. Lett. 81. Sol. P. L Nowik. E. Kuznietz..H. (1977). A.. R. 1976. and J. Growth. ed. Wedgwood. M. G. F.. de Novion. BT.E. Derjagin. 1968. Fournier. Flahaut. Ellinger.. Conf. New York) p. Chim.. Chem.. T. Mat. 1075. Blank and R. (1976a). . Fiz. Proc. Rev.. (1972). Spirlet. M.J. Soc. Haessler. J. Rev.W.) (Academic Press. J.. D. Tro~. F. Mulak. F. 243 I. E. Rev. Bull.P. A. Phys. Perels. Proc. eds. 187..) (Academic Press. 1972. Phys. Sci. Aldred. G. M. Moscow. Mueiler. A. (Paris) Suppl. A. 30. Lander. 1977h. S. 187..H. Zygmunt. Sci. 150. in The Actinides: electronic structure and related properties. in The actinides: electronic structure and related properties (A.J. 1957.J.J. J. Mulak. Aldred. G. Lam. Polon. Kanter.J.. Rev. .. Palewski.. F. Misiuk.. vol. Mat.. J. Suppl. Mulak. Phys. Aldred. Sol. (A.) (Academic Press.W. Sc. 1977. Leciejewicz. in Proc. 1969. 1964. Lin. Misiuk. Wohlleben. Less-common.H. 1053.D. A. C. Kmetko. T. Wroclaw) p. eds. 1979. 20. in The actinides: electronic structure and related properties. G. Sol.H. 24. Palewski.K. Solids. J. J. 1030.. Ser. New York) p. Jr. B14.J. Chim.. eds. 1972b. Proc. in The actinides: electronic structure and related properties.H.. 640. J. Trzebiatowski. G. Lovell. Proc. I and II. 1973. 4. 32.D. J.) (Ossolineum. Tro~. D. Aldred. Wedgwood. Zolnierek. San Francisco No... 391. Lander. J. Kuznietz.T. G. 39. Klein Haneyeld. Lindner.R. Stat.B.H. Actinides. New York) p.. M. Rev. Simpson. New York) p. New York) pp. 39. Jr. 40. 123. 697.. Acad. Lin. ICM. A. E. Aldred. M. A. 1971b. Paulikas. 1971a. US 64. Mukaibo. J. Chem. Kanellakopulos. Czopnik. Polon.. Lander.Y. R. Shenoy. Chim. Ser. Darby. Proc. M. Chu. 1974. 102.. G..H. Acad. Phys.. Struct.H. Phys. 1972. Phys. Bull. Kuznietz. 1974. Maino.J. Chem. Darby. Masaki. D.D. Czopnik. G. Campos. W. 5.) (AIME. Vogt. 1975. Lam. 1969b.. Physica 86-88B+C 152. L. Sol. 1972c. 459... Czopnik. D. A.. Z. 657.A. Lam. Lander.H. Misiuk. Lander. Misiuk. Sperlin. J. 1971. Bull. 1970. Poion. Nucl. M. Lander. G. Leciejewicz. 20.H. Rev...H. C. A.T. D. Acad. B.. AIP Conf. Kamimoto.W. Britz. A. Jr. Sol. Phys. K57. M. 1977a. A. G.W. Phys. 1970. 459. 1976.. Mueller. Y.H. Y. CharviUat. K.B. 31. A. Reddy. no. 1970. J. C 8. P. Tro~ R.. Palewski. Vogt. (b) 46. J. Mat. D. in Transplutoniumelements (W. Lam. 59.M. 5035. M. Kuznietz. B.. Jr. J. Phys..J. Sci. C1-917. Suski and R.B.P. Jellinek. Nauka Moskwa. 1969.B. A. Phys. A. Chem. T. 48. I. 1974a. 18. H. Anderson.. 109-179. J.H. F. M.D. Mueller.B. J. J. vols. M. p.H. Sci. Ka6zer. Mulak.H.. 1977. D. (A.. Corenzwit.. 1974. 349. J. AIP Conf. Ligenza. D..D. Lander. Electr. Fradin. Phys. 35. J. Suski. Sci. Kazmierowiez. and A. J. J. Nat.. O. eds. Misiuk. 1969.446 W. Zygmunt.H. 13. New York) pp.R. D. Proc.T. Rev. Lander. eds) (Academic Press. Kaufmann. /driller and R. A. G. 137.. Lander. Lam. R. Freeman and J.A. 445.J. Rev... 1972a. Darby. Freeman and J. Phys. Lander. Phys. Kruger. 20. D. R. 1976. Lain. Tagawa. Rev.P.. R.H. Met.H. TRZEBIATOWSKI Darby. J.. in Plutonium and other actinides (H. Mueller. B14. Physica 86-88B.T. Dunlap and G. J. W.H. New York) p. Sci. B. I (A. de Phys. A. 4. Appl.H. Bull... Phys.H... 1972.H. eds. Solid State Comm. 1979. A. Stat. T. 1972. S.J. Baskin. 1976.. Czopnik. W. O. B. Lander. Phys. B6. Nuci. M. F. D.-Tro~. D. Ser. 317. 708. Solids.T.. G. J.A. 1974b. Mueller. J. 241. vols. Nowik. I and II. J. eds. Novotny. Acad. G. H. S.R.H. Sei. J.J. Lam. A. Polon. BI4. Mueller.T. 337. G. Marples. A. A. Nucl. Stat. 1880. 393.. 892. Lam.J. 1956.J. Conf. Heaton.T. Mfiller. 30.) (Academic Press. W. 1975. A. $8. 1642. Shenoy. Aldred. 108.F. Tro~. Conf. Leciejewicz. Koeling. 1969. Murasik. Phys.. 351. Murasik. 117. T.. Kaufman.. G. D. N. D. Sci. Mueller. 479. D. C. Met.D. Nevitt. A. Appl. Chim. Phys. Leciejewicz. Troc.J. A. Int. 1977.M. Koeling. Acad.B. M. Phys. B. Sol.A. B. Freeman and J. Mulak.R. (J. Phys. Lander. M. J.F. Takahashi. J. Lain.L.A.T. 233. Sparlin. Trzebiatowski. 152.T. 891. Murasik. 295. 2nd Int. 4064. Stat. B.J. Blank and R. A. 1171. Hill. A. A. 119-184. 1976.) (AIME. E. A. Matthias. W. O. 5035. Leciejewicz. 1974. Harvey. Freeman and J. Chim. Lindner. Magnetism. J. 1969a. Dunlap. Marples. 606. Dunlap. Ser. 733. Darby.V. Stat. Leciejewicz. 149. Czech. 1451. 4.. Henkie. . AppL Phys. 34. Phys. 343. Lam. P. Ser. Pietraszko.A. Zh. J.. 38. (b) 73. B. Soc. A. Suppl.D.K. 510.. 17. Lab. 30. Neorg. 138. 1974. 2nd Int. C 9.S. Phys. Sol. Murasik. Tagawa. J. 1974a. Tro~.F.J.H. J. S. Phys. 791. Phys. Wrociaw. J. Z. 1594. A. 16. 4333 (1973). Sol. 269. 1975. and D.L. Tro~. 489.. Smetana. Przystawa. D. K163. and R. J. Actinides (J. Mulak. Acad. SatyaMurthy. Rosenfeld. S.. Z.H. Science. 1971. Rev.J. Polon. Czopnik. 7. 1971b. T. 1970. LH. Bull. Schinkel. W. Spidet. J. Sci. Lander.H. T. 5. Phys.B.A. V. 193.E. (a) 13. Dunlap. Univ. 383. Astron. Phys. Proc. W. Conf. Suski and R. Electr. G. Actinides (J.. 675. Leciejewicz. Lain. 487. Ross. Davidson. Atoda. A. J. Naoumidis. 1976. 53.. Tro~. J. Erd6s. Smith. Phys. Star. Trzebiatowski. Appl. Smith. 1973. Physique. H. Thesis. Murasik. Euert.A.H. Raphael. in Proc. Soc.. Haire. 1967. C. 10. Fields. A. J. 1963. (a) 19. AIP Conf.) (Ossolineum. B.R. Rodier. Stocker. A. C. Chim. Sci. W.E. Eiectr. W. K. B 9. (b) 64. Phys. W. J. Proc. H. W. 30. K85. Harvey. ~liwa. S. B8. 641. J. Brit. 24. 8. Chem. Sol. Sol. Suski and R. C. p. T. Popielewicz. Blank and R. Chim. Sci.. Ceram. H. 1977. Chim. C. Struct.W. Ser.L. Phys. Hrebik.. Przystawa. Raphael. Sternberk. Mosk. 1966. A. 87.. 535. eds. Chem. no. Slovianskik. Brodsky. Warren. in Proc. Price. Mueller. W. K147. Fiz.W. J. M. T. J.J. C. M. Int. 2nd Int.. W. Bowska and Z. Stat. C 1-744.. Nicolas. Praweczki. Proc. Bg. J. NoSI.) )Ossolineum. Slovyansky. M. Stat. de Novion.H.. 1971a. F. A. Stat. V. 102.. Mydlarz.) (AIME. no. Stalinski. 1943. J. Pletyushkin.W. B. J. 52. Tro6. Struct. Wedgwood. Mydlarz. 1972. Solids 33. Phys. 17. Polon.. B21. Mat. 1972. B4. 1960. J.. Zygmunt. Bull. 1974. Phys.J. 1977. Sci.. Ligenza. J.J.L. Conf. preprint no. J. Chechernikov. (Paris). J. Wrociaw... Sol.. J.I. M. Sol. de Phys. M. 267.W. A. Menovsky.. Sol. Acad. 1451. D. Ellinger. 1978.. de Phys. Woifers. 76. B. Stat. 1967. K45.F. A. K89. Z.J. C. W. Zachariasen. 1954. J. A. Palewski. Murasik. Suppl... Zygmunt. Soc.K. G. 31. Sci. 1969a. R. 1976. Sci.Y. Ser. 1974.. Suski. J. W. no.M. A.. G. B. J. Slat. J. A. Biegafiski. Haire.. Wroclaw) p. G. Appi. AIP Conf. C... Fr..H. V. Bull. F.. 1974b. Tro6. Sternberk. 2158. Phys. 1972. V.E.J.. D. Tro~. Ser.. Int. 101. Suski and R. T. A. B9. Ligenza. 340.. 11. 28. 1979. J. Wroctaw) p. Menovsky. A. W. Sorge.G. Phys. 317. 74. T. Phys. Phys. S. 1976.. Sevastianov. Lindner. A. Polon. Slat. Hill. Zentko. Stewart. Matthias. 147. K107. de Novion. Mag. 261. A. Appl. 1976. 397. Stat. Khimii. T. Stalinski. 3. 1973. Sechovsky. Phys. Electrochem. 217. eds. L. Soc. Mulak. Huang and R. 1974b.. G. 1967.. Kikuchi. Z. Ross. Hrebik. 125.G. Phys. Brodsky. G. Biegafiski.J. Olsen. J. Tanaki.) (Ossoiineum. Menovsky. Am. 1483.G. J. J. 297.. Obolenski. Smith. Ligenza. 605. 23.H. Struct. 1041. Ansorge. Mulford.T. F. Chim.D.. C.. 1972. J. Olsen. 4035. E. N. 1969b. Leciejewicz. V. eds. Smith. Reddy. Stat. Sol.V. A. J. Robinson. Am. Solid State Chem. 356. Min6ral Crist. J. Conf. 1970. W. 32.. 1977. Sampson. V. Phys. Lukaszewicz. R. Actinides (J. Smetana. T. Sternberk. Phys..C. Nellis. N. Hill. Nellis. 23. 1963. Nasu. 1971.B. Bull. 21. Sandenaw. J. Leciejewicz. 1358. T.ACTINIDE ELEMENTS AND COMPOUNDS Misiuk. Stat. R. New York) p. 1979. Phys. A. in Proc. 1977. Suski.B. Lam. Mulak. Rev. Acad. A.R.. 1972. A. Nucl. 447 Chem. 17. 4. J.. 38. Phys. Murasik. Rev.. W. J. Mulak.R.R. M. Solids 31. Menovsky. 23. 969. A. Wrociaw) 1977 p. 1975. Solid State Commun.L.. Sci. Mitchell. Fillion. 1962. Vest. SoL (a) 28. 96. 1975. Bull. 1972. Zygmunt. Electr. Mydlarz. R. Phys. 112. Polon. Niemiec. G. Smetana. Mydlarz. 200. Sasa Y . Brodsky. H. 1965. 2187 (1974). P. Suski.J. High Magn. J. Ceram. Acad.M.. J. Sol. in Plutonium and other actinides (H. Soc. Int. Suski. Sci. eds. 1975. 1973. E. Z. Swec. 5.. 403. 337. 1974a. Nellis. Star. Tro6.. Rare Earths and Actinides Durham (Inst. Suski. de Phys. eds. T. Trzebiatowski. Polon. Bull. Bull. 1972a.. Struct. Lain. Fournier. Trzebiatowski.. du Plessis.. A. T. Plutonium-Verlag Chemic. Gr~nvold. Mag. Polon.) (AIME. Tro~. Sci. R.. Acad. Polon. 14. J. Sci. (b) 43. Mag. 1976b. Palewski. J. Int. Ser. Brodsky. eds. Acta. Ser. R. Polon. Bull. Brodsky. 26. VI. J. Westrum. 1967a. Z. Phys.. Misiuk. Polon. T. Phys. J. Phys. 1977.L. Paris. Bull. 9.E. New York) p. in Plutonium and other Actinides (H. (a) 14. Sci.L. W. A. Phys. Suski and R. de Phys.. Acad. Magnetism. (a) 12. Chim. 373. Acad.. p. Sci. T. Palewski. W. Zygmunt. T.K. and E. Trzebiatowski. W. W. Trzebiatowski. Sci. Salmon. p. Wroclaw) p. Dunlap.. Sci. Mag. 10. 3. Phys. CNRS.. Trzebiatowski. 161. 34. Chem. Phys. W. 1971. W. Flotow. 59. 34. Niemiec. Z. Wood. Electr. 1967b. C.. Rev. and W. Tro6. Bull. Mydlarz. Bull. Trzebiatowski. Sci. S6r. ~liwa. 401. Tillwick. B. Suppl. Sol. Sci. Ser. Stat.W. Int. in Proc. Stat. Kletowski..W. 42. 1960. 277. Chim. Mulak. Phys. no. Wroclaw) p. Trainor.. Ser. Sci. Polon. 172-5. Dig. 1969. C 5. Sci. Bull.H. C 5. F. Kuznietz. W. S~pichowska. Suski.. W. p. J.. 543.. W. J. in Physique sous champs magn~tiques intenses. mag.. eds. L. H. A. SCpichowska. 1952. 1954.. Electr. BI0.R. W. J. Suski.. G. E. W. AlP Conf. Chem. Acad.. J. Rao. Conf. W. Polon. Rocz. A. (a) 27. 147. 9. W. Tro6. J. 4. R. 525. 15. W. 1979. 517. Sol. 1963. Chim. Sci. 1976. Ser.. W.R.. Wedgwood. 1976b.. Trzebiatowski. 1976a.J. Trzebiatowski. W. B. Zygmut. Sci. Chim. G... Sol. A. Wedgwood. 457. Wojakowski. T. W. K51. 1972b.in Conf.. A Misiuk. Wojakowski. TRZEBIATOWSKI Trzebiatowski. 28. Wojciechowski. Trzebiatowski. Suski. 1511. 1962. Sci. D. 110. 12. Mydlarz.. 1961..) (Ossolineum. W. Mydlarz. Lindner. Chim. Chim. Ser. Westrum. W. 1964. Zolnierek. Tro~.. Polon. P. Phys. Trzebiatowski.. 57. R. 687. Ser. 43. Waiters. W. Cox. B. Palewski. Tro6.F. A52. Rocz. 1962. Proc. 4.. 3. Tro~. Acad. Sci. 4902. 1976a. 1976a. 1976. Suski. E. Acad.M. 3. Suppl. 1287. Sci.S. Chim. Mag. T. Proc. J. W.. Ser. Moscow. Acad. ~liwa. W. J. Mydlarz. Chim. Shenoy. Bull. 1961. 3618. Mat. R. 1970. Bacman.. Phys. Sci. 117. Sol. 48. Chem. Chim. Mat. A. Suski. P. 661. Stat. Misiuk. Suski. 1979. voi. Takahashi.. 329. A. Czopnik. du Plessis. 3. M. 1968. 1966. 1974. 1965. Acad. Sci. T. Suski. H. no. Polon. J. Jr. Chem. 399. R. Trzebiatowski. Rev. W. Culbert. Bazan.. KII3. A. Sci. Actinides (J. 681. A.. Chim. R. 495.. Phys. W.. Jr. R.. 395. B. London) pp. Ser. 1977. S~r. T... Taube. l lth Int.. W. Wojakowski. Actinides (J.U. Trzebiatowski. Zygmunt. Conf. Trzebiatowski.) (Ossolineum. F. 12. Trzebiatowski.. Palewski.W.B. Polon. Henkie. M. in press. J. Phys.. 1968. 195. 2427.. W. 1963. Wojakowski. Mulak. . 83.. A. P. Phys. in Proc. 1975a.. in Proc. 1975b. 1976b. R. 37. Sci. Trzebiatowski. Sci. S~r. CNRS p. R. F. Sci.. Bull. 499. Sci. Polon. Misiuk. 2nd Int. M. Propric~t& physiques et structurales des d~riv~s s~mimetalliques. 1971. A. Chem. 1972. Sol. 75. D.J.. W. Sol. 24. Conf. Acad. Rocz.448 W. M. Acad. Tro~. W. Warsaw.D. Chim. 319. P. Trainor. 3012. 15. W. Palewski.L. 2nd Int. Suski. 695. Wolfers. Z. 155. Physics of Semiconductors.. (a) 14. Z. V. 19. de V. p.. T. Polon.F. 10. Henkie. SCpichowska.A. Tro6. A. Mulak.. Acad. Henkie. Suski. A. Stat. Wojakowski. Smith. Bull. A. de V. Z.E. Chim. A. S~pichowska. Suski. Trzebiatowski. A. Trzebiatowski.. Acta Phys. 8. Stalinski. 437. 11. J. Tillwick. 1978. 224. Veal.F. Misiuk. M. Lett. Conf. Osborne. Polon. Trzebiatowski. Rocz. W..V. Ward.. Chem. W. Bull. Sci. Bull. K157. A. Rocz. Phys.. W. 37. A. 69. Westrum. Coll. 629. D. Blaise. 1972. Polon. 1972. Leciejewicz. Acad. W. 1972. Palewski. Struct. 1964. 483.B. D. A. Suski.. Stewart and J.. 1971. Mat.J. Stalinski.A. 44. Phys. Suski and R. Stat. A. Blank and R. Sci. J. 12. 1974. W. Suski. Chem. 1972. B 26. Jap. Phys. Phys. J.. 139.. 210. 1978. Yeliseyev Neorg. 1977. Soc. (a) 25. A.. J. Stat. 1974a.. 1828. Ligenza. Siovyanskich. S. Mat. 1973. W. T. H. Stat. A. 1976. 1974b. Zo|nierek. Ellert. Leciejewicz. 1972. G. Stat.K. R6v. 48. Sol. Suski. Zygmunt. 14. K77. Z. Zygmunt. Min6rale.. (a) 22. J. 8. S.V. Ptasiewicz. Murasik. 659. A. Sol. Leciejewicz. Ligenza. 449 Zygmunt. and Takada. Phys. R. Zygmunt. Czech. Mat. 731. 4. Czopnik. Tro~. M. Stat. 75. Zygmunt. Phys.ACTINIDE ELEMENTS AND COMPOUNDS Yamada.. Sol. A. Mag. Phys.I. Sol.. Phys. E. 34. 1968. A. Yamada. J. Chim. A. Mydlarz.. Mag. . Duczmal. (a) 18. Theor. 1972. M. W. 51. J. and Takada. Phys. Yarembash. 624... 1174. Zelen~. Progr. A. 1973. (a) 9. chapter 6 AMORPHOUS FERROMAGNETS F. LUBORSKY General Electric Company Research and Development Center Schenectady. 1 Edited by E. NY 12301 USA Ferromagnetic Materials. 1980 451 .E.P. Wohlfarth © North-Holland Publishing Company. Vol. . . . . . . . . . . . .2. . . . 3. 3. . A p p l i c a t i o n as s c f t m a g n e t i c m a t e r i a l s . . . . . . . . . . . .3. . . . . . . . M f s s b a u e r s p e c t r o s c o p y r e s u l t s . . . . . . . . . . . . . . . . .1. . . . . . . . . . . . . . IntrodL ctic n . . . . 1. . . . 6. Frel: a r a t i o n . . . . . . . . . . 3. . 1 I. . . . . . . . . .1. . . . . 2. . . . . . Q u e n c h i n g f i o m the m e l t . . . . . . . . . . . . .4. . . . . .5. . . . . . . . . . . . . . . H i s t c r y . . . . . . . . . . . . . . . . . . . . . . 2. . . . . . . . . . . . . . . . 1. . . . . . . . . . . . . . . . . o t r q ~ y . . . . .4. . . . . . S u s c e p t i b i l i t y and p e r m e a b i l i f y . . . . . .2. . . . . . . . . . . L o s s e s . . M a g n e t o s l r i c l ion . . . . . . ~ c o p e o f 1his r e v i e w . D e t r a i n s t r u c t u r e . . . . . . . . . .1. D e s c r i p t i o n s o f s t r u c t m e . . . . . . . . . . . . . .7. . . . . . . . . . . . 4. . . . . . . . . S t r u c t m a l resuTts . . . . . . F u n d a m e n l a l m a g n e t ' c I:roperties . . . . S t r u c t u r a l a n d c o m p o s i t i o n a l a n i s o t r o p y . . 8. . . . . 6. . . . . . . . . . . . . . . . . . . . . . . . . E l e e t r o d e l ~ o s i t i o n a r d c h e m i c a l d e p o s i t i o n . . . . . . . . . . . . . 3.3. 2. . . . . . .2. . . . . . . . . . 6. . 4. 7. . . . . . . . . . . . . . .2. . . . .3. . . . . . . . 64. . . . . . . . . . . . . . . . . . . . . . . . 3. . . . E x p e r i m e n t a l t e c h n i q u e s . . . . .4. . . . 4. . . . . "[he s f r u c t u r e c f a m o r p h o u s m e t a l l i c a l l o y s . . . . . . . . . . . . 6. . . . . . . . . . . . . . . . . S t r a i n . . . . . . . . . . . . . . . . . . . . 9. . . . . . . . . . S t a b i l i t y . . . . . . . . . . . . Ref~rer ces . . . .3. . . . . . . . . . . . . . . . . S p u t t e r dcposit:'on . . . . . . . . . . . . . . . . . M a g n e t i c m o m e n t a n d s a t l : r a l i o n m a g n e t i z a t i o n . . . . . . . . . . . 1. . R e m a n e n c e . . . . . . . . . . . t i o . .2. . . . 4. . 453 453 455 456 4~7 457 458 459 460 460 467 467 468 474 476 ~81 4~2 491 497 501 5134 5(5 507 510 510 511 514 514 517 517 518 523 525 . . . . . . . . P r e v i o u s r e v i e w s . . . . . . . . . . . . . 2. . . . . . . V e c u u m d e r o s i t f o n . . . . . . . . . 1. . . . . . . . . . . . . . . . . . . ExcFange ~nisotrcpy . . . . . . . . .s a l m ~ t i c n l . . . . . . . . . . .3. T h e o r e t i c a l a n d t e c h n o l o g i c a l s i g n i f i c a n c e . . . . . . . . . . . . 4. . . . . . . . . . .4. . . . . . C o e r c i v e f o l c e . . . . . . . . . . . . . . M a g n e t i c a n i s o t r o p y . . . . . 4. . . . .1. . . . . . . . C u r i e t e m p e r a t u r e . . . . . . . . . . . . . . . . . D i r e c t i o n a l o r d e r a n i s o t r o p y . . . . 2. 5. . . . . . 10. . .t o .m a g n e t o s t r i c t i o n anL. . . . . . . . . . T e m p e r a t u r e d e p e n d e n c e c f m a g n e t i z a t i o n . . . . .CONTENTS 7. . . . . . . . . . . . The principal order present is imposed by the roughly constant separation of nearest neighbors. This was based on evidence that the electronic band structure of crystalline solids did not change in any fundamental way on transition to the liquid state. rather than long-range order so that ferromagnetism. However. observing only one broad diffuse peak in the X-ray scattering pattern in the non-magnetic high phosphorus alloys. for example directional ordering due to magnetic or stress annealing. The first report of an amorphous metallic alloy appears to have been made by Brenner et al. should not be destroyed in the corresponding amorphous solid. (1960) on the preparation and properties of amorphous metallic alloys. History Because of the lack of atomic ordering it was believed for many years that ferromagnetism could not exist in amorphous solids. that amorphous solids would be ferromagnetic. on the basis of theoretical analysis. in 1960 Gubanov predicted. Simple amorphous solids have random structures but with differing degrees of short range order depending on the nature of their atomic bonding. I. form structures similar to the random packing of hard spheres. However. Such alloys have been in use for many years as hard. Introduction The terms amorphous solid and glass have no precise meaning. Both methods propelled a liquid alloy drop onto a cold surface where it would be spread into a thin film and thus rapidly solidify. wear and corrosion resistant.1. This implies that the band structure is more dependent on shortrange.I. Miroshnichenko and Salli (1959) 453 . These terms are generally accepted to mean "not crystalline on any significant scale". not all disordered materials are amorphous since there are disordered crystalline alloys where different atoms irregularly occupy sites of a regular crystal lattice. They introduced two new methods of achieving very rapid quenching from the molten state. In this work they electro-deposited nickel-phosphorus alloys. Thus amorphous metals in which nearest neighbor central forces dominate. (1950). The present great interest in amorphous metals research stems from reports by Duwaz et al. coatings. which depends on short-range order. Other types of order may also be present. 7 T]* and the relatively low coercive force of 3 0 e [240 A/m]. This appeared to be a typical soft ferromagnetic alloy with the large saturation magnetization of 7 kG [0.10e [8 A/m]. reported by Duwez and Lin (1967). . A real technological interest developed after Pond and Maddin (1969) reported on the preparation of continuous ribbons of amorphous alloy. units will be used throughout with S. (1975) first demonstrated the reduction of coercivity in these alloys. However the early amorphous alloys of CoP. (1975a) showed that annealing under tensile stress reduced the coercivity of an Fe-Ni-P-B-Si alloy to 3 mOe [0. the study of the effects of the electron donor characteristics of the metalloids on magnetization and Curie temperature have led to the *c. in the order of 0. Their method consisted essentially of directing a molten stream of the alloy onto the surface of a rapidly rotating drum. expected to have no magnetocrystalline anisotropy. Many series of alloys have now been reported composed of the transition metal alloys with a wide variety of metalloids. Luborsky et al. This gives rise to a large strain-magnetostriction anisotropy. It is now clear that this is the result of the large strain introduced by the rapid quenching in the splat technique. These processes are now generally referred to by the onomatopoetic term "splat quenching. The melt quenched alloys of Fe-P-C appeared to be compositionally much more homogeneous but still developed coercivities of a few oersteds [160 A/m].3 A/m]." The new amorphous and metastable alloys prepared from such equipment were used in the early work to explore the many possibilities opened up by these new rapid quenching techniques. At about the same time Egami et al.PI~C~0. Simpson and Brambley (1971) appear to have been the first to point out that the amorphous alloys. The first alloy with a substantial magnetization. should have very low coercivities. At this point it was now clear that amorphous metallic alloys could be prepared in large quantities at low cost. further confirming Gubanov's predictions.8 A/m] by suitable anneals and showed that the changes in properties correlated with the relief of internal strains.g. These high coercivities are now understood to arise from compositional inhomogeneities demonstrated by Chi and Cargill (1976) from small angle X-ray scattering analysis and from strain-magnetostriction anisotropy. units in [ ]. prepared by deposition methods had coercivities as high as 10-20 Oe [800-1600 A/m]. down to less than 10 mOe [0. Zero magnetostrictive alloys have been reported in the Fe-Co system.E. many orders of magnitude higher than in the commercially available Fe-Ni alloys.~4 F. was Fe.% Si containing some ferromagnetic element partially substituted for the Pd. LUBORSKY almost simultaneously reported a device for spreading such a liquid alloy sample between two mutually approaching pistons. In the past few years there has been a literary explosion of both theoretical and experimental results on amorphous magnetic alloys. Amorphous alloys of Fe-Ni-P-B prepared by the melt-quenching technique into ribbons by solidification on the surface of a rapidly rotating drum exhibited even lower coercivities.I. The theoretically expected retention of ferromagnetic behavior in amorphous solids was first demonstrated by Mader and Nowick (1965) in work on vacuum deposited Co-Au alloys and soon thereafter by Tsuei and Duwez (1966) in work on splat-cooled Pd-20at.s. to understanding the origins of the extrinsic properties so important in the practical application of a magnetic material. permeabilities and magnetizations which make them competitive in quality to existing commercial alloys. the studies of the mechanisms responsible for the low temperature embrittlement and magnetic anneal instability have led to the prediction and preparation of alloy compositions possessing greatly improved stability. this has only limited applicability because most of the interesting amorphous alloys have no simple or single crystalline counterpart. to prepare homogenous alloys which can be studied as a function of composition and temperature without complicating interference from structural phase transitions. increased attention is being given to the production of wide ribbon filaments. Other properties have unexpected features and ambiguities. Although. One of the singular advantages of studies on amorphous alloys is that we can vary the composition continuously. to the preparation of alloys to compete for particular applications. These results will be described in detail in the main text.. a few years ago. Curie temperature. spin waves. Each of these will be discussed in some detail in the forthcoming sections of this review. For example. Much of our understanding has come from comparing the properties of the amorphous alloy with the same or similar crystalline alloy. e. the magnetic and structural stability has been evaluated at higher temperatures and found to be adequate for most foreseeable applications. by suitably annealing amorphous alloys.2. a variety of compositions have been demonstrated to have dynamic losses. The third and perhaps present stage of work is showing an increased subdivision of interest prompted by an increased awareness of potential applications. Theoretical and technological significance Until recently the major efforts in solid state physics have been confined to understanding the properties of crystalline solids. magnetostriction. The second stage started to systemize the results into an experimental and theoretical framework and then moved towards interest in particular properties. and to evaluating and understanding the long term stability of these alloys. although amorphous solids consist largely of random aggregates of atoms their densities are only slightly different from the density of crystals of the same composition.AMORPHOUS FERROMAGNETS 455 development of high moment. Some of their properties are entirely as predicted. Three overlapping stages can be identified in the development of amorphous magnetic alloys as just summarized. temperature dependence of magnetization. The first stage was concerned with preparing this new state of matter by a variety of techniques. 1. this statement was thought to be entirely . For example. the magnetization. high Curie temperature alloys. hysteresis. critical behavior. Amorphous solids now represent a new state of matter. confirming its existence and the existence of ferromagnetism in the amorphous solids. how does the amorphous atomic structure affect all of the magnetic characteristics.g. Microscopic information has been obtained from studies of the properties of single crystals. However. anisotropy. and coercive force. The broad theoretical question is. the transition metal-metalloid (TM-M) alloys and the rare earth-transition metal (RE-TM) alloys.~hough the alloy remains amorphous. the Curie temperatures and mechanical properties change on annealing at temperatures well below the crystallization temperature. Co or Ni with the remainder being B. Jones (1973) provided an extensive compilation of developments in splat-cooling and metastable phases. Si. The RE-TM alloys are cove~ed in col. LUBORSKY true. All of these changes can have effects on the observed properties. Some of the alloys have been treated to develop losses and permeabilities competitive with some of the very expensive Fe-Ni (Permalloy) alloys. more or less. These good properties have been. higher permeabilities and are expected to be competitive in cost. the structural features obtained in both metastable crystalline and amorphous . the amorphous phase is not a si~bl~ ground state of the s0ild. Once made the same metalloids stabilize the amorphous phase but their presence drastically alters the magnetic properties of the alloy by donating electrons to the d-band and thus lowering M~ and To. For example. with high magnetizations may compete in higher power transformer application where the Fe-3% Si steels are now used. work published up to the e~nd of 1968.~6 F. achieved in some melt quenched alloys and we can account for their behavior by the same models as used for conventional crystalline soft magnetic materials taking into account the presence of the anisotropies mentioned above. Previous reviews There have been a number of reviews covering the general phenomena of rapidly quenched metals. These amorphous alloys have considerably lower losses. 1. C. mainly done in his laboratory. ch. The TM-M alloys typically contain about 80at. The presence of the metalloids is necessary to lower the//nelting point making it possible to quench the alloy through its glass temperature rapidly enough to form the amorphous phase.3. It is clear that many of the amorphous magnetic alloys will become useful soft magnetic materials. it has now been recognized that phase separation. Giessen and Wager (1972) reviewed the structure and properties of amorphous metallic phases produced mainly by quenching from the melt. That is. Other alloys. diffusion of various species and structural relaxations all occur e~ev. 2. or AI. but unfortunately the reported alloys have a somewhat lower saturation magnetization than the Fe-3% Si. The presumed isotropic character of the TM-M amorphous alloys had been predicted to result in very low coercivities and hysteresis loss and high permeabilities. 1967) ~eviewed in some detail most of the early work. Duwez (1966. Giessen and Willens (1970) emphasized the underlying principles 0f the work reviewed and Anantharaman and Suryanarayana (1971) classified the information obtained from the alloy systems studied.E. Giessen (1969) alphabetically classified by alloy. P.% Fe. There are two technologically important classes of magnetic amorphous alloys. 5. all the properties of technological significance for application as soft magnetic materials. It included an analysis of the methods available for quenching from the melt and an understanding of how they work. (1975a). Scope of this review In this review we will first describe the preparation of amorphous metallic solids. Most often this is done by analyses of X-ray. ch.e. derived both experimentally and theoretically is covered by Cargill (1975a). alloys which require more or less rapid quenching to achieve the amorphous phase. The various methods used to prepare amorphous metallic alloys. the response of the as-quenched structures to annealing. 1. the magnetic properties reported will be presented and the origin of these properties will be discussed. thus depend on various kinetic barriers to growth of crystal nuclei. by Tsuei (1976). Preparation Amorphous alloys are all in a metastable state. During quenching. They argue that any liquid can be made into an amorphous solid if cooled rapidly enough. electron or . if nuclei are present. Our present state of understanding of the resultant atomic structures will then be described and the experimental methods used to obtain structural information. Jones and Suryanarayana (1973) published a comprehensive annotated bibliography covering the period up to near the end of 1972. The review is restricted to the ferromagnetic alloys possessing stability at least up to room temperature. to be described next. Cohen and Turnbull (1964) have discussed the origins of these barriers and their dependence on the parameters of the materials. Their preparation. Gyorgy et al. and finally the properties and applications of splat-cooled alloys. and stability at room temperature. 5 of this series. by Mizoguchi (1976). The rare earth-transition metal alloys will be covered in vol. There are various techniques in use to determine whether a particular metallic alloy is amorphous. allow a variety of different alloys to be prepared. or to nucleation barriers which hinder formation of stable crystal nuclei. The status of our knowledge of the structure of metallic alloy glasses. and by Luborsky (1977b). i. Our understanding of the formation and stability of amorphous structures was reviewed by Takayama (1976). Reviews have also been written covering specifically the magnetic properties of amorphous metallic materials. 2. the alloy must pass rapidly enough through the temperature range where nucleation can occur so as to prevent nucleation. (1976b) and by Alben et al. consisting of an atomic arrangement which has no long-range periodicity. The information available to evaluate amorphous metallic alloys for use as soft magnetic materials was reviewed by Egami et al. (1977). This scope covers mainly the transition metal-metalloid alloys. (1976). by Hasegawa et al.4.AMORPHOUS FERROMAGNETS 457 phases. Finally. The state of understanding of the origin and behavior of ferromagnetism in amorphous solids was covered by Cargill (1975b). 2. The properties and understanding of the behavior of almost pure transition metal amorphous films were critically evaluated by Wright (1976). approximately 2R here. Disagreement still exists concerning the evidence which is necessary to uniquely characterize a particular sample as amorphous. 2. Vacuum deposition The criteria for the formation of an amorphous phase by vapor deposition can be described in terms of whether the added atom is prevented from diffusing more than an atomic distance before it is fixed in position by additional atoms arriving.1. These are usually prepared by the direct solidification from the melt since they require easily attainable cooling rates to inhibit crystallization.~8 F. Following Chopra (1969). Amorphous materials such as common glasses and plastics are familiar articles of use to everyone. Ts. Thus virtually all of the atoms are adsorbed. At substrate temperatures below ~ 3 ! T~ it is doubtful whether the liquid phase ever exists. Qd is the activation energy for diffusion. However. = aZv e x p ( . k is Boltzmann's constant and Ts substrate temperature.) (2) (1) where a is the atomic jump distance. These higher cooling rates are a necessary condition for achieving the amorphous state in metallic alloys. For metal atoms the thermal equilibration time is considerably shorter than the average desorption time. from density measurements and particularly from changes in properties on heating through the crystallization temperature. Thus the disordered or amorphous phase is highly likely to be formed. Typical values of the parameters.E. an equilibrium is set up between adsorbed and desorbed atoms. All of the techniques to be described result in effective cooling rates orders of magnitude faster than used for conventional silicate glasses or for casting of ingots into molds. the arrangements of the atoms cannot be uniquely determined from these analyses. After arriving at the surface an atom is free to diffuse until it is fixed in position for example by arrival of other atoms.Qo/kT. The presence on the substrate of different adatoms might both reduce the mobility and increase . for representative cases. Strong inferences come from examination in the electron microscope at resolution of the order of a few angstroms. magnetic coercive force. v is the vibration frequency. the average distance traveled by an atom in time t is given by = (2tD~)ta where D~. from Scott and Maddin (1976). mechanical hardness and in other properties. show that the adatom cannot diffuse more than an interatomic distance before it is frozen in position. LUBORSKY neutron scattering experiments. the surface diffusion coefficient. at the crystallization temperature there are rapid changes in resistivity. = h/kTs. is given by D. For example. heat evolution. Vapor quenched amorphous alloys are almost always deposited onto a substrate at a temperature well below the glass temperature. An atom can be taken to be free to move for aiR s where R is the deposition rate. When a stream of atoms arrives at a substrate at a temperature Ts. Crystallization temperatures for these are summarized in table 1. Wright (1976) has recently reviewed these results for the transition metal elements.AMORPHOUS FERROMAGNETS 459 the distance that an individual atom would need to diffuse to form an ordered array. Even then most results are suspect due to trapping of impurities from the vacuum into the film. Thus deposition must be carried out at very low temperatures. as discussed in volume 2 ch.6 Tc (amorphous) Tc (crystalline) < 1 (in alloys) Material Fe Co 38 0.7 nm/s]. 5.2--0.3-0. 25 A at 50 K Increases with impurity content to 8 0 K at ~ 1 % Films with several percent of occluded gas Ms (amorphous) M5 (crystalline) 0. The preparation of pure amorphous films of transition metal elements is difficult and produces films which crystallize well below room temperature. partly because of the ease of preparing these alloys by the melt quenching techniques and partly because of the large difference in vapor pressure between the constituents.6-0. The alloys of amorphous metals are much more stable and therefore potentially useful. A power dissipation of 200 watts will give deposition rates of . Sputter deposition has been used TABLE 1 Comparison of amorphous and crystalline saturation moments and Curie temperatures for the transition metal elements (Wright 1976) Crystallization Temperature. K Comments 4 (150 A thick) Thinner films transform at higher temperatures.g.2. In particular.6 0. The preparation of transition metal-metalloid alloys have not been investigated very extensively by vacuum deposition. Sputter deposition The criteria for formation of an amorphous film by sputter deposition is the same as described for vacuum deposition. 2. e.00 < 1 (in alloys) Ni 70 0. The advantage of sputtering is that the deposit composition will be essentially the same as the source material.95-1. As an example Bagley and Turnbull (1970) have prepared Ni-P alloys.4 0 0 A / r a i n [0. Extrapolation of properties from results on "dirty" films unfortunately is often necessary. the rare earth-transition metal (RE-TM) alloys are of interest for magnetic bubble applications. but flash evaporation was necessary.8 .. Sputtering is typically carried out in a partial pressure of an inert gas. they have also been made by evaporation. such as argon at 10-1Torr using 14 MHz frequency. Although these are usually made by sputtering. bonding and atomic size effects. 1. In contrast to the melt quenching and sputtering techniques where the solid product has the same composition as the melt.460 F. Typical bath compositions and deposition parameters may be obtained from a number of reference sources. without crystallizing. is concerned with their preparation by direct solidification from the melt. A small quantity.%. and NiCoFeP. (1960). The kinetic factors discussed by Turnbull (1969) and by Spaepen and Turnbull (1976) are the nucleation and crystal growth rate and diffusion rates compared to the cooling rate. there is also a good chance of incorporating hydrogen into the deposit.E. ternary and more complex amorphous alloys such as NiP. and kinetic factors tend to be dominant. The structural factors are concerned with atomic arrangement. NiB. which will change the magnetic properties and stability. such as Brenner (1963) or Simpson and Brambley (1971). 2.4. Electrodeposition and chemical deposition Both electrodeposition and chemical deposition have been used for many years to prepare binary. the deposit composition varies widely depending on the deposition conditions and bath composition. NiCoP. The alloy must have a high resistance to homogenous nucleation of crystals and the Tg must occur at temperatures not too far below the liquidus. 2. CoP. The factors controlling Ts and crystallization are both structural and kinetic. up to 100 rag. The amorphous alloys are formed on deposition from conventional electrolytic or electroless baths provided a sufficiently high percentage of phosphorous or boron is deposited. in both electrodeposition and chemical deposition. 5. These are described next. of the metal or alloy is melted in . in the region of 1030at.3. Thus a low eutectic temperature compared to the melting point of the metallic element coupled with a metal-rich eutectic composition favors the formation of the amorphous phase. shown schematically in fig. LUBORSKY extensively to prepare rare earth-transition metal films for bubble memory applications as is discussed in volume 2 oh. 2. the alloy must cool through the temperature range Tm to Tg.4. was developed by Duwez and Willens (1963). Much of the present interest in amorphous metals in general. In addition.I. Since the pioneering work of Duwez et al. a number of devices have been reported for obtaining the necessary high quenching rates and for producing continuous filaments. These factors tend to have limited predictive value. and amorphous magnetic metals in particular. The interest in this method stems from the wide variety of alloys that can be made as well as from the potential low cost of preparation. the melting temperature to the glass transition temperature. Quenching from the melt To form the amorphous phase by any of the liquid quenching devices. The gun This technique. the foils are transparent to the electron beam and hence can be directly examined in an electron microscope.4. The melt does not fall through the orifice because of high surface tension.. When desired. A two-piston device using magnetic yokes . the molten metal passes through the orifice and spreads onto a copper substrate in the form of thin foils (up to 15/~m in thickness). The shock wave is generated by the rupture of a thin myler diaphragm located between the highand low-pressure chambers by means of an inert gas at high pressure. the substrate can be maintained at low temperatures. The thickness of the foils varies. Apparatusfor splat coolingby the gun technique. a number of variations of this device with differences in either the melting technique or the process of releasing the piston have been developed over the years. Near the edges and holes. the foils obtained with the "gun" device are not easily suited for the measurement of either physical or mechanical properties.~ MYLARDIAPHRAM ~~[ Fig. either a ceramic insert can be kept at the bottom of the crucible or the metal can be melted by radio-frequency induction-heating. utilizes the concept of catching a molten droplet between a stationary anvil and a fast-moving piston. tungsten and zirconium. Based on this simple model. triggering the piston motion. 2.AMORPHOUS FERROMAGNETS 461 HIGHPRESSURE~ . During its fall the molten droplet cuts a beam of light. Ejected by means of a shock wave. Graphite appears to be the best material for the container for metals and alloys which do not react with carbon. Because of their uneven cross-section. Piston-and-anvU and double piston The next technique. In case of reactive and refractory metals like tantalum. developed by Pietrokowsky (1963). a graphite crucible with an orifice of about 1 mm diameter at the bottom.2. The product is an irregular thin foil. 1. porous in nature and with varying crosssectional area.After Duwezand Willens(1963). but the cooling rate is considerably reduced.E. has recently been described by Cahn et al.3.4. The vanes atomize the drop and project it against a surrounding copper cylinder. solidified at quenching rates comparable with those of the piston-and-anvil PHOTO-CELL ( ~ LIGHT COPPER PLATES Fig. The centrifugal force thus developed ejects the metal onto a copper drum surrounding the crucible. shown schematically in fig. Copper plates are forced together when activatedby moltendrop passing the photocell. In the rotary splat quencher described by Cahn et al.. (1976). With this device. Torsion catapult Roberge and Herman (1968) developed a technique based on a spring-loaded catapult device. and then centrifuging the melt in the crucible.462 F. . a levitated melted drop falls onto a pair of rapidly rotating vanes in vacuo.4. m. roughly ten times that obtained in the "gun" technique. This was achieved by melting the material in a graphite crucible with a 0. In this technique the alloy is melted in a crucible placed at the end of a torsion bar and then catapulted against a cold copper substrate.e. bulk foil specimens were obtained. After Cahn et al. However. the torsion bar is abruptly stopped when it strikes a shock absorber.6 mm diameter hole near the top. i. The thickness may well be up to about 100t. The final product obtained in all the above cases is a foil of almost uniform thickness suited for both physical and mechanical property studies. 2.4. (1976). Centrifuge and rotary splat quencher Kumar and Sinha (1968) built a simple apparatus to solidify a melt rapidly into foils. 2. while the melt continues to travel at a high speed until it strikes the cold conducting substrate. During its motion. 2. Since the foils or flakes formed are quite thick. 2. LUBORSKY for driving. (1976). since the extraction of heat is from both the surfaces of the foil. the overall cooling rate in this technique is still of the order of 105 °C/s. Apparatus for the two-piston technique of splat cooling. the cooling rates are expected to be at least two or three orders of magnitude less than those obtained by the "gun" technique. In their technique. A ~ ~ GAS M£LT DRUM I --I Fig. with an average thickness of 40 to 60/~m and suitable for physical and mechanical tests can be obtained. Some efforts made in this direction toward obtaining rapidly-quenched foils in large quantities are described next. Both reactive and refractory metals can be quenched since there is no container problem. with quenching rates of the order of 107 °C/s. as shown schematically in fig. the thickness along their entire length tends to be irregular. from a graphite mould. If very fast cooling rates have to be realized. the fact that they are only 89% dense suggests that the mechanical properties may not be truly representative of the behavior of the material. 3. 2. The greatest advantage of this method is that foils. 3. without any porosity. In spite of the continuity of the foils. the thickness of the foils will. the size and amount of the product is limited. have to be small.4. Plasma-jet spray Moss et al. Filamentary casting This technique of casting produces flat filaments with a thickness of 5 to 50/Lm.AMORPHOUS FERROMAGNETS 463 technique. It was developed by Pond and Maddin (1969). In this method. .6. necessarily. the molten alloy is forced through a sapphire orifice. and allowed to strike the interior of a spinning drum. After Pond and Maddin(1969). Although the products of this technique have been used for the measurement of mechanical properties.4. 2. foils obtained by the catapult technique are free from effects of plastic deformation.5. In contrast to the piston-and-anvil technique. In all the techniques described so far. (1964) developed the plasma-jet spraying technique. producing material continuously at the rate of a few grams per minute. Apparatusfor continuouscastingof ribbons. fine powder of the alloy is injected into a high-temperature plasma and the molten droplets impinge at a high velocity onto a cooled copper substrate. But it is possible that there need not be any restrictions as regards the length of the sample. (1974). This has been discussed qualitatively by Pond et al. Double roller casting of ribbons. melt temperature and others. drum velocity. Thus wide ribbon may be produced simply by making the orifice rectangular or elliptical in . In both cases. ejection pressure. The cooling rate is estimated to be lOS°C/s. ~ is the density of the molten alloy and or is the velocity of the ribbon which is essentially the surface velocity of the drum. 5). Liebermann and Graham (1976) have derived the expression for the cross-section of the ribbon produced Ar = ¢rck2(p/8~) ll2Vr (3) where ~b is the ejection orifice diameter.- GAS RIBBON Fig. (1970). 4) consists of melting a few grams of alloy and then ejecting it into a pair of rapidly rotating steel rolls. The drop solidifies while passing through the rollers. the solidified fiber is thrown off the drum as a continuous ribbon. 4. (1970). By adjusting the process variables. Variations of this technique are now in common use. Another development in this direction is due to Chert and Miller (1970). Thin uniform ribbons from 10 to 100/~m thick are obtained. for example. LUBORSKY pneumatic cage raises the mould slowly so that the impinging melt does not hit the previously solidified ribbon. the geometry of the filament can be controlled. A similar technique. After Babi~ et al. held together under pressure.464 F. such as orifice size. P is pressure of ejection of the melt as supplied by an inert gas. . with rolls covered with a hard chrome surface rotating at a high speed has been reported by Babic et al. The width of the ribbon is primarily controlled by the orifice diameter and shape. Their technique (fig.E. where the melt is ejected onto the outside of a drum or the inside tilted lip of a drum (fig. Its length is limited only by the amount of material in the mold. The edge of the rapidly rotating disk contacts the clean surface of a molten metal alloy. the crucible melt extraction technique and the pendant drop melt extraction technique. A schematic diagram of the crucible melt technique is shown in fig. adheres to the disk and is brought up out of the liquid. The pendant drop melt extraction method is shown schematically in fig.7. now in the form of a fiber. Care must be exercised to keep the surface clean of slag and other impurities by operating under an inert gas or in vacuum.4. temperature of the melt and other parameters. As a result of thermal contraction and centrifugal force. short fibers are produced directly. A more complete analysis of the casting of ribbons. 5. as well as free jet casting. The great advantage of this is that it eliminates any orifices and crucibles and their attendant problems. this technique is readily run in a vacuum system using an electron beam for heating. speed. contact depth. By varying the disk geometry. is thrown free after some residence time on the disk. Because of its simplicity. The various instabilities in the molten jet and solidifying puddle were described. shape. As the periphery passes through the liquid metal. Melt extraction There are two melt extraction techniques capable of producing amorphous fiber in a continuous manner. Single roll casting of ribbons. (3). (1976).P . . 2. 6. has been reported by Kavesh (1977) leading to expressions for both ribbon thickness and ribbon width. The molten drop is supported by its own surface tension on the end of a rod of the same material. a variety of ribbon geometries may be made. the metal. 7 and is a very similar technique. Results by Liebermann and Graham (1976) on an F e . By introducing notches on the wheel. some metal solidifies.B amorphous alloy agreed with the predictions of eq.AMORPHOUS FERROMAGNETS 465 ~ G A S ~ M E L T Fig.N i . These were reported by Maringer and Mobley (1974) and by Maringer et al. 7. . This procedure is commonly practiced to produce polymeric and oxide glass filaments where the materials have high viscosities and low surface tensions in the liquid state.. 2. Crucible melt extraction. Free jet spinning Free flight spinning involves the formation of a free jet of molten metal and the transformation of the jet to a solid. Pendantdrop melt extraction. A cylindrical jet of molten metal however is relatively unstable because of its low viscosity and high surface energy. LUBORSKY ~. Kavesh (1974) has described a process used for melt spinning of amorphous metallic alloys... . and finally the solidification of the jet. 6. Water is satisfactory for alloys with melting points below about 700°C. It consisted of the steps of forming a free jet of molten alloy in a gaseous or evacuated chamber. . . traversal of the jet through an interface into a liquid medium where the liquid flows in the same direction as the jet and at essentially the same velocity. I ELECTRONBEAM ~ o MELT FILAM ENT .' . After Maringerand Mobley(1974). .... ) FIBER Fig.. (1976)..8.E.' ~ ° / . After Maringeret al. . ~ . Fig. .4.4~ F. Several processes are described by Kavesh (1974). . MELT STOCK . above 700° a refrigerated brine is satisfactory. voids. and finally very short-range variations due to atomic size variations generally susceptible to examination only by X-ray. been concerned with this short-range atomic order. The distribution functions are sometimes presented in slightly different forms as G(r) = 47rr[P(r) - Po] and W(r) = P(r)/Po (5) often called the "reduced radial distribution function" and the "pair correlation function" respectively. The average number of atoms is then 4~rr2P(r)dr. where P0 is the average atomic density. Structural disorder is the lack of crystallinity and refers to the global way in which atoms fit together. Chemical disorder is concerned with local environments. Most work on the structure of amorphous metallic alloys has. (4) Radial distribution functions are defined for systems of different atoms as weighted averages. The weighted averages depend on the composition and on the scattering factors of the individual species. in terms of the external size and shape of the solid. such as magnetic moments. some understanding of the structure of these alloys is necessary. Following Alben et al.AMORPHOUS FERROMAGNETS 3. (1977) we will distinguish between two types of disorder. where P(r) is the atomic distribution obtained from experimental X-ray or neutron scattering or by calculation from models. 3. composition gradients and other heterogeneities resolvable by optical microscopy or other techniques of similar resolution. Then RDF(r) = 4~rr2p(r). Comprehensive reviews of the structures of amorphous alloys have been given by Cargill (1975a. the chemical species and relative positions of the nearest neighbors to an atom.1. 1976). structural and chemical. . in terms of voids and gradients resolvable only by electron microscopy or small angle scattering. A useful and accessible characterization of the structural arrangement of the atoms in amorphous solids can be given in terms of a radial distribution function. then atomic scale properties. attention is being given to larger scale structural effects which may strongly influence the technical and normally extrinsic magnetic properties such as coercive force. RDF(r). of course. are controlled by Chemical disorder. inclusions. For example. losses and permeability. The structure of amorphous metallic alloys 467 In order to understand the details of the magnetic properties. For identical atoms this describes the average number of atoms at distances between r and r + dr from some chosen atom as origin averaged by taking each atom in turn as the origin. Since the most important magnetic interactions are dependent on what happens at quite short range. Descriptions of structure Structure can be discussed on many levels. more recently. electron or neutron diffraction techniques. However. in terms of cracks. The interference function I(K) is then calculated using dispersion corrected atomic scattering factors for each atom present. This shoulder represents the second nearest neighbor local configuration and is absent in interference functions from liquids. and (c) RFD(r) vs. The area under the first peak in the RDF(r). electron and neutron scattering Experimentally._. . j. The positions of each peak indicate the atom-to-atom separations involved in this short-range order. i 0 I 2 3 fir I (b} 4 ' 0 t O| I J I I I I I I0 15 20 25 30 KfI (ol -0 2 4 6 8 rl.5 nm] indicating the existence of short-range order out to this distance. X-ray. vary slightly depending on the function • I I I I I I I I II I [ I I I I I I I • I ~ I 2" 0I . Cargill (1975a). Krl. 8 where rl is the value of r for the first diffuse peak. The common feature in all of these spectra is the shoulder on the high K side of the second peak. for polarization.~) (c) Fig. RDF(r) and G(r) spectra are shown in fig. 8. r(max). The positions of the maxima. The RDF is then. (b) G(r) vs. In many of these alloys oscillations occur in G(r) out to 15 A [1. r for alloys with only one metal atom. d---~) . oo RDF(r) = 41rr2P(r) = 47rrZP0 + (2r/~r) [ K[I(K) . 0 (6) Some typical I(K).2. L U B O R S K Y 3. Measured intensities are corrected for background. called the first coordination number. Metal-metalloid alloys (a) I(K) vs. electron or neutron scattering intensities as a function of K = 4~r sin 0/A where A is the wavelength of the radiation and 0 is the scattering angle. and for Compton modified scattering. .1] sin(Kr) dK.E.468 F. is associated with the average number of near neighbors.2. 2 0o76P22 Ni76P24~ :oli°""A/W_ i-: 0 - o!. the RDF(r) is obtained from X-ray. r/rl. Experimental techniques 3. . I. Analysis by Chaudhari and Graczyk (1974) of dense random packing models for amorphous solids show that the atomic arrangements predicted by these models should produce the observed dark field contrast. In interference micrographs these features show up as clusters of parallel fringes. struetural stability and glass formation criteria. 3. rather than an amorphous structure in germanium. These regions of contrast in dark field electron microscopy have been called "coherently scattering domains" by Chaudhari et al.2. Dark field examination of amorphous alloys typically shows features or graininess on the order of 5-15 A [0. An irreversible change in heat capacity is observed by differential scanning calorimetry in a number of metallic glasses at temperatures well below crystallization. This has been associated with a structural relaxation and is accompanied by small changes in the Curie temperature. The graininess in the dark field micrographs of several amorphous metallic alloys was reported by Herd and Chaudhari (1974) although fringes in interference micrographs have not been reported for metallic alloys. These studies have been used to predict the useful life of the alloys. Calorimetry Calorimetric studies of amorphous alloys have provided substantial fundamental information concerned with configurational entropy. (1976) to study crystal growth in Fe-C and by Walter et al.3. 9.5 nm] in size. 3. Electron microscopy Electron microscope observations have yielded very little direct information about atomic arrangements in amorphous metallic solids. (1972).AMORPHOUS FERROMAGNETS being examined r(max). RDF ~> r(max). The kinetics of the onset of crystallization have been studied calorimetrieally by Clements and Cantor (1976) and both calorimetrically and magnetically by Luborsky (1977a) in a variety of magnetic alloys.2. by Shingu et al. by Duwez (1967) and by Revcolevschi and Grant (1972). these differences typically are less than 1% and thus may be ignored. crystallization and structural relaxation effects. W. These Curie temperature changes have been reported by Chen et al. These observations were initially interpreted as evidence for a microcrystalline. . and to identify their structure and composition by making use of selected area diffraction.2. for example by Mader (1965). The electron microscope is very useful to detect the first appearance of crystallites on annealing. This was normally interpreted as indicating the absence of crystalline regions.5-1. (1977) to study crystalization of FeNiPB. Analyses have been reported for example by Bagley and Turnbull (1970) for crystallization of Ni-P. 469 (7) For the metallic glasses. Two topics are of particular interest here. atomic bonding. G ~>r(max). (1976) for a variety of alloys as shown in fig. Normal high resolution bright field examination of thinned specimens are free of any features. to follow their growth. 64 and 0..-e-o'e'''e'''e- ' ' E}.71 +--10% with most of the values at 0.470 F. Curie temperatures as a function of anneal temperature for amorphous alloys (FexTI-x)75P16B6AI3. The calculated densities are usually within +__5% of the measured densities. These density results illustrate the structural similarities between various amorphous alloy compositions.e.. The value of 1 .z~.~ ' ~ ' e ' ' e ' ¢ -Oy' p55c ZX " / . 3.E.. dense in the sense that they contain no holes large enough to accommodate another sphere. Samples heated at a rate o f 20 K/min to each anneal temperature Ta in sequence and then immediately cooled. Even better agreement between calculated and measured densities can be obtained by using the packing fraction.m. They are random in that there are only weak correlations between spheres separated by five or more sphere diameters.. Density The accepted approach to modeling the atomic arrangements in metallic glasses is based on the structures formed by the dense random packing of hard spheres (DRPHS).'m''''m'" 3¢ f 5Moo. This requires specifying the atom radii. (1976)..- 20Ni A.e..78 or 0..2.x is given on each curve. Note that ~ varies only between 0. Note also that the packing fractions vary linearly with metalloid or metal content. On the basis of such models the packing fraction and thus the densities may be calculated.. calculated from measured densities of closely related alloys. K 700 Fig. 500 500 700 300 500 ANNEAL TEMPERATURE. E/ 50C ' ' ' ' _. Measured densities and calculated packing fractions are given in table 2...-o-" 75Cr.e. Resistivity The low temperature electrical resistivity of amorphous ferromagnets exhibits an anomalous minimum with a logarithmic increase below the minimum which .~ 25Cr='~:Je "': .-O" ~ 60C I.o400 t 50Ni 60Ni zv. It appears best (Cargill 1975a) to use the 12-coordinated Goldschmidt radii for the metal atoms and tetrahedral covalent radii for the metalloid atoms.5%. 9. The amorphous alloys generally are only about 2% less dense than their corresponding equilibrium crystalline mixtures.5. This is somewhat larger than the value expected for the packing of hard spheres.t . ~l.71 --.~ "~" 30Ni 450 TSMo ~ . 3.. '~''~z~ 40Ni..e. Such structures are arrangements of rigid spheres (the atoms).2. L U B O R S K Y 650 500 Fe.4. Chen et al. 0898 0.0895 0.671 0./A 3 -q* Reference Cargill (1970) 18.678 0.693 0.720 0.63 0.0837 0.0885 0.05 7.665 0.0921 0.677 0.205 7.0847 0. (1976b) - 7.252-+0.46 6.90 7.AMORPHOUS FERROMAGNETS 471 TABLE 2 Measured densities and calculated atomic packing for some amorphous alloys (in part from Cargill 1975a) Composition Alloy Niloo-xPx x p g/cm 3 po at.0 1.73 7.8 24.PI~CIo FesoPI6C3BI 4*2615 Fe?sMo2B2o 4*2605A Fe75PI6B6AI3 Co75PI6B6Ai3 Ni75P)6BsA13 Fe38Nia9PI4B6A13 Tsuei and Lillienthal (1976) Allied (1975a) Allied (1975b) Chen (1975) Sherwood et al.0902 0.54 7.0869 0.714 Co~oo-xPx Davis (1976) Cargill and Cochrane (1974) Fe)oo-xPx I.668 0.27 .00-+0.2 15. 2826B Fe32Ni36Crl4P12B6 4.0904 0.10 7.0900 0.10 8.0837 0.51 7.89 7.688 0.9 7.6 - 8.0836 0.0933 0.0909 0.13 Fe29Ni49PI4B6Si2 4.0897 0.815 0.641 0.672 0.95 7.ogan (1975) Fe.50 0.04 7.676 0.0896 0.7 7.726 0.667 0.685 0.0911 0.698 0.6 21.0 0.79 7.0960 0.0838 0.0900 0.93 7.97 -+ 0.0917 0.0 23.6 14.680 0.6 7.415 0.128 7.39 7.97 -+0.687 0.71 7.0 20.741 0.5 16.0905 0. 2826A (FexCol-x)soPl~C7 1.0954 0.025 6.665 0.735 0.686 0.0917 0.091 0.0887 0. (1975) Chen (1975) Davis (1970 Davis (1976) Davis (1976) Lin and Duwez (1969) Fujimori et al.94 7.33 8.681 0.695 0.0 18.04 7.29 0.668 0.0 19.658 0.64 8.0983 0.3 22.672 0.0867 0.4 21.708 0.678 0.0882 0.80 7.0 26.0940 0.04 7.80 7.1 22.654 0. 662 0.777 Reference Fujimori et al.35 0.0685 0.TMno.658 0.) Composition x 0.0687 0.0704 0.75 8.43 8.99 8.659 0.26 10.37 0.85 9.00 8.0695 0.80 8.30 0.0774 0.04 9.53 10.11 ±0.13 8.657 0.0982 0.660t 0.78 8.51 -+0.33 10.0685 0.265 0.15 0.54 ± 0.5 16.0687 0.693 0.07 0 0 p g/cm3 8.0687 0.0685 0.5 1.0698 0.686 0.666 0.E.658 0.71 ---0.70 10.0691 0.55 8.656 0.89 8.0697 0.695 0.60 8.658 0.0693 0.04 10.jhoe-~Px 0.0695 0.0684 0.41 po at. (1976) (FexCol-x)~sSiloB12 0 0.0 15.0696 0.0676 0.728 0.04 10.5 19.695 ff.25 -+0.691 0.662 0.03 8.651 0.05 9.35 15.36 9.5 calculated assuming ~ = 0.0676 0.5 20.49 10.678 0.//~3 0. (1976b) Kazama et al.0680 0.928Cuo.658 0.2 0.688 0.19 10.1029 O.665 0.3 16 17 18 19 20 21 22 23 24 25 26 0.0689 0.0685 0.0691 0.695 0.80 8.03 15.s24Sio.1 10.0687 0.0708 0.49 10.91 8.693 0.656 0.1045 Alloy (FexCol-x)TsSilsBio r/* 0.691 0.694 0.25 0.176)lOo-xCUx 0 2 4 6 8 10 12 14 (Ph-xNi~)75P2s (Pdo.752 0.48 10.691 0.42 10.46 8.669 0.06 7.0700 0.o72)too-xSi~ (Pdo.5 17.472 F.691 0.0674 0. LUBORSKY TABLE 2 (cont.656 0.39 10.0694 0.656 0.46 8.57 ± 0.40 10. (1973) Marzweii (1973) Chen and Park (1973) Crewdson (1966) Chen and Park (1973) PdsoSi2o (Pdo.670t 0.38 (Pdl-xMnx)77P23 Marzwell (1973) .765 0.693 0.100 0.5 18.0680 0.44 10.689 0.0696 0.84 8.00 8.0681 0.07 9.17 0.0696 0.0694 0.75 0.0685 0.0689 0.71 9.658 Chen et al.0702 0.694 0. 0860 0:0832 0.697 0.875 1.0954 0.72 7. 53. except as noted) and "tetrahedral covalent radii" for metalloid atoms (from L. "The Structure of Metals and Alloys.08-+ 0.59 7.657 0.697 0.93 7.375 0.645 0.705 0.7 7. Pauling. p.0752 0.0985 0.53 7.689 0.50 0. t Twelve-coordinated atomic radius for Mn was taken from W.0957 0.0976 0.697 0.625 1.702 0.52 7.P.unpubL Luborsky.83 9./A 3 0.681 0.48 9. "Nature of the Chemical Bond.0 473 Alloy (Pdi-xNix)80P2o p g/cm 3 10. Met#as ® alloy designation.0953 0..702 0.0907 0.70 0.05 -+0.06 7.02 9.46 7. Press. 1960).700 0. al.50 0. Ithaca.37 A) is larger than that given by Elliott (1.80 0.701 0.0950 ~* 0.375 0. Hnme-Rothery.875 1.703 0.0950 0.50 0.40 0..0897 0.0957 0.674 0.97 9.674 0.0977 0.20 0.25 0.14 -+0.0 (Fe~Col-x)soB2o 0 0.706 0.75 0. al.05 7. 870.05 7. unpubl. Institute for Metals.39 Po at. (1973) (FexNi~-x)soB2o O'Handley et (1976a) O'Handley et (1976a) Luborsky.50 • 0.0991 0.625 0.1004 0.0969 0.0867 0. New York. .0913 0.70 7.0 1.707 0. New York.46 7.0892 0.700 0." First suppl.688 0.. Elliot.676 0. O'Handley et al.84 7.0790 0. # Allied Chemical Co. 1947: this value (1.30 0.709 0.--(4¢d3)(R3)po.0725 0. (1976a) * 2605 * Packing fraction . al.0778 0. p.689 0. 1965.692 0. al.22 8.05 7. London.75 7.0953 0. "Constitution of Binary Alloys.681 0.50 0.39 7.707 Reference Chen et ai.05 8.125 0.~)." p. unpublished O'Handley et (1976a) al. 246.25 0.0981 0." 3rd ed.86 -+0.75 0. Luborsky et al.0965 0. al.) Composition x 0.83 7.21 -+0.AMORPHOUS FERROMAGNET~ T A B L E 2 (cont.05 8.650 0. Cornell Univ.0844 0.706 0.05 6.714 0.50 0.0966 0.0 (Fex Nil-x)soPj4B6 4 2826 0. McGraw-Hill.65 7. (1975) Allied (1976a) Luborsky. al. unpublished O'Handley et (1976a) O'Handley et (1976a) O'Handley et (1976a) O'Handley et (1976a) Luborsky.30 .52 -+0.94 7. with (R 3) calculated using Godschmidt atomic radii (12-fold coordination) for metal atoms (from R.625 0. .. Numbers refer to Allied Chemical Co. Although this behavior is also characteristic of the Kondo effect. Tx.. 10.. Hasegawaand Dermon (1973). (1977). FeCoSiB. LUBORSKY Cochrane et al. Subsequent heating and cooling is then reversible if Tx is not exceeded. Similar measurements have been reported by a number of other workers as referenced by Cochrane et al.474 F. (1975) have shown to be non-magnetic in origin and to be associated with the amorphous structure. 180 E Y 160 ==L . This comparison for NiP is shown in 200 . FeNiPC.. The temperature dependence of resistivity for a number of alloys is shown in fig. the initial sharp drop in resistivity indicates the beginning of crystallization.--~'~ 2826 120 I00 800 2605A i I 200 I i 400 : I 600 I I 800 i I000 MEASUREMENT TEMPERATURE. 11.. .3. . These curves were obtained by heating at a constant rate..E. This results in smaller eddy current contributions to the permeability and losses and is especially important at higher frequencies...~-. model qualitatively accounts for the major features in the radial distribution functions.. 2826A . Resistivities of the amorphous alloys are generally 2 to 4 times larger than the corresponding transition metal crystalline alloys without the glass formers. 3. Metglas ® compositions as listed in table 9 and measured by Teoh et al. (1976b). K Fig. . It is now clear that the dense random packing of hard spheres. Fujimori et ai. One of the advantages of the amorphous metallic alloys for application in devices is the higher resistivity compared to the conventional metallic materials. 10. The available data for the change in resistivity with composition is shown in fig. ~ .. The first heating at temperatures below crystallization causes a structural relaxation which changes the resistivity slightly. DRPHS. I I . (FesoNI20)75PI5CIo 2605 ~ -F'esCo95SilsBfo ~. Temperature dependence of resistivity of some amorphous alloys.. . showed that it was not caused by magnetic scattering. Cochrane et al. Structural results The principle source of information on the atomic arrangements in amorphous alloys comes from diffraction results. and is marked with an arrow.. Fujimori et al. /7 . 12. as discussed more recently by Cargill (1976). 12 from Cargill (1975a).AMORPHOUS FERROMAGNETS 475 Fig. However recent results reporting the partial interference functions associated with individual atomic pairs are not in complete agreement with the calculations of the DRPHS model. FeCoSiB and FeCoPC. Cargill (1975a). Hasegawa and Dermon (1973). 11. fig. Fig. (1976b). FeNiPC. Comparison of reduced radial distribution functions G(r) for DRPHS structure and for amorphous Ni76P2~. Dependence of resistivity on composition for some amorphous alloys at room temperature. Small angle X-ray scattering provides results related to compositional homogeneity. Their size does not change on annealing but their number increases. (1976b). The first two maxima in I(K) become slightly higher after anneals at 300°C for varying times.~ [25 nm] apart. The rolling also produced very large increases in coercivity and decreases in remanence. On annealing. 3.1. indicating no inhomogenieties were present but subsequent annealing again developed scattering regions.4.476 F. structural relaxation effects and the relaxation or reorientation of directional order. The theoretical analysis of the factors controlling the ease of formation and the stability of the resultant amorphous alloys have been reviewed and discussed in many previous reviews. It is believed that these regions influence the magnetic properties. from the thermodynamic . LUBORSKY Annealing of amorphous structures reported by Waseda and Masumoto (to be published) indicates that detectable changes occur in the atomic structure in amorphous FesoPI3C7 before any indication of crystallization is detected by transmission electron microscopy or by appearance of crystalline features in X-ray interference functions. ~ 100-300A [10-30nm] in the film plane and ~>2000 A [200 nm] normal to the film plane.2 nm] in diameter. these inhomogenieties decreased in size in contrast to the results on the melt quenched Fe40Ni~V~4Bt. Luborsky et al. on the other hand. and constitute about 1% of the volume of the sample. In the same paper Luborsky et al.4. The magnitude of oscillations at larger K values also appears to increase. Subsequent annealing returned these parameters to values representative of annealed specimens which had not been rolled. These changes appear to have no direct effect on magnetic properties. (1977) indicates that the scattering regions in the as-cast material are . Chi and Cargill (1976) have interpreted their results as showing that this electroless deposit contained anisotropic inhomogeneities. (1976b) report that cold rolling the Fe40Ni~P~4B6 alloy reduces the intensity of the small angle scattering. suggesting the possibility of phase separation taking place.E. while annealing increased the small angle scattering. for example in the extensive general review by Jones (1973). reported no detectable change in the diffuse X-ray scattering pattern from amorphous Fe40N~P~4B6 both after cold rolling and after annealing to temperatures just below d¢tectable crystallization. interpreted as improving the homogeneity. Crystallization The formation and resultant stability of amorphous alloys are important topics both theoretically and technologically. Small angle X-ray scattering has also been used to characterize the inhomogeneities in Co-P. Cold rolling produced a completely flat I(K) versus K curve. Stability There are three kinds of stability of significance for amorphous magnetic alloys: their resistance to the initiation of crystallization. 3. These will each be discussed briefly here. More detailed analysis of these results by Walter et al.3 2 A [3. ~ 250 . There have been three approaches to relating the stability of the glass. The most stable configuration corresponds to the situation when all the holes are filled. In a similar manner the stability of the glass after formation is generally measured by the magnitude of the quantity zlrx= r x . The first is based on Bernars model of randomly packed hard spheres as developed by Cargill (1970). All of the available information on the time-temperature behavior for the onset of crystallization in amorphous alloys of potential interest is summarized in fig. Luborsky (1977a) has clearly shown that the end-of-life as far as magnetic applications are concerned corresponds to the onset of crystallization. At the onset of crystallization. At such a point the liquid is particularly stable against crystallization. the deeper the eutectic the better is the glass forming ability. to its microstructure. As the temperature decreases from Tm the rate of crystallization will increase rapidly but then fall rapidly as the temperature decreases below Ts. Calorimetric . corresponding to about 20at. Although this simple geometrical model has been successful in accounting for the observed glassforming ability of many metallic alloys it would be surprising if only the atomic radii were important. The ability of an alloy to be quenched into the glassy state is generally measured by the magnitude of the quantity A T~ = T m . Cohen and Turnbnll (1961) noted that the composition most favorable for glass formation is near the eutectic. the coercive force and losses increase and the remanence and permeability decrease all at a very rapid rate for a small increase in temperature. i. They showed that under certain circumstances a nearly free electron gas will produce a barrier against crystallization. (9) where Tx is the temperature for the onset of crystallization. In this model the metal atoms are assumed to form a random network of close packed hard sheres and the smaller metalloid atoms fill the holes inherent in such a structure. i. Polk (1972) and Turnbull (1974).e.r.AMORPHOUS FERROMAGNETS 477 viewpoint by Turnbull (1974).. CoSiB. and NiSiB. Chen (1974) discusses the effect of atomic sizes and interatomie interactions. 13. its ability not to crystallize. Note that there is no direct relation between the ease of formation and the resultant stability of an amorphous ally. Thus if one quenched a molten alloy rapidly enough to a temperature below Tg a quasi-equilibrium amorphous phase is obtained.e. and most recently by Takayama (1976). The third approach was suggested by Nagel and Tauc (1975. 1976) and is based on the role of the electron gas. Bennett et al. and suggested that it is chemical bonds which are the dominating factor in glass formation and stability. This is near the eutectic composition of many of the alloys and is in the range of the stable glass compositions. The results were obtained by transmission electron microscopy and diffraction studies for FePC.%. chemical bonding. In the second approach to understanding glass stability.Tg (8) where T~ and Tg are the melting and glass temperature respectively. (1971). 6 3 AI ' 115 ' .. and FeCoPBAI alloys.''' . the curves for CoSiB.g.. . and other terms have been omitted because they have an insignificant temperature dependence in this region of temperature. e.f .K -I Fig. (10) These incubation times are a common feature of phase transformations.. NiPBAI. t3. (1974) applied this approach to the interpretation of the formation and stability of some glasses and Davies (1976) recently reviewed this subject. FeNiB. i .-~ // / NiT5Si8BI7 75 [6~ 3/ .02 " / . They may be considered to be the time required for a population of nuclei characteristic of the annealing temperature to be achieved.E. . NiSiB from Masumoto et al.. (1976). FeCoPBAI from Coleman (1976).'. I i i ~ t 300 I C°75Si Il5B / ~ .T /. Time for the start of crystallization as a function of temperature. These discontinuities are the result of the formation of different phases. FeNiB and FeNiPB. 13 are close to straight lines represented by an Arrhenius relation for the time for the onset of crystallization tx = to~ exp( AEx/kT). (1976).. FeNiPB from Luborsky (1977a). studies were used for the results on NiP./'. LUBORSKY i05 104 = i i i 450 I ~ i b i TEMPERATURE. It can be readily shown that eq. The existence of an incubation time therefore implies that no suitable sized nuclei exist in the as-quenched glass. NiSiB and FePC.8 IO00/T. P7 //// I°-i."/ Fe45C?30PI6B. at temperatures below the break a single metastable crystalline phase forms while at temperatures above the break small metastable crystals form in the amorphous phase..~. The results in fig.~ 1. =C 400 350 I .:. CoSiB. Both calorimetric and magnetic tests were used to obtain the crystallization results on FeB.. (I0) can be derived from transformation theory where AEx is the activation energy for viscous flow. FePC from Masumoto and Maddin (1975) and Masumoto et al.. It is of interest to note that some of the t ..'" . NiPBA1. FeB. NiP from Clements and Cantor (1976). Davies et al. It is therefore apparent that extrapolation of high temperature results to lower temperatures may be very misleading.T curves are discontinuous.~8 F.17 ' ~.4 /I ..." .6 ' . ... 5 6.8 477 405 487 442 441 - 507t 9 -87?t 9t 7f - 1. the more complex the alloy the greater is AE~. Similar correlations between thermal stability as measured by AT~ and AEx were discussed experimentally and theoretically by Chert (1976).0* 2. rather than to the start of the exotherm. . (1976) Luborsky (1977a) Masumoto et al. t t Tx f r o m D S C at 20 deg/min by extrapolation. but using the time of transformation to the peak in the exotherm.0 1.1 2. AEx. 13.9 1.Tg Reference 10t 16 - Coleman (1976) Coleman (1976) Chen (1976) Luborsky (1977a) Chen (1976) Masumoto et al. (9) and as obtained from scanning calorimetry.8** 3.AMORPHOUS FERROMAGNETS 479 Luborsky (1977a) showed that the activation energies for the onset of crystallization. to obtain AE~.0 2.5 T~ °(2 417 Tx. Calorimetric measurements were made at a heating rate of 5 deg/min and 40deg/min respectively. (1976) Masumoto and Maddin (1975) Luborsky (1977a) Masumoto et al. (1976) Clements and Cantor (1976) Clements and Cantor (1976) Clements and Cantor (1976) 456 4. Some results are shown in table 3.6B6AI3 FeTsPt6B6AI3 Fe4oNi4oP.MxPl3C7 and by Luborsky (1977a) in Fes0-xNi~P.1 2. (1976) in the series Fes0-. obtained from the slopes of the lines in fig.4B6 and Fes0-xNi~B20 alloys.6 - * The low temperature activation energy. to determine T~ the temperature for the beginning of the crystallization exotherm. ** Evaluated from time to reach peak in crystallization exotherm.2** 3. t Tx f r o m DSC at 40 deg/min. The values of AEx also appear to correlate well with the number of atomic species in the alloy. The effect of alloying elements on the crystallization temperature has been studied by Naka et al.4* 3.7** 5.9 3.6* FesoB2o NbsSisBi7 Nis3P17 Nis4P16 Nis2P18 2. The effect of this difference in measurement on AEx appears to be small.4B6 Co75P16B6AI3 FesoP13C7 Fe4oNi4oB20 CoTsSilsBlo eV 6.0 2. TABLE 3 Activation energy for crystallization of various amorphous alloys (Luborsky 1977a) AEx Alloy Ni75PI6B6A13 Fe45Co3oP. correlate well with the values of ATx for the stability of amorphous alloys as given by eq. indicating two different modes of rearrangement as discussed by Chen and Coleman (1976).=.2. These structural changes produce a small change in Curie temperature (fig. the trends are in opposite directions. Fe. --. taking for the number of outer electrons for Ti. Fe80-x NIxPI4B6 "FeBo-xNix B20 • 300 4'o ~.. Cr. 14.~. V.E. Co. This change in Tc after structural relaxation is mostly the result of the change in the interatomic distances... For Feso-xMxPI3C? alloys from Nal~a et al. An 450 JCr~ -~/*~-ENix ~ "~Fe PI4B6 80-xNixB20 w n-" 2 . For Fes0-xNixPtLB6 • and Fes0_zNi~B~ • from Luborsky (1977a) at a 40°C/rain heating rate and dashed lines for two hour anneals.~ ~ -\ m CO 35C .. 40( ~E %-. 4 through 10 respectively. open symbols.. LUBORSKY Although the use of a constant rate of heating will give interesting correlations. the relative valency did seem to correlate with the trends in Tx. ot. but may also be affected by the change in average coordination number. . Temperatures for the start of crystallization.. and both magnetic and mechanical properties are drastically altered. Thus they conclude that the crystallization temperature is predominantly governed by the nature and strength of the bonding of the atoms in these alloys. Heating as-cast samples results in two broad peaks in differential scanning calorimetry. Their results of T~ as a function of average outer electron concentration show this correlation.." .480 F. % Fig. Structural relaxation Irreversible structural changes are observed at times and temperatures well below those necessary to initiate crystallization. concluded from their results that the atomic size of the alloying elements had little or no effect on Tx. 14. Naka et al. thirdly. the results cannot be extrapolated to other temperatures of interest and do not necessarily correlate with isothermal results as seen by comparing the 2 hour anneal results for the FeNiPB alloys with the scanning results in fig. 3. and Ni. .4. ~.~ . Mn. (1976) using a 5°C/min heating rate. 9) without a significant change in saturation moment. second that the electronegativity also had little or no effect but. as a function of frequency) can all be understood using the same underlying physical principles applicable to crystalline alloys with appropriate modifications to take into account the differences in structure and composition. By minimizing the internal strains.. and losses.3. and magnetostriction A) and the extrinsic properties (coercive force.AMORPHOUS FERROMAGNETS 481 additional and major change occurs associated with the relaxation of internal strain. produced either by annealing in a magnetic field or by annealing in a mechanically stressed condition. and the resultant anisotropy. (1976) and Luborsky and Walter (1976). is minimized leading to a reduction in coercive force and losses and an increase in permeability and loop squareness. or stressed condition. This will also be described more fuRRyin a later section. Fundamental magnetic properties The intrinsic properties of amorphous ferromagnets are still not quantitatively understood. under the influence of its own self-demagnetizing field. Therefore the magnetic moment of an atom is not expected to be identical on every site. the strain-maguetostriction interaction. Mr/Ms. Tc. 4. Hc. Directional ordering. I~.3. externally applied field. This ordering again emphasizes the fact that these amorphous alloys are far from being homogenous structureless arrays of atoms. This stress-relief occurs at temperatures below T~ in most alloys of interest. In a qualitative sense. both similar to that found in conventional crystalline alloys. The rate at which this happens may limit the usefulness of some of the alloys in applications where t h e initial ordering direction is different from the resultant magnetic or stress fields encountered during use. Thus the . Directional order relaxation In contrast to the crystallization and structural relaxation effects which are irreversible processes. directional ordering is a reversible process. (1975).F e and Ni-Ni pair ordering and from metalloid-metal ordering. the intrinsic properties (magnetic moment. Ms. for example. W. and permeability. as first noted by Luborsky et al. 3. The relaxation or reorientation of this anisotropy can occur at quite low temperatures in some amorphous alloys.g. e. Mechanical properties are also known to alter drastically during this low temperature annealing. The basic problem is to incorporate into the existing theoretical approaches the structural distribution contained. Curie temperature. This directional order arises from F e . remanenceto-saturation ratio. but this is believed to be due in large measure to diffusion of certain atomic species over relatively large distances. The origins and kinetics of directional ordering in amorphous alloys will be discussed more fully in section 6. The local environment around each atom in an amorphous solid differs from site-to-site in contrast to the regular crystalline lattice. as discussed by Walter et al. results in a magnetic anisotropy which can markedly influence the magnetic properties of the amorphous alloy.4. in the radial distribution functions described in the previous section. In atoms. The effect of this distribution is not apparent in the magnetic moments. the high spin atomic-like state is retained. they just fill or empty. F 4. in units of emu/cm 3 [Tesla]. The moments are lower because of the change in the local chemical environment provided by the presence of the metalloids. Ms. When atoms interact. what were degenerate orbitals become split into low energy bonding orbitals and high energy antibonding orbitals. states of high spin have low electron-electron Coulomb repulsion energies.1. discussed by Albert et al. The success of rigid band theory in certain alloy systems is due to a fortuitous cancelling of errors and both theory and experiment show that the band structure does change shape. The addition of metalloids also changes the d-bands and does not simply transfer charge. The moments of most amorphous alloys are lower than those of the pure crystalline transition metals which they contain. Hence. or as saturation magnetization for the alloy. Magnetic moment and saturation magnetization The saturation magnetization of a material at a temperature of 0 K is one of its basic properties. (1977). atoms usually have large magnetic moments. The band theory of magnetism is an approximate single particle picture whereby an electron interacts with other electrons through an effective potential which has a spin dependent part. A better picture of magnetism in glassy alloys. the rigid band phenomenology will be used in much of the discussion of experimental results because of its simplicity in correlating data. Because the d-bands are not rigid the plotting of moment against average number of valence electrons. may be obtained from Alben et al. When the bonding energy is comparable to the Coulomb . Thus the 3d-electron magnetic moments should be discussed in terms of the band theory of magnetism. However. critical behavior or anisotropies. but their 3d-electrons are just as "itinerant" as in crystalline transition metal alloys. The rigid band theory is based on the assumption that the d-bands do not alter on alloying. but it has no theoretical basis. When the Coulomb energy is large compared with the bonding interactions. A brief discussion of this approach. There is a competition between the reduction in Coulomb energy for high spin and the energy reduction in filling the lowest energy orbitals with pairs of electrons with zero total spin. applied to amorphous alloys. (1977). However.E. the Slater-Pauling curve. the direct effect of the structural disorder on the moments is very small. Measurements are usually expressed as average moment per magnetic atom in units of the Bohr magneton. LUBORSKY hyperfine interactions will show a distribution of values. . Metallic glasses are rather poor conductors. is without theoretical basis. tzB. but is necessary to account for the details of the M~issbauer spectra and nuclear magnetic resonance. The rigid band model is often used to correlate results.~2 F. follows from ideas of local chemical bonding. by Hund's rules. These same metalloids are necessary for preparing and stabilizing the amorphous phase as discussed previously. The major change in magnetic properties observed in amorphous alloys comes from the change in the electronic environment caused by the metalloids. The simplified rules based on the rigid band model... Magnetization in 41rMs for FePGe. CoAl. Wright (1976) has recently reviewed the status of the 2. CoSi • Felsch (1970). FeP A Durand and Yung 0977).. CoP <>Kanabe and Kanematsu (1968).. ~7 Cargill and Cochran¢ (]974). I ' I ' I ' 1 < ~ ~ .. Magnetic moments at 0 K as a function of solute concentration. However. . . a compromise is reached whereby the moments are reduced.C ~a Fe. @ Q Wiesner and Schneider (1974).. 0 . FeB [ ] Durand and Yung (197/). o.... these are very difficult to obtain and have usually been prepared only i n a n impure state. 15.. but this was not confirmed by the results of Shimada and Kojima (1976)."~ . The results for the amorphous cobalt alloys all appear to fall approximately linearly as expected.. Fe-AI Fe-P ~ "-.1~ . -Ga []. The behavior of the amorphous iron alloys is very different..P.. V Simpson and Brambley (1971). as occurs between 3d orbitals in transition metals. in fact.. CoP Pan and Turnbull (]974) and Simpson and Brambley (197]). by vacuum deposition onto cold substrates. Some results for iron-metalloid and cobalt-metalloid amorphous alloys are shown in fig. co-si o ~Fe -s. 15 as a function of metalloid content.. indicate that the moment of the transition metal decreases linearly with additions of metalloid at a slope depending on the electrons available from the metalloid. CoSi Parsons et al. Fe S-i"" .5I I I0 i \ "".. that work reasonably well. -As. as occurs between transition metal 3d states and metalloid s and p states. Data for related crystalline alloys are shown by the smooth curves with no data points. FeB3_xPiTGe ~ 0. • Pan and Turnbnll (1974). the moment is further reduced or even eliminated. 2HB for each Si or C atom and 1Hs for each B atom. FeSi Shimada and Kojima (1976).TAs. Amorphous alloys shown by solid curves with data points: FeSi O Shimada and Kojima (1976) and Felsch (1970). \ <~ ° I = I = 20 3Q 40 ATOM PERCENTSOLUTE Fig... information on the pure amorphous elements is obtained from impure films by extrapolating back to zero impurity or solute level./C0-AI ~'~---o~ ~ ". Where bonding is still stronger.. approximately 3HB for each P atom. "~k~.~... (]958). """ -o0 I...AMORPHOUS FERROMAGNETS 483 energy. Co and Ni would be the simplest to understand. ~ o . The magnetic moments of the simple amorphous transition metal elements.:. Apparently a small amount of impurity was necessary to stabilize the strong ferromagnetism in the amorphous FeSi reported by Felsch(1970). Fe. Crystalline alloys shown by broken curves with no data points: FeAI. In most cases. ~ x01~. p electrons to fill the d band of the transition metal atoms. atoms in the general amorphous alloy (TM)l-z-yFzOy to be expressed as /. (1977) showed that a somewhat more satisfying fit to the data was obtained using individual moments varying with composition.E.1.1x +0. as . TM.6.6 and 2. because of their greater stability. A variety of ternary alloys with a single transition metal element were reported by Yamauchi and Mizoguchi (1975). Thus m = 0. Co and Fe and assigning an integral number of electrons transferred from the metalloids. This accounts for the reduction of magnetization of both the crystalline and amorphous alloys with increasing metalloid content. 19.6 Bohr magnetons. 1.484 F.0 and each boron by 0. We can correlate the behavior of the magnetic moment in amorphous alloys containing 3d transition metals on the basis of the rigid band model. are in quite good agreement with the rigid band model but using /~si=0. and f and g are the number of electrons transferred from the F and G atoms respectively. 18.gy (12) where F and G represent the metalloid or glass forming atomic species. 2 for C. 16-18 and the effect of changing the transition metal alloy is shown in fig. 1. 19. Using these values. Examples of the effects of the metalloid species and concentration on the moment in amorphous alloys are shown in figs. 18. (1977) studied the moment and Curie temperatures of amorphous alloys of (Fe-Ni)s0(P-B)20.3 Bohr magnetons.6b .x _ y) (11) or for the moment per atom of alloy as t~ = m(1 -z-y)-fz. There is considerably more information available for amorphous alloys than for pure elements. as shown by the alloys in fig.gy]/(1 .z - y)-fz . In all cases it appears that the saturation moment is the same or less than its value in the crystalline state (table 1). and on the effect of the transition metal alloy composition. Thus the moment per atom of alloy can be written as /~ = 2. 2 for Si and 3 for P. as shown in fig. Since the number of nearest neighbors in an amorphous alloy is essentially the same as in the fcc crystalline phase we can assume that m is the same.6. L U B O R S K Y information available on "pure" amorphous elements.t = [m(1 . shown in fig.0 . 1 for B. /~Fe=2. 15.6 for Ni. m is the original number of unpaired spins in the transition metal alloy. All of their data on the effect of the metalloid concentration. Co and Fe respectively. the agreement between the observed and calculated values is usually quite good. shown in fig.0z . The data agree reasonably well with the rigid band model using the same moments of 0.6 and 2. 3 y (13) in Bohr magnetons for FexNibPzB~ Instead of using the rigid band model as above. Becker et al.6 for Ni. Becker et al. that is. by assuming that the metalloid atoms contribute some of their s. Thus we expect the magnetic moment of the transition metal.1 Bohr magnetons and assuming that each phosphorus atom reduced the moment by 1. P .% B I iO0. 17. ~O0~ "CRYST. 0t. The individual atomic moments of Fe and Ni are then given by #Fe = 2. For the Fe rich alloys in the Fe-Ni series of IQ t.20x (14) in FexNi. described by Kouvel (1969) in his analysis of crystalline alloys.v i i i u_ 1.57 + 0. (1964).ot..80(1 -. Fe75P25_yBy I I r e 7 5 I I 5 I0 y. When this is done the best fit to the same data in the amorphous F e ./~~ ~ ? ' / .1 electrons and each boron atom 1. Dashed curve is for crystalline FePB from Fruchart et al. ~ Fe 82 Fe c PIO0-c-y By ~..B alloys required that each phosphorus atom transfers 2. Z= 14 13t 12 y.et%P Fig.6 I o o ~.2 electrons..0.-x. Saturation moment per atom of alloy at 0 K for FePB amorphous alloys from Durand and Yung (1977). (b) on substitudon of P for Fe for various B contents. I~rand and Yung (1977)...AMORPHOUS FERROMAGNETS 485 ~ . 16. .. Saturation moment per atom of alloy at 0 K (a) on substitution of B for Fe for various P contents. % B 15 20 Fig.z_yPz By ! 5 I0 15 z.. .N i .X) /~Ni .20 + 0. ' ~ / "FeB2PXCIB-X .~ + _ _ i- -A_~~ . V. . o I-- r re^^P B^^ . ..0'.0 Fig.E.Co70 Px B30_ x ~< 0. 0 ¢:z3 I 5 n 15 L 20 Fig. • O'Handley et al.5 IRON.~ ~U X v U . FeNiB. Moment per transition metal atom at 0 K of amorphous alloys as a function of transition metal composition. . Saturation moments per transition metal atom as a function of phosphorus for various amorphous alloys. FeCoB.-" 0 J J . ot.~ 6/// (Fe-Ni)8oPI4B 6 r~ o ~9Pi3B8 o 0 0 ~ 0.-" it/ (Fe-Ni)80 B20/. .x ~ ~ L0 z 0 F-LzJ Z + Co80PIoPIoIa~-.. LUBORSKY ~ 2. 1976a.~ --~--.486 F.re80 r13~7 ~'°-Fe78PxC22_ x ---~= o Fe40 Ni4oPxB20. 1976a.5 Ni8oPI 0 BIO 0 I0 x.C ° 7 5 Px B25-x "A. FeNiPB O Durand 1977. A Becker et al.. O'Handley et al..%P 0975).. 1977. (1977).X < ~ 7°---"e-. ^ . remainder of data from Yamauchi and Mizoguchi (Fe-Co)80 B20 .j i j ~J z 0 b- s ~'ll/ . FeNiPB O Becker et al. + Becker et al. (1977). 18. "'~ . x 1. 19. AMORPHOUS FERROMAGNETS 487 amorphous alloys the results for the various metalloids shown in fig. 19 are consistent. That is, the reduction in moment is greatest for - P I 4 B 6 , less for -P~3B8 and least for -B20 alloys. The results for FexNil-xPt3Bs reported by Durand (1977) show a pronounced change in slope. This is interpreted on the basis of a roughly constant moment per Ni atom for 0.3 < x < 1 but a progressive decrease in moment for 0 < x < 0.3. Normal ferromagnetic ordering was reported only for x > 10at.%. Below this iron content various types of ordering appeared from mictomagnetic (superparamagnetic) to spin glass behavior as x decreased below 10at.%. A very detailed investigation of the moments and Curie temperatures of amorphous alloys in the entire accessible region of F e - P - B alloys was reported by Durand and Yung (1977). The result of replacing P by B for various constant Fe contents is shown in fig. 16. One of the remarkable features of these results, also shown by the Curie temperature results to be discussed later, is the change in slope as P replaces B. This change in slope is related to the change in slope exhibited by the crystalline alloys of FeTsP25-yBy reported by Fruchart et al. (1964) and shown by the square data points in fig. 16. These results suggest the existence of two different short-range orders in the amorphous alloys, probably corresponding to the • and 6~ crystal structures. Further results also reported by Durand and Yung (1977) for the change in moment when one metalloid substitutes for Fe, the other metalloid remaining constant, are shown in fig. 17. The extrapolation to "pure" amorphous Fe from both sets of data yields a value of 2.35/~B. Assuming that the electron transfer model is valid and independent of short range order variations the boron would donate 1.4 +-0.2 electrons and the phosphorus 1.6-+ 0.2 electrons. These values for the number of electrons transferred are compared to other values reported in table 4. Note the rather large variation in the values reported for each element. The magnetic moments for a wide variety of transition metal alloys with TABLE 4 Electrons transferred from the metalloids in amorphous alloys based on the rigid band model Alloy Fe-Ni-P-B Fe-Ni-B Fe-P-B Fe-Co-B-P Fe-Ni-B-P CoP B 0.3 1.2" 1.4 1.6 C Si P Reference 1.0 Becker et al. (1977) 2.1 Becker et al. (1977)* 1.6 Durand and Yung (1977) 2 . 4 0 ' H a n d l e y et al. (1976a) 5 2 < 5 < 5 Kanabe and Kanematsu (1968) Cargill and Cochrane (1974) Pan and Turnbull (1974) Simpson and Brambley (1971) CoBP, FeBP FeCP, NiBP 1 2 2 3 Yamauchi and Mizoguchi (1975) * Moment of transition metal varies linearly with alloy concentration. 488 F.E. LUBORSKY -Pl0Bi0 glass formers from the work of Mizoguchi et al. (1973, 1974) are shown in fig. 20 as a function of the average number of outer electrons, N. This Slater-Pauling presentation is also shown for the crystalline alloys by the dashed curves. The approximate shape of the Slater-Pauling curve is retained for the amorphous alloys but the curve is shifted by the same assumed transfer of electrons from the P, B to the transition metals. The room temperature saturation magnetizations are of more practical importance. These are shown in fig. 21 for a variety of alloys as a function of transition metal. The effect of the transition metal additions to amorphous Co-SiB is shown in fig. 22 from Fujimori et al. (1977). The relative number of electrons donated can be obtained from fig. 21. The number of electrons donated can be listed as -P13C7 > -$15B10 > -P16B6A13 > -P~4B6 > -Si9BI3 > -B20 based on the relative magnitudes of 4~rMs. The trend with transition metal content is the same as for the corresponding crystalline alloys although there are anomalies. For example crystalline F e - C o alloys show a peak in magnetization at about 35% Co. The peak appears to be present in the F e - C o - B , but at about 15% Co, while it appears to be absent in the other F e - C o amorphous alloys. T h e origin of these differences has not been examined and is not understood. The trend with additions of other transition metal elements, e.g., Cr, Pd, V, and Mn as shown in figs. 20 and 22 is also approximately as observed in the crystalline alloys without the glass forming atoms. The saturation magnetizations at r o o m temperature for a variety of alloys, most of which are not in any of the previous figures, are listed in table 5. The effect of pressure on the m o m e n t of amorphous iron alloys was reported by Mizoguchi (1976). A microbomb technique was used. The value of (dfddp)/i.t for (Fel-xMx)s0PioB10 was found to be about - 2 x 10-2 kbar -1 [ - 2 x 10 -1° i.-: ~ z O LcJ Z .,,~/-... ",~o---bcc Fe-Co ~:).cl~ " ~ - - b c c Fe-Ni _bcc Fe-V---~ ~'~'~e-fcc Fe-Co bCCFe-Cr/-~/ '~ ~ 71 F.-Si /// i ~1; I ";,~ N - o-Ni + Fe-Mn riFe-Co (o Fe-V • Fe-Cr o Fe-Ni cc Co-Mn~," "N~. 7 c co_ _ . " p-- V r - " I 8 I 9 ] Io -IvCo-V c o-M ro Fig. 20. The saturation magnetization of quasibinary amorphous alloys of 3d transition metals (Ai-xBx)s0PioBm0shown by solid curves. The average moments per metallic atom, At-~Bx,are plotted as a function of outer electron concentration, N, of the metallic atoms. Mizognchi et al. (1973, 1974). Crystalline alloys without P, B shown by dashed curves. AMORPHOUS FERROMAGNETS 489 16 12 Fo 0 0 0.5 x 1.0 Fig. 21. Saturation magnetization at room temperature as a function of composition for Fe-Co-Ni amorphous alloys. FeNiB, FeNiPB Becker et al. 0977); FeNiSiB Masumoto et al. (1977); FeNiB, FeCoB O'Handley et al. (1976a, 1976b); FeCoPC, FeCoSiB Fujimori et al. (1976b); CoNiPBAI, FeCoPBAI, FeNiPBAI Gyorgy et al. 0976). I I I i C ~ . ~ 50 0 ' ' laxCOl_x178SiloBi2 ' , ' 0.1 x 02 Fig. 22. Saturation magnetization per gram at room temperature for some amorphous -SiB alloys, Fujimori et al. (1977). 490 F.E. L U B O R S K Y TABLE 5 Saturation magnetization and Curie temperatures of some* a m o r p h o u s alloys 4~rMs at 300 K kG t~o fl]atom of alloy 1.35 . . 1.68 - Alloy Mo emu/g 151 . 187 - Tc K Reference Fe75P15Clo FesoP16C3B i #2615 - 11.5 . 14.9 17.1 17.1 Fe4oNi~oPi4B6 #2826 8.7 619 (M) Chien and H a s e g a w a (1976b) 596.5 Tsuei and Lilienthal (1976) 590 (M) Chien and Hasegawa (1976b) 565 H a s e g a w a and O'Handley (1976) Egami et ai. (1975a) Flanders et al. (1975) 537 (M) Chien and H a s e g a w a (1976b) Egami et al. (1975a) 520 H a s e g a w a and O'Handley (1976) Becker et al. (1977) 7.9 8.5 15.8 - 0.88 0.98 1.59 1.55 1.63 1.68 1.43 1.03 1.02 0.04 0.07 96.7 108 190 185 194 186 166 120 116 4 7 - Fe4oNi4oP14B6 FesoB2o # 2605 16.0 15.8 4.9 14.0 12.0 14.0 13.5 6.5 6.0 15.0 10.0 11.5 10.7 6.7 6.3 11.8 647 O'Handley et al. (1976a) 685 (M) Chien and H a s e g a w a (1977) 647 H a s e g a w a et al. (1976a, 1976b) 651 652 Becker et al. (1977) Durand and Yung (1977) Flanders et al. (1975) FesoB2o Fe29Ni49P14B6Si2 # 2826B FesoP12.sCT.5 586 (M) Tsuei et ai. (1968) 630 > 800 662 -765 673 688 ~600 -700 190 Fujimori et al. (1974) Fujimori et al. (1976b) Sherwood et al. (1975) S h e r w o o d et al. (1975) Pujimori et al. (1976b) O'Handley et al. (1976a) O'Handley et al. (1976a) O'Handley et al. (1976a) Kikuchi et al. (1975) Kikuchi et al. (1975) Sherwood et al. (1975) O'Handley et al. (1976b) Pan and Turnbull (1974) Simpson and Brambley (1972) Massenet et al. (1974) FesoPl3C7 Fe75P16B6AI3 Co75PI6B6A13 Co75SisBlo Fe4oCo4oB2o Fe4oNi4oB2o Cos0B2o Fe4~Co.C13C7 Fe4.sCoTo.sSilsBio Fe3Co72PI6B6A13 Fe6Co74B20 NissPis FesgGe4~ 12.8 - AMORPHOUS FERROMAGNETS TABLE 5 (cont.) 41rMs at 300 K kG 6.4 2.9 0.2 0.0 13.1 13.1 ~o 491 Alloy Fe44Ge Fe35Ge Fe3o.sGe jS/atom of alloy - M0 emu/g - Tc K 340-+ 30 35 ---!35 729 733 Reference Fe25.TGe (Fe0.sNi0.2)TsSil0Bn (Fe0.sNi0.2)TsSisBJ4 Masumoto et al. (1977) Masumoto et al. (1977) 4t Allied Chemical Co. Metglas® designation. * Data for various alloy series are given in figures. (M) Determined from M6ssbauer spectra. (N/m2) -l] w h e n M = Fe, Co or Ni. F o r M = Cr or Mn it is a b o u t an order of magnitude greater. F r o m the t h e r m o d y n a m i c relation b e t w e e n t h e pressure d e p e n d e n c e of magnetization and v o l u m e magnetostriction p(dMIdp ) = (1/V)(OVIOH) (15) w h e r e p is the density, the value of (IlV)(OVIOH) is estimated to be a b o u t 10 - 9 0 e -~ [ - 10-7(A/m) -1] f o r M = Fe, Co or Ni. This is a b o u t the s a m e value as for crystalline F e - N i alloys. 4.2. Curie temperature In spite of their chemical and structural disorder, a m o r p h o u s f e r r o m a g n e t s m o s t often h a v e a well defined magnetic ordering " C u r i e " t e m p e r a t u r e , To. This has b e e n confirmed f r o m m a g n e t i z a t i o n - t e m p e r a t u r e , M t s s b a u e r and specific heat m e a s u r e m e n t s . As with the Ms m e a s u r e m e n t s , these results do not provide u n a m b i g u o u s a n s w e r s concerning effects of structural disorder on T¢ b e c a u s e chemical effects m a y be responsible f o r the differences. T h e coupling of m o m e n t s in a m o r p h o u s magnets, as in m o s t other magnetic materials, is due to the e x c h a n g e interaction. Only itinerant e x c h a n g e b e t w e e n 3d m o m e n t s is of i m p o r t a n c e in the transition m e t a l - m e t a l l o i d alloys. Itinerant e x c h a n g e arises b e c a u s e the single site e x c h a n g e t a k e n together with the intersite electron hopping t e r m s p r o d u c e a correlation b e t w e e n m o m e n t s on different sites. This m e c h a n i s m depends on the b a n d structure and can lead to f e r r o m a g n e t i s m , a n t i f e r r o m a g n e t i s m or c o m p l e x spin arrangements. T h e theoretical t r e a t m e n t of spin ordering in a m o r p h o u s solids is a m u c h m o r e difficult p r o b l e m than in regular crystalline lattices and has not b e e n satisfactorily solved. I f the molecular field a p p r o x i m a t i o n is used, e v e n though its use is doubtful, the p a r a m a g n e t i c 4~ F.E. LUBORSKY Curie temperature can be expressed as Tc = [2S(S + 1)/3k] ~. Yq (16) where S is the spin number, k is Boltzmann's constant and Jq is the exchange interaction between atoms at the position rt and rj and can be expressed in terms of the radial distribution function. The Curie temperatures of amorphous transition metal-metalloid alloys are always found to be significantly lower than those of the pure crystalline transition metals. This reduction of Tc in the amorphous alloys appears to be largely the result of chemical composition and/or chemical disorder. A summary of some results from Wright (1976) for the pure transition metals was included in table 1. This shows the decrease in Tc for the amorphous elements compared to the crystalline elements. The results for some alloys are given in fig. 23 as a function of solute concentration for amorphoug alloys of FeP, FeB, CoP and F e P C compared to related crystalline alloys. The trends in Tc for the crystalline alloys are given by the broken curves with no data points; the solid curves for the amorphous alloys are shown with data points. Curie temperatures vary with transition metal content as shown in fig. 24 for F e - N i alloys and in fig. 25 for F e - C o and C o - N i alloys both with a variety of glass formers. The variation of Tc with transition metal content for a fixed metalloid composition may be systematized using a phenomenological model as 1400 •~,,CoSi 1200 I000 I I I i I | FeSi "'~-. ~ ".--... 800 P Fe3P__ Fe85-xPiSCx t-FeP F%C__ 600 40C 0 I I I I I I 5 I0 15 20 AT. % SOLUTE 25 30 35 Fig. 23. Curie temperatures as a function of solute concentration. Crystalline alloys shown by the broken curves without data points; FeAl, FeSi, CoAl, CoSi Parsons et al. (1958); Fe3P, Fe3C Chen (1973). Amorphous alloys shown by solid curves with data points; CoP • Pan and Turnbull (1974), V Cargill and Cochrane (1974); Fess-xP15C,C) Chen (1973) where at.% solute = 15+x; FeB [] and FeP (> Durand (1977); and electrodeposited FeP • Logan and Sun (1976). AMORPHOUS FERROMAGNETS 800 (Fe'Ni)78BI4Si8 ~ (Fe,Ni)80B20~cf~~ 493 ~ 600 ~ ~ ~: {Fe,Ni)BOPloBl 0 f-,. /~.,.~,%/.,.\,,~.,, ,. ~ou . o F~,=N;I_~._~L_ ~'.~ ~ .,/\ "(Fe,Ni)8oPI2B8 ,--,-.,78 ~lZ~,lr.l ~. . / \ 200 / . //s~ *'s ,(Fe,Ni)78Pi388 (Fe,N~175 Pit B6 AI$ o 0 0.6 0.8 I.O IRON, X Fig. 24. Curie temperatures of amorphous Fe-Ni alloys as a function of transition metal composition. Solid lines calculated using phenomenological model; dashed lines follow the data• FeNiB and FeNiPB Bucker et al. (1977); FeNiSiB Masumoto et al. (1977); FeNiPC Hasegawa and Dermon (1973); FeNiPBA1Gyorgy et al. (1976). 0 0.2 0.4 - 8oo~ I ' ' ' (FelC0)ToS;,~B,~.' 600}- Ire,~'m75r16"tM'3 ~ Q. I,,-,,' ' ' ' I .v" ..--~ - ~'~ s / / / s S R/ j (C0,Ni)78PI4B 8 J ," 400 / Q= .I • // V J i S / / / / ¢ 200 Fex Gel-x i • s S s ,ff S/ // (Co,Ni)75PI6B6AI3 I I 02 ( S 0.4 f I X 06 I I 0 18 I 1.0 Fig. 25. Curie temperatures of amorphous Fe-Co and Co-Ni alloys as a function of transition metal content. Solid lines for Fe-Co alloys calculated using phenomenological model. FeCoSiB and FeCoPC Fujimori et al. (1976b); FeCoPBA] and CoNiPBAI Gyorgy et al. (1976); CoNiPB Aunamou (1976); FexGez_xMassenet et al. (1974). 494 F.E. LUBORSKY described by Kouvel (1969). For this purpose it is adequate to use the molecular field model, suitably modified so that individual atomic moments vary in magnitude with their local environment. Only nearest neighbor interactions are considered. For the disordered crystalline alloy an explicit quadratic equation in Tc is derived whose physically meaningful solution is Tc = ½(T'AA + T'BB) + {~(T'AA-- T~B)2+ T'AsT'BA} t/2 (17) where T'AA, T'~B, T'AB and T'BA are interaction temperatures defined in terms of transition metal composition, magnetic moments, exchange coefficients, spin quantum numbers and number of nearest neighbors. If we neglect the variation of the individual atomic moments with changes in their local environment than eq. (17) reduces to Tc = ½[TAA(1 --X)+ TEEX]+{~[TAA(1 --X)-- TEEX]2+ T2AEX(1--X)} I/2 (18) assuming TAB = TEA where x is the transition metal concentration in the case of binary alloy. Note that for x = 1, x=0, T~ = TEn Tc= TAA. (19) This approach does not predict a critical concentration for the onset of ferromagnetic behavior and thus cannot be applied to the Ni-rich amorphous alloys which become non-magnetic. The cubic equation in Tc of Foo and Wu (1972) is required for this latter case. The solid curves in fig. 25 for the Fe-Co amorphous alloys were calculated using this equation. The interaction constants to obtain this best fit to the experimental results are given in table 6. The data for the Co-Ni alloys in the TABLE 6 Curie temperature interactionconstants (BxAi-x)yGi0o_y (Fe-Co)78SioBi2 (Fe-Co)75SitsBI0 (Fe-Co)75P16B6AI3 (Fe-Co)soPlaC7 (Fe-Ni)TaBlaSis (Fe--Ni)78Bi2Sito (Fe-Ni)8oB2o (Fe--Ni)8oPjoBjo (Fe-Ni)8oPI2B8 (Fe-Ni)79PI3Bs (Fe--Ni)soPi4B6 (Fe-Ni)75P.Cio (Fe-Ni)75PI6B6AI3 (Co-Ni)75PI6B6A! 3 (Co-Ni)TsP14Bs TaB K 693 660 600 595 753 731 652 653 608 627 615 585 600 630 -- 6 7 0 TAs K 908 866 804 838 790 780 1029 797 808 799 751 693 750 - TAa K 718 675 635 650 -43 134 - 185 145 -93 - 307 - 219 - 118 - 1180 - Range of validity 0<x < 0< x < 0< x < 0 < x < 0.4 < x < 0.5 < x < 0.35 < x < 0.5 < x < - < x < 0.45 < x < 0.4 < x < - < x < 0.3 < x < no no 1 1 1 1 1 1 1 1 1 1 1 1 1 AMORPHOUS FERROMAGNETS 495 same figure could not be fitted to eq. (18) because of the large change in atomic moments with compositon and the large critical concentration. The solid curves in fig. 24 for the Fe-Ni alloys were also calculated using eq. (18). This simplified equation could only be fitted to the data for x ~ 0.4, as shown by the solid lines. The dashed lines are simply drawn through the data points. The constants for the fitting are also given in table 6. Mizoguchi et al. (1973, 1974) has reported Tc values for a wide range of quasibinary transition metal amorphous alloys with the composition (AxBi-x)80Bl0Pl0. These are shown in fig. 26 plotted as a function of average outer electron concentration, N, together with the Curie temperatures of the corresponding transition metal crystalline alloys without the metalloids. There is a significant difference between Tc of crystalline bcc alloys and crystalline fcc alloys, suggesting the complexity of the effect of crystal structure on T~. In the amorphous systems T~ is a smooth function of alloy composition over the entire range. We can compare the exchange interaction term in eq. (16) for various crystalline and amorphous alloys. For Cos0Bl0P~0, taking into account the change in spin, S (cryst.) = 0.86 and S (amorp.) = 0.5, then ~ Jq (amorp.)/~ Jq (cryst.) = 1.1. Assuming only the short-range exchange interaction, the average J between nearest neighbor Co atoms seems to be the same in both pure hcp Co and in the amorphous alloy, since the coordination number is almost the same in both cases, i.e., Z = 12. However this is not the case for Fe. For Fes0B~0PI0, Y~Jq (amorp.)/Y~ Jij (cryst.) = 12J (amorp.)/8J (cryst.) ~ 0.7. The nearest neighbor interaction, J, is estimated to be roughly half in the amorphous Fe compared to that in pure bcc Fe, taking into account the difference in coordination number. 1500 i I .bcc e-co fcc DCC I-e-v ~ I000_ fcc C o - F e - - - ~ " . e - f c c s,'~ ",,, Co-Ni ,,, mFe-V eFe-Cr +Fe-Mn oFe-C0 oFe-Ni ACo-Cr ; ~ / f b c c F e - N i / f ~'Tcc bo-br 'x ~ ^ /" f /.~'-fcc Co-Mn ~, ,,," bcc Fe-Mn ~ !"~.. ...__ , ,/ / ".,, ~ / ", ~ cc F e - N i - - ~ 0 I 8 N 9 I0 Fig. 26. Curie temperatures of quasibinary amorphous alloys of 3d transition metals (Aj-,Bx)soP~oBt0 as a function of average outer electron concentration N of the metallic atom. Corresponding crystalline alloys, without P and B, are shown by the dashed curves. Mizoguchi et ai. (1973, 1974). 4~ F.E. LUBORSKY The pressure dependence of Tc has been measured by Yamauchi (1975), as reported by Mizoguchi (1976). In the series (FexTM~-x)s0Bl0Pl0 for TM = Mn or Cr, dTJdp = - 2 K/kbar [ - 2 × 10-s K/N-m -e] and for TM = Ni, dTJdp = -0.7 K/kbar [-0.7 × 10-s K/N-m-e]. In recent papers Durand (1976, 1977) and Durand and Yung (1977) studied the concentration dependence of the electronic and magnetic properties of F e - N i P-B amorphous alloys. The results for the magnetization have already been discussed. The change in the magnetization and the change in Curie temperature when B substitutes for P in F e - P - B at constant Fe concentration, shown in fig. 27, again suggests the existence of two different short-range orders in the amorphous alloys. One corresponds to the ~ structure and the other to the e, structure in crystalline Fe3P~_xB~, as reported by Fruchart et al. (1964). This correspondence betwen the amorphous and crystalline characteristics is the clearest example of the retention of the short-range order in amorphous alloys. Another interesting set of results reported by Durand and Yung (1977) on the F e - P - B alloys is concerned with the concentration dependence of moment and Curie temperature when one of the metalloids is substituted for the iron. The results for the substitution of B for Fe at different fixed concentrations of P are shown in fig. 28a, and the results of substitution of P for Fe are shown in fig. 28b. By extrapolating the apparent linear trends of Tc with composition Durand oof rcRYsT F.75 ,e, 800 ' ,,oLL/'-II IO J• II-,, I0 15 y,ol.% B -77..o"o 5 20 ~/.÷ *....--~_~,,,~:..7 "'5"- ,,.~x/''~., / ~ _n.-.Fe-_, Fe8$ uz /~e8oP20-ySy 600 / ~ ~ " ~ ~ " o~/''v " ~../~ S/ FecP[oo-c-yBy SS fS 550 + /S S ••/ • '* Fe4oNi4oP20.yBy 5O0 s 4," S S S S y, ot % B Fig. 27. Curie temperature of amorphous alloys as a function of glass-former composition. Solid lines for FePB Durand and Yung (1977). Dashed lines for FePB • and FeNiPB • Becker et al. (1977). Crystalline FePB from Fruchart et al. (1964). AMORPHOUS FERROMAGNETS I I I 497 650 Feloo-z-yPzBy ¢o) 9 B7 6 / 0 ..+.~'~="~Y 4, z =14 .+l~l~j ,tl, ~v: '...~ . ..~ /' / j, ~ ./., 600 550 v 500 I y,at.% B . . . . . . . . 650 FeIO0-z-yPzBy 600 550 0 5 y '--u.,~"' Io' Y.,,.'~:: a J i ~7 (b) z ,at.% P 10 ' ' 1'5 Fig. 28. Curie temperatures of amorphous Fe-P-B alloys as (a) boron or (b) phosphorus is substituted for iron. From Durand and Yung (1977). and Yung (1977) obtain the value of To = 320 K for "pure amorphous Fe'" from data on the Fe-B system and essentially the same value of To = 335 K from data on the F e - P system. Curie temperatures of a number of alloys mostly not found in the figures are listed in table 5. 4.3. Temperature dependence of magnetization The effect of measurement temperature on saturation magnetization is shown in fig. 29 for a variety of amorphous alloys and in fig. 30 for a series of (Fe-Ni)~B~0 alloys reported by Luborsky and Walter (1977a). These curves appear superficially the same as observed for crystalline alloys. However, if we plot magnetization vs. temperature in reduced coordinates, as in fig. 31, we see that the amorphous alloys all fall below the theoretical curve, especially at low temperatures. This appears to be a general feature of the behavior of amorphous alloys. The mechanism responsible for this lowering is not clear. The theoretical treatments can be classified into two categories. In the first, a unique constant exchange interaction between the magnetic atoms is assumed and the amorphous nature of the alloy is taken into account by calculating a random distribution of the local anisotropy field. Such an approach has been described by Harris et al. (1973, 1974) and by Gubernatis and Taylor (1973). In the second approach to treating this problem, a distribution of exchange integrals is assumed in order to reflect the structural fluctuations in the amorphous alloy. This approach has been developed by Handrich (1969, 1972), Kobe (1977), Montgomery et al. (1970), 498 F.E. LUBORSKY Fig. 29. Saturation magnetization as a function of temperature for various amorphous alloys. The numbers refer to the Allied Chemical Co. Metglas® alloys: 2605 is FesoB2o, Hasegawa et al. (1976a); 2615 is FesoPi6C3Bn, Hasegawa and O'Handley (1976); 2826 is Fe4oNhoP~4B6, Hasegawa (1976); is 2826B is Fe29Ni49P14B6Si2,Egami and Flanders (1976); 2826A is Fe32Ni~Cr14PnB6 Luborsky (unpublished). The -PI6B6AI3 alloys from Gyorgy et al. (1976); (Fe0.oTCo0.93)TsSi15Biofrom Fujimori et al. (1976b), . . . . . . . . . . . . . . . v - Fig. 30. Saturation magnetization as a function of temperature for Fe-Ni-B amorphous alloys. Luborsky and Walter (1977a). . .. Richter et al. ."~. . CoP Cargill and Cochrane (1974) and Pan and Turnbull (1974).. Amorp. Ni (IMPURE) 0 .~'~... K a n e y o s h i (1973).0 . T curve will fall below that for the crystalline counterpart. "\'.'..0 "~. 22. as shown. It is defined as the root mean square deviation from an average exchange integral between nearest neighbor spins. 23.3. . . ... A value o f 8 = 0. and for other . % P ./(S+ 1)](TJT).~ ~-" . . .[(1 + 8)x] + B. 31.[(1 ..._ _ •. contrary to the observed spectra.'\ .3 fit their magnetization results best. Also shown in fig.. FesoB20 .5 oao oo x. . 82 = (AJ2)/(J) :... a I .. ... (21) The larger the value of 8 the larger the decrease in the reduced magnetizationtemperature curve. FeB Chien and Hasegawa (1977). The first model h o w e v e r predicts that amorphous alloys should exhibit a structureless M6ssbauer spectrum. Co75P25 '~:'~ .0. Bs is the Brillouin function and 8 is a measure of the degree of disorder. . (1968). Tsuei and Lillienthal (1976) have compared their results for FeTsPisCi0 to the theory.AMORPHOUS FERROMAGNETS 1. in good agreement with the hyperfine field distribution obtained f r o m M6ssbauer s p e c t r o s c o p y results.\~ \~'. F o r crystalline nickel. CoP:I9.8)x]} (20) where x = [35~. 20.~. Thus the second approach is preferred. FePC Tsuei et al. ~o. Reduced magnetization-temperature dependence of various amorphous alloys compared to the molecular field theory calculation for J = ~ and compared to crystalline Ni. . Both approaches predict that the M vs.6 At.. . FeBoPl3C ? T/T c Fig. The effect of fluctuations in the exchange interaction leads to the equation for the reduced magnetization a = MdMo = ~{B.. (1975) and Y a m a d a and Wohlfarth (1975). Of the various theories the molecularfield approach of Handrich (1969) or the approximate Green's function approach of Tahir-Kheli (1973) are the easiest to present although the band model of Y a m a d a and Wohlfarth (1975) may be the most correct one. Ni 499 • ". . . 31 is the curve calculated f r o m molecular field t h e o r y (MFT) with ] = I.CRYST. amorphous Ni Wright (1976).5 1.0. ~ l 0 0. Also.E. (22) where Mo. . In crystalline ferromagnets of these alloys the values of B or D as determined from magnetization. This appears to be the case also for amorphous ferromagnetics. Chien and Hasegawa (1977) obtained for Fes0B20 B = 2 2 . by as much as a factor of two. In crystalline ferromagnets the T ~/2 term is dominant. long wavelength. Cargill (1975b) and Kazama et al. . M6ssbauer and ferromagnetic resonance all agree with those evaluated from the spin wave dispersion coefficient from inelastic neutron scattering.~2. assuming that the hyperfine field Heff is proportional to the magnetization M. /~ is the Bohr magneton in emu (9. These discrepancies are not understood. The large value of B in amorphous alloys has been interpreted as a "softening" of the exchange interaction. (1976). The available results for the value of the spin wave coefficient D are . The spin wave behavior may be inferred from low temperature magnetic measurements and from inelastic neutron scattering measurements.+ 1 x 10-6deg -al2 and C = 1. spin waves.61 x 10-5 eV/K) with D in eV . or from M6ssbauer measurements. assuming a dispersion relation of the form E(K) = OK 2 (23) the spin wave dispersion coefficient D may be determined. From neutron scattering.5 x 10-s deg -5/2. The values of D and B should be related by B = ~(3)(gl~/M)(k/4~'D)3/2 (24) where g is the g-factor (~2. Quantitative agreement between theory and experiment for amorphous magnetic metals is not expected since the Heisenberg localized moment models are generally not applicable to conductors and realistic models for the atomic arrangements of the amorphous alloys have not yet been used.27x 10-21emu).5~ F. Although there appears still to be a linear relation between l I B and T 312 for amorphous alloys the curve falls well below the curve for crystalline ferromagnets. reasonable agreement is obtained between the experimental and theoretical curves. LUBORSKY elements and alloys.4-+ 0. In amorphous alloys the value of B determined from neutron scattering is always smaller. to obtain B in K -a/2. For example. ~ is the zeta function. equal to 2. there is a reasonably good linear correlation between T 312 and I / B (Cargill 1975b). than the value obtained by the other techniques. while the small value of C / B implies that the exchange interactions damp out rapidly beyond the first nearest neighbors. MT: are the magnetizations at temperatures 0 and T and B and C are constants characteristic of the low temperature. the change in magnetization with temperature is given by (Mo . k is Boltzmann's constant (8. From magnetization measurements directly. At low temperatures demagnetization in crystalline materials is attributed to thermal excitation of long wavelength spin waves. The values of B in amorphous alloys are typically larger (and D smaller) than related crystalline alloys.M r ) / M o = A M / M o = B T 3/2 + C T 5/2 + .612. M is the magnetization in emu/A 3.1). FeCoSiB <>. Kazama et al. FeNiPBAI V. 32 for values derived both from magnetic and neutron scattering results. Since it was previously noted that in crystalline alloys l i B o~ T~r2 we would have expected D3/2= T~12 i. FeNiPB ~ . Lynn et al. o (FexCrl_x)8OPi3C7 (Fex Col-x)8oPI3C7 ¢ (Fex CoI-x)75 Sil5 BlO v Fe80B20 A C0100_xPx . (1976).e. The single phase crystalline alloy developed by further annealing had a value for A of . Solid symbols determined from inelastic neutron scattering. A zero magnetostrictive composition occurred at (Fe0.d. CoP A. FeCoPC [Z.1o3 I Fig.i. Simpson and Brambley (1971) prepared CogtP9 by electroless deposition and reported a value for linear magnetostriction A of -4. However a plot of D vs. open symbols determined from magnetic measurements. Chien and Hasegawa (1976b). Chien and Hasegawa (1977).AMORPHOUS FERROMAGNETS 501 summarized in fig. Magnetostriction The literature on magnetostriction of amorphous alloys is not very extensive." / ~ . Only qualitative observations of magnetostriction were made by observing changes in the hysteresis loop 20 v Fe8oPI6C3BI` ' .4.~ /// //v///MAGNETIC °o L~ .oe Fe75PI5Cio "~ IOC • C°80 P20 IE • (Feo. Axe et al. (1975). FeCrPC 1-1. FesCo92.96). / / " ~ ~ .. D = Tc in view of eq.Pt6B6A13.1 1 x 10-6... (1976). [] v =" ~. i.e. This increased on annealing even while remaining amorphous. (1975) and C).%" == " v / / ~ / / . 4. Cargill and Cochrane (1974). ~ .3Ni0. CoP A. (1975) reported on the magnetostriction within the ternary region of the transition metals for roller quenched amorphous ( F e .7)75PI686AI3 ~ F 4o. FePCB V. Sherwood et al.3 x 10-6 for the as-deposited alloy. 5 I io TC3/2 K3/2 1'5 2o.. FePC O. With addition of nickel the iron content required for A = 0 appeared to increase somewhat. Tsuei and Lillianthal (1976). /" o / " •. FeB V. Both appear to follow coincidently an approximate T 312 proportionality. ..04Co0. This has approximately the same Fe/Co content for which A = 0 in crystalline alloys. Experimental correlation between the spin wave coefficient D and the Curie temperature of amorphous alloys. 32. Mook et al. Tc produces a non-linear relation. e G <> . FePC ~ .N i Co)75P~6B6A13. (24) where B oc D -312. . LUBORSKY caused by application of tension.6 0. / (Fe.. FeNiPC average of values from Arai et al. The magnetizations all showed a composition dependence which was similar to that found in crystalline N i .Co175PI6B6AI3 y -O - ./'Y 0. 33." / °° 0 F- (Fe.. A series of N i . FeNiPB Flanders and Luborsky (unpublished).NI) 80PI4B6 80B20 I (~ t Z"" . Quantitative values of A.C0)80 B20 . 33."'&"~"~. FeCoB O'Handley (1977). on crystallization could be accounted for by the change in Young's modulus. varied from 25 x 10-6 to 36 x 10-6 depending on the direction of field and measurement. were reported by Brooks (1976) for the series (Fel-xCox)75PI6B6AI3from 0 ~ x ~ 0..8 x.C o .97.E. (1975) studied the magnetostriction of Fes0P13G from -76°C to room temperature.4 . 0 012 0. The magnetostriction constants however were all negative in sign (table 7) unlike the behavior observed in the related crystalline Ni-Co-Fe.. IRON Fig. (1976). .Ni)8oPIsC7 I0 ""-(Fe..20 0 pL~ Z ~E /" // .P alloys were prepared by electroless deposition by Simpson and Clements (1975). They conclude that the change in A. FeCoPC and FeCoSiB Fujimori et al.. '(Fe. These samples were all found to crystallize first to a metastable single phase with A.. Tsuya et al. (1976b).~.~. about half as large as in the amorphous phase but with amost no change in M. Magnetostriction was also studied by Arai et al.F e alloys. The perhaps surprising result found was that the material did not appear to be isotropic. values of A.-.F e . . FeNiB Flanders and Luborsky (unpublished) and O'Handley (1977). Saturation magnetostriction for various amorphous alloys with changing transition metal composition.C o .- - -. (1976) in three 40 T =_o x 30 (Fe..502 F.. . FeCoPBAI Brooks (1976). These results are shown in fig.Co)75PI3C7 .. (1976b) Arai et al.0 -11. (1976a) including the f o r c e d volume magnetostriction. (1976b) Sherwood et al.9Ni37.N i system the m a x i m u m was near 90 K for the compositions with x = 0.gNi35. Metglas® designation.1 -3 -4. A simple ternary .4 Fe0. Again As was f o u n d to be not quite isotropic.4.4 -0 -0.0 <0. 7 ) and (Fem-~Cox)75SlsBi0 (0. In the F e .3 Fe0. (1975) Arai et al.sP24.% Co. (1976) Simpson and Brambley (1971) Co~.0 -9.sNi42.0 5.2Ni39.0 31. at approximately the same composition as for alloys with other metalloids as shown in fig.AMORPHOUS FERROMAGNETS TABLE 7 Magnetostriction of some* amorphous alloys at room temperature Alloy CosoB20 Fes0B2o #26O5 Fes0PioBiC3 #2615 Fe4oNi40Pi4B6 #2826 Fe29Ni49P14B6Si2 #2826B Fes0PI3C7 A~x 106 -4.5 Fe6Co74B20 Fe3Co72PI6B6AI3 Fe4aCoT0. (1975a) Fujimori et al.0 31.0 29.C o system the magnetostriction went through zero near 96at.3SilsBi0 Co75SilsB~0 Co91P9 12.4 Fe 3.6Co35. In the F e . Some additional results on these same alloys were reported b y Fujimori et al. (1975) Fujimori et al. F o r Fes0PI3C7 they f o u n d a b r o a d m a x i m u m in As near 130 K.3Co39.0P17. series of a m o r p h o u s alloys: Feso-xNixPi3C~ (0~<x ~<40).0 11.9Co36. (1974) Tsuya et al.5 - 503 Reference O'Handley (1977) O'Handley (1977) O'Handley (1976) Egami et al. 33. The value o f As decreased nearly monotonically with increase in Ni f r o m 31 x 10-6 for Fes0P13C7 to 15 × 10"~ for Fe4oNi40P13C7.0 11.TCo46. * Values for other alloys given in the figures.2 and 0. (0 <~ x ~< 0 .0 -8.3P18. 1975b) O'Handley (1976) Egami et al.5 -4.s Ve4.3 # Allied Chemical Co. (1975a.0 19.6Ni3LIP22.0 3.0 30.sP16. (1976) Simpsons and Clements (1975) Simpson and Clements (1975) Simpson and Clements (1975) Simpson and Clements (1975) Simpson and Clements (1975) O'Handley et al. (1975a. 1975b) O'Handley (1976) Egami et al. (Fel_xCox)~lat3C7.0 31.75 ~< x < 1) with the results also shown in fig. The temperature d e p e n d e n c e of As was not a simple function. 33. which sums the strain derivative of pseudodipolar interaction energies over nearest neighbors adequately describes the magnetostrictions of crystalline Fe and Co. Furthermore. 4. Saturation magnetostrietion for various amorphous alloys with changing glass former compositions. The saturation magnetostrictions reported in the above references are summarized in table 7. O'Handley (1977) has discussed the possible origin of magnetostriction in amorphous alloys. 33.E. A localized spin model.~/I" ! o o I. Above the Curie temperature typical MSssbauer spec30XlO -6 I I I I i o i =- F e 9 3 _ x P x B 4 A 3 I~ 20x10 "~ Fe91-x PX B6AI3. L U B O R S K Y zero magnetostrictive alloy was reported by O'Handley (1976a) with the composition Co74Fe6B20.5~ F. 34. and in fig.5.. Band models which adequately describe the magnetostriction of crystalline Fe-Ni alloys do not appear to apply to these Fe-Ni and Fe-Co amorphous alloys. The magnetostrictions of the complete series of (Fe-Ni)80B20 and (Fe-Co)s0B20 amorphous alloys were also reported by O'Handley (1977). This amorphous alloy has a higher saturation magnetization than the other zero magnetostrictive alloys so far reported (see table 7) which contain phosphorus and aluminum or silicon in addition to the boron.IJJ Z 2E /°~ x \ l 10 20 x Fig. When generalized to consider the amorphous alloys the model suggests that the short-range order of cobalt-rich amorphous alloys resembles that of their crystalline counterparts. it can yield information about the true zero field magnetization. FePB and FeNiPB.. These results are also shown in fig. and in fig. FePBAI Brooks 0976). Interpretation of the results in terms of a quantum-statistical mechanics theory suggests that one anisotropic mechanism for magnetostriction dominates in the Fe-Ni-based glasses while another mechanism is also important in Co-rich glasses. 34 as a function of metalloid content. 10xl0"6 0 I ~ . 33 as a function of transition metal content. MSssbauer spectroscopy results M6ssbauer spectroscopy yields information on the magnetic properties of individual atoms rather than on assemblies of atoms as in conventional magnetization measurements. Flanders and Luborsky (unpublished). its preparation and thermal-mechanical treatments. The broadening is attributed to the broad distribution of hyperfine fields. This anisotropy. (1976a) using ferromagnetic resonance and scanning electron microscope measurements. or from chemical inhomogeneities. and its local variations. The same conclusion was reached by Hasegawa et al. Results for Ms of Fes0B2o from Chien and Hasegawa (1977) are shown in fig. depend on the alloy. The magnitude of the total anisotropy. Fujimori et al. The hyperfine field obtained from the M6ssbauer spectra. The distribution of hyperfine fields varies with the alloy for reasons that are not defined in detail but are related to the random nature of the structure. The motion of the domains under the influence of the internal material . Domain structure It is clear from the preceding sections that the amorphous alloys are not magnetically isotropic. Below the Curie temperature the spectra consist of six peaks symmetric with respect to their center but very broad compared to corresponding crystalline alloys. 31 compared to some other amorphous alloys. magnetostriction and other anisotropies. Thus amorphous FesoB20 reported by Chien and Hasegawa (1977) has a narrower distribution of hyperfine fields than Fe75PmsC10 reported by Tsuei and Lilenthal (1976) and Fe40Ni~P~4B6 reported by Chien and Hasegawa (1976a). and from magnetization measurements by Luborsky et al.AMORPHOUS FERROMAGNETS 505 tra for amorphous ferromagnetic alloys such as Fe. These strains interact with the magnetostriction resulting in an anisotropy which together with the other anisotropies present determines the average magnetization direction. (1976). from domain structures by Becker (1976). On cooling these as-prepared samples the average direction of magnetization typically begins to tilt out of the ribbon plane presumably due to changes in strain. assumed to be proportional to the magnetization. together with the sample shape then determines the domain structure. K. undoubtedly because of the variability of the strains developed during the solidification of the ribbon.P~sCi0 show two peaks characteristic of quadrupole splitting. These differences in magnetization direction have also been deduced from other observations. M6ssbauer spectroscopy has also been used to determine the average direction of magnetization by using the well known fact that for Fe s~ the intensities of the six lines of the hyperfine spectra have an area ratio of 3 : b : l : l : b : 3 . has a temperature dependence typical of amorphous ferromagnets. (1975). 5. of course. from these sources will. to 4 for the axis of magnetization in the sample plane. The value of b varies from 0 for the axis of magnetization perpendicular to the sample plane. (1976b) and by Obi et al. non-uniform strains. Results by Chien and Hasegawa (1977) indicated that the magnetization stayed nearly completely in the plane of the ribbon for the as-prepared ribbon. The anisotropy may arise from field or stress annealing. For example. Results for other alloys are not entirely consistent. as expected. The patchy nature illustrates the irregular distribution of anisotropy. Becker (1976). Ribbon thickness 40 ram. .9 measured in the easy axis direction and Fig. 35.and Co)in 80e alongribbon axis. to reduce the strains to zero. Similar domain structures were reported by Fujimori et al.E. 35.(b) higher magnification within patch in zero applied field.5~ F.6 are typically obtained in a variety of compositions. (a) low magnification. Values between 0. as revealed by Bitter solution. After annealing. Some typical domain structures in as-cast ribbon of Fe40Ni40P~4B6 reported by Becker (1976) are shown in fig. Patches of fine domains observed on as-cast ribbon Of Fe4oNi4ePm4Bs. The domain configurations can be observed directly. LUBORSKY parameters and the externally applied fields determine the static and dynamic magnetic properties.3 and 0. Their labyrinthine structure shown in the higher magnification views changes with strain and with field. (1976c). The direction of magnetization is then determined only by the field applied during the anneal and by the sample geometry. These effects and their disappearance on annealing all suggest that their origin is due to internal strains. the labyrinth patches disappear and are replaced by a simple structure of only a few domain walls.No applied field. ribbon axis horizontal. Values of Mr/Ms of 0.8-0. These strains produce a normal component of M which results in a low Mr~Ms value in the as-cast ribbons. <> incomplete anneal. i IIH i i . In addition. in the field annealed samples. [ ] annealed along width of ribbon. The hysteresis loops measured in the easy axis direction.5 IH 0 i 200 400 MEASUREMENTTEMPERATURE. Sample annealed to obtain various values of M. . O.K I I I I 600 Fig. Its origin is varied and sometimes not completely understood.AMORPHOUS FERROMAGNETS 507 less than 0.Ot . Luborsky (unpublished). have been obtained.1 measured perpendicular to the easy axis. In the following sections the various anisotropies existing in amorphous alloys will be described.. However. This was confirmed by dynamic observation of the walls during reversal by Shilling (1976) and by measurements using a small ac field superimposed on the de reversal field as described by O'Handley (1975). it has become something like folklore that in an ideal amorphous alloy the atomic scale anisotropy would be averaged away so that there would be no anisotropy effects visible. Results for some of the alloys are shown in table 8 and in fig. In many cases. •o i t "-.IM. 6. Details of this have been reported by Becker (1975). Magnetic anisotropy Amorphous solids usually are assumed to have no long-range order and thus should be isotropic on a macroscale. Temperature dependence of the remanence to saturation ratio of Fe40N~P~4B6. Only a few walls are nucleated which are then free to sweep through the sample. magnetic anisotropic behavior is observed. 36 as a function of temperature. 0 annealed in field along long axis of ribbon.H loop with only a few Barkhausen jumps. 36. it reflects the existence of short-range order in the amorphous alloy. Chi and Albert (1976) have shown from a simple model calculation that when the local random anisotropy is small the coercivity is indeed small but high coercivities are abruptly obtained as the local anisotropy increases and dominates the behavior. I.0. are thus quite square and show a typical wall nucleation limited M . ~ . 508 .q ""~ . ~.a~ °~ °~ °~ ~=~ ~ ~ .'.) '~ r.. ' .'-..~ 0~ 0 0 r.- E~ o o o c5c5 0 0 oo ~ 00 0 ¢!1 o ¢"-I od +1 dd +1 o ~ Z 0~ ¢.S . 0 L~ Q. .ID I= I= I= b.< . 0 • . h" ÷1 v l a : l la:l ~ la:l V V V v v o ~m ~ ~ ~ ~ • gd ~ ~ o ~e ae ae a~ ~e N~ e e 509 .q.) L) ..m e~ 6 6 6 6 6 o ~ oo o 6 . An important example of non-uniform strains is observed on drum quenched alloys of the (TM)s0(P.510 F. These strains couple with A to produce an anisotropy. The domain structure and their disappearance on annealing reflect this perpendicular KA and its removal. The nonuniform strains develop during the preparation of the ribbon and result in a periodic fluctuation in the perpendicular component of anisotropy along the length of the tape. The magnitude of A and the direction and magnitude of or will then determine the direction and magnitude of K~. 33 and 34.e. anisotropy fields greater than 2~rMs are observed even with no external stresses. namely 2~'Ms. Structural and compositional anisotropy Anisotropic microstructures can arise in amorphous alloys prepared by any of the techniques previously described. This has been discussed by Becker (1976) and Fujimori et al. or. i. The magnitude of Ku depends on the composition and conditions of preparation..P films have been interpreted by Chi and Cargill (1976) as showing the presence of oriented ellipsoidal scattering regions. Thermal annealing removes the internal strains causing the anisotropy to disappear. (1976c). Internal strains. assumed to be of high Co concentration. 6.e. Small angle X-ray scattering observations on these electrodeposited C o . AI. sputtered or electrodeposited films due to the differential thermal expansion between the film and the substrate.of 10-10000/~ [1-1000 nm]. The changes in A with composition for a variety of alloys were shown in figs.1.)20 type. L U B O R S K Y 6. 2. i. The resultant anisotropy field can then be no greater than that for long rods. Annealing at temperatures well below crystallization reduced the perpendicular anisotropy and the small angle scattering suggesting that the annealing resulted in some homogenization of the alloy. These microstructures may involve density or compositional fluctuations which produce internal shape effects. These alloys show a weak perpendicular anisotropy whose origin is believed due to such compositional fluctuations. Such fluctuations are often of the scale that can be seen by microprobe analysis or small angle X-ray scattering. Uniform strains are often induced in evaporated. Some values of A reported for some of the commercially available alloys were listed in table 7. In some amorphous alloys of Gd-Co. . Ka.2. The amorphous electrodeposited Co-P and CoNiP alloys have been studied in some detail. arise from the original solidification or from subsequent fabrication. which may be uniform or non-uniform. A. ch. B. Strain-magnetostriction anisotropy Most amorphous ferromagnetic materials have non-zero magnetostriction. variations in magnetization. and is discussed in vol.. The origin of this anisotropy in the rare earth-transition metal alloys is believed to involve short-range structural or compositional ordering developed during the preparation of the alloy.E.. 5. in the range. for negligible non-magnetic interaction enrgy then f ( c ) = ~Nnc. The dependence of K . of the type leading to precipitation as expected. The same values were obtained by cooling in .AMORPHOUS FERROMAGNETS 511 6. on Fe-Ni composition follows the theoretical dependence for non-ideal solid solutions with a negative interaction energy. can be changed reversibly by changing the field direction and anneal temperature. The direction and magnitude of K. obtained by annealing in a field for 15 min at increasing temperatures are shown by the solid circles in fig. is the concentration of the dilute species.. Magnitude of magnetic ordering anisotropy In the case of magnetic ordering. are shown in fig. The reported values of K. If neither constituent is dilute. Directional order theory predicts the dependence of the magnitude of the directional order anisotropy. Their results for the maximum values of K. 37.the concentration of the ordering species. For dilute solutions for monatomic directional order f(c) = c where c is. These relations for amorphous F e . This results in a uniaxial anisotropy arising from the ordering of both the magnetic and non-magnetic atoms. applied at a temperature below the Curie temperature.B alloys were studied in detail by Luborsky and Walter (1977a). 6. For diatomic order f(c) = c 2 where c. In amorphous alloys we expect the interaction energy to be negative. following Slonczewski (1963). Directional order anisotropy As in crystalline alloys. at x = 1 is interpreted as due to ordering of the boron. For non-ideal solutions the effective non-magnetic interaction energy must be included in the expression for f ( c ) as described by Luborsky and Walter (1977a). CA and C~ as given by K.N i .. i. = A f (c )(M ~ Mo)2(Mo/ Mo)210 (25) where A is a constant which depends on the atomic arrangement and the range of interactions considered.e. M0.. and the concenetrations of the ordering atoms. (1977) studied the magnetically induced anisotropy in (FexCol-x)~Si~0Bn amorphous alloys. i. MT. i.cb 1 2 2 (26) where N is the number of atoms per unit volume and n is the number of possible orientations of each pair referred to a crystal lattice. 37. at the measurement temperature.e. but assuming ideal solutions. The temperature dependence observed fits the theoretically expected dependence on anneal temperature. leading to precipitation.1. K. on various parameters.3. It will be seen that the behavior of Ku in amorphous alloys is very similar to the behavior in thin films or bulk alloys of NiFe.e.. 0. Fujimori et al. is expected to be a function of the anneal temperature.3. The non-zero value of K. and at 0 K. the amorphous alloys also order under the influence of a magnetic field or stress. Mo. the magnetization at the anneal temperature. the magnitude of K. It is clear that the amorphous alloys are more closely related in their behavior to the quenched crystalline alloys rather than to the annealed crystalline alloys.___.2 . Solid symbols • for maximum values obtained by heating 15rain at successivelyhigher temperatures and • by coilingfrom 380° at 1. was further demonstrated by Fujimori et al. 6. The general requirement that two different metal atoms are necessary to obtain a large K . 38. Directional order theory predicts a decrease in induced anisotropy as the anneal temperature increases. the rate determining step in the reorientation has been associated with the excess vacancies present. Magneticallyinduced anisotropy as a function of composition.512 F. as observed by Fujimori. The decrease in Ku on further decreasing the anneal temperature is the result of the slower kinetics of orientation at low temperature.' 32~o~ / ) SiI0 812 :w~2000 / I(Fe xCoI-x78 I "Ii \\\\ ~'~ ' ~ 0 I i i i i i I 0. (1977).. These results are shown in fig.6 0. Developedby annealing to equilibrium at various temperatures given by open symbols from Luborskyand Walter (1977a).6 deg/min as shown by the solid squares.E. 37. Although these results are of interest from a practical viewpoint they are difficult to interpret quantitatively in terms of directional order theory because of the uncertainty as to the anneal temperature and the uncertainty as to whether equilibrium was achieved at any temperature.6deg/min.---I .2. The Fe40Ni~P14B~ alloy surprisingly exhibited simple first order kinetics in the reorientation of its 0 0. (1977) by adding small amounts of Pd. Reorientation kinetics There have been a few studies of the kinetics of the reorientation of K. LUBORSKY • 4000 • .3. In the quenched alloys.0 ATOMIC FRACTION IRON Fig.8 1./ • ~" I~Z__ ~" ~. as will be discussed in the next section._ z/J. T h e time constants for this reorientation for various amorphous alloys are shown in fig.--. suggesting that equilibrium was not achieved. ~\\~ 3oo . calculated from data of Fujimori et al. It has thus been suggested that the disordered structure of the amorphous alloys has produced a similar atomic environment and thus similar kinetics for the reorientation. Ni or Cr as well as the Fe to CoSiB. 39 compared to similar crystalline alloys without the metalloid additions. a field at a rate of 1.4 0. From Fujimori et al. FePC Berry and Pritchet (1976).o5 ~ Io4 ~= 103 101 2 II/ i :7 ANNEALED....AMORPHOUS FERROMAGNETS 600 513 400 (YxC°l-x)TBSiloB 12 Fe 0 f " 2 200 ...~ . ..'" • j. . Crystalline alloys shown by broken curves .. . anisotropy as measured by the changes in its remanent magnetization ratio Mr/Ms. Ni. 20-50 Fe-Ni.." ..oNe/ • ... Q Berry and Pritchet (1976).0 2./ ../ 7 Fe40NI40PI4 86 . .o... . Time constants for the reodentation of the induced anisotropy in some amorphous alloys shown by the solid curves with data points: FeNiPB O Luborsky (1976). The m a x i m u m magnetically induced anisotropy for small additions of Fe.I Fig.4 i i 1.500 400 200 150 .40 Fe-60 Ni. Pd or Cr to CoSiB. FeNiB Luborsky and Walter (1977b). °C 300 .'11 I-/~" F o . . 16 Fe-84 Ni.2 2. P d ~o.I! • ...6 i 1'.~. This suggests that a uniform atomic environment exists around the reordering species. . / .8 I 2.' /:7 /1~ !...05 X 0..pr~o.. Z 05 FeTsP=5 c Zff .J" 75 . .7 ~.Y 1.. . 20 Fe-20 Fe-20 Ni-00 Co.''" ~. references given in Luborsky (1977b). Note that the time constants obtained for the TEMPERATURE.. (1977).. 9 - - ~ ~.. 38./" p/ / QUENCHED. i I i i i .:/ :ii!'. the kinetics could be fitted with a distribution of time constants or by second order kinetics with equal concentrations of the two species...4 1000/T. !: ¢ ": l.. / ~i~" I. . 39. • • • 15 Fe-85 Ni... On the other hand the reorientation kinetics of the Fe40Ni40B20 alloy did not exhibit simple first order kinetics. . . Maximumvalues from heating 15 min at successivelyhigher temperatures. 0 0. K-I Fig. . It is thus concluded that stress induced directional ordering involves different atomic species or motions than those involved in magnetically induced ordering. 7.sMn37. For 180° walls. The intrinsic coercive force was near zero on one side and 7200 Oe [90 A/m] on the other. This raises some interesting. In addition.3. this ordering presumably occurs via the interactions of the strain produced with the magnostriction. He.sPI6B~AI3by Sherwood et al. as Hc = 4S(AK) 1121dM~ (27) where S is a constant determined by inclusion size and density. These activation energies are about twice as large as the values for magnetic ordering. 250 and 250 kJ/mole] respectively. and unanswered questions concerning the atomic arrangement necessary to develop this effect. Fe4oNi~PI4B6 and FesoB20 was 2. the coercive force can be written from dimensional analysis. there are several approaches to calculating the coercive force. (1976).3.6 and 2. 2. K the anisotropy. the magnetization at 15 kOe [190 A/m] was only 7.P15C10. LUBORSKY Fe40N~P~4B6 alloy by Luborsky (1976) using magnetic measurements and by Berry and Pritchet (1976) using measurements of the AE effect using a vibrating reed. Coercive force If we assume that magnetization reversal takes place by domain wall motion. determined from the internal friction measurements.514 F. in terms of the material parameters. 6. fluctuations in anisotropy or other factors. In one approach given by Gyorgy et al. d the ribbon thickness and Ms the saturation.E. See for example Gyorgy (1975) or Chikazumi (1974).5 K. Cooling in zero field produced a symmetric loop with Hci= 1600Oe [20Aim]. surface roughness. Stress-induced order These alloys are also susceptible to stress induced ordering as studied by Berry and Pritchet (1975. The activation energy for stress induced ordering.2. for Fe.6eV [210. In another approach Hasegawa (1976) wrote . As in crystalline alloys. 6. 1976) using internal friction measurements. agree with each other.5 emu/g. By cooling in a field an asymmetric hysteresis loop was measured at 1.4. This appears to be the first demonstrated example of exchange anisotropy in an amorphous transition metal-metalloid alloy. A is the exchange constant. (1976) it was assumed that walls are pinned only at the surfaces. the final state produced by the two ordering processes must be different. Exchange anisotropy Evidence for ferromagnetic-antiferromagnetic "exchange anisotropy" has been found in the amorphous alloy Fe37. Magnetic saturation could not be achieved by any treatment. then the wall behavior is governed only by eddy current damping. Results for an amorphous alloy. The coercive force is then givn by nac = (*rILH~IMs)'12 (29) where f is the frequency. The solid line was obtained from the theoretical relation normalized to the room temperature value of /arc and K was determined from ferromagnetic resonance. 40 where temperature was varied to vary K and Ms. Co). 41 as a function of transition metal content and in table 8 for alloys in the as-cast and in the annealed state. large enough to reverse the magnetization. in fig. 40 I I 1 I I ~2 "~. (1976c) assumed that the major contribution to the H~ arose from the strain-magnetostriction anisotropy fluctuations so that H¢ o~ . Co data at low concentrations and the dashed curve was normalized to the data at high Fe. 40.~JMs. The comparison of this functional relation to some results on an unannealed ribbon is shown in fig.AMORPHOUS FERROMAGNETS 515 Hc = (2K/Ms)f (28) if we assume reversal by domain wall motion where f = Y. L the domain wall spacing.~X stands for the fluctuation in X within a region corresponding to the domain wall width. Here .H¢ ~20 . Results for He of other amorphous alloys are shown in fig. The agreement is not very satisfying. Luborsky (unpublished).~s and Ms.K I I I I 600 Fig. cracks. they calculated the solid and dashed curve in fig. Temperature dependence of coercive force for Fe4oNi~P~4B6: • unannealed sample. The decrease in Hc on annealing results from the decrease in the strain-magnetostriction anisotropy. Using measured values of . and/3 is the damping constant. H the maximum drive field. The dynamic response of domain walls is of considerable practical as well as fundamental interest. In the case of (Fe.0 Fujimori et al. 42. Co concentrations.Si15B. and stress may be varying from sample to sample. AXIX. © annealed sample. with walls free of pinning sites. When an ac field is applied. . theoretical relation given by solid line. Hasegawa (1976).2K ="~S f LED L6 Oi I 200 400 M E A S U R E M E N TT E M P E R A T U R E . Note that the values of He for the annealed samples depend on their magnetic history. Other factors such as surface roughness. 41 where the solid curve was normalized to fit the Fe. ....06 ~ ° o • Ho =0. . Masumoto et al.10 0. .. ~. .. .02 I I fl/3 I I see-l/3 I I 0. / .( Z) Fig.5 X I I l I I.6 i. . 0977). ..• ANNEALED 0 I "i ..14 / H o :0. ...4 Fig...18 ~ I t i i I H0=0.. I I 0. A . ...•. "" 0. .E... • .. Gyorgy et al.. .1 * . 0. Dependence of coercive force on composition. ... . • FeCoSiB and © FeCoPC as-cast Fujimori et al.2 0. ... LUBORSKY i I I t I I o 0.'. .2 (FexCoI X175SIi5 o 0 16 (rexC0f-X)eOPt3C-/ C. ..516 I I F...~ . 41.O i. 0. H0. The alternating current coercive force as a function of the drive field frequency at three field amplitudes. (1976). .37 Oe 0.11 Oe 0. .. Solid line calculated by normalizing to fit FeCoSiB data. . (1976c).• . .. 42.. & ."" • ... ~ . .79 Oe .A. . ---°~o-o-. dashed line calculated by normalizing to fit FeCoPC data..o~ / ~ / / // o/ // (Fe X Nil_x)?aSiloBi2 AS CAST . . A • FeNiSiB as-cast and annealed. (1975).0.AMORPHOUS FERROMAGNETS 517 are very similar to results obtained on conventional SiFe and Permalloy. it has been shown. as reported by Luborsky et al. (1976a) reported values of Mr/Ms from less than 0. in a variety of alloys by Luborsky (1977b). (1975). Its value is determined by the magnitudes and directions of the anisotropies present.3SilsBl0 by Fujimori et al. in F%Co72PIsBnA13by Sherwood et al. can be discussed in terms of a model similar to the one applied to discussing the coercive force. 8. considering the energy required to bow out the wall. Luborsky et al. After a stress-relief anneal as first described by Luborsky et al.. (1976b). for example by Gyorgy (1975). L ~. as indicated in fig. Subsequent annealing of the low magnetostriction . (1975) the dominant anisotropy remaining appears to be that due to directional order as described in a previous section of this chapter. Since the magnitude and the direction of the strain may vary with the details of the quenching the resultant anisotropy and thus Mr/Ms would be expected to vary.) = 330. X(calc. Remanence-to-saturation ratio As in crystalline materials the remanence-to-saturation ratio of a magnetic material is important theoretically and technologically. This is due to a frequency dependence of the domain spacing L. 36. With decreasing magnetostriction the permeability of the as-cast alloys also improves considerably as measured in Fe4. The value of MJM~ is then determined by the direction and magnitude of the directional order anisotropy. that the susceptibility X = M~dI[18L(AK)'/2] (30) where d is the sample thickness and L is the domain spacing. for example. and in Fe6Co74B20 by O'Handley et al.M / H . From the equation of motion of a wall and at low frequencies. In amorphous alloys of the transition metal-metalloid type the anisotropies in the as-quenched ribbons appear to be dominated by the strain-magnetostriction interaction.1 to 0. Susceptibility and permeability The low field susceptibility X . In the Fea~Ni~P14B6 amorphous alloy. = B / H = ( H + 4~rM)/H of as-cast alloys is relatively low but improves with annealing at temperatures and times below crystallization.TCoT0. as is indeed the case. in reasonable agreement with values measured. The permeability p.01 cm and with d = 2. depending on the magnetic field and heat-treatment used. Typical values reported for M J M s for some other alloys both before and after a stress relief anneal are listed in table 8 but these may also vary widely depending on their thermo-magnetic history.5 x 10-3 cm.9. 9. (1976b). The slopes vary as H~/2 as expected but an ft/3 frequency dependence is found rather than fl/2. From the observed domain patterns for an annealed alloy. a.. Luborsky et al. frequency for amorphous alloys and commercial alloys.. ... commercial alloys at 50 (3. ~ I I04 H\'... ~ 4-79 Mo-PERMALLOY SUPERMALLOY . . .g... .~.. the total power losses are often expressed as the sum of a hysteresis loss and eddy current loss as W = ~?Bl"6f+ eB2f2 (31) when f is small. . ~ ~' %"% i'I _ _ . .~.. 43. HZ Fig.~ ... Typical "initial" impedance permeability vs.. when core losses are significant in applications._ ]. 1 104 0.. . .. Losses At intermediate and high inductions.. ~ " ~ - o • ~ ~ ~ m . 10. . e. Improved permeabilities are expected for the amorphous alloys if smoother surfaces were prepared as is done for the commercial alloys. 43 compared to some conventional soft metallic magnetic materials. . . the hysteresis loss term is I I 1 I | I05 .. . LUBORSKY alloys has little effect on their properties. however.E. Luborsky (1977b).. .L'..-4Z .. . V. .. ...~r.. .. .. " ~ . At higher frequencies the amorphous alloys compare somewhat more favorably to the crystalline alloys because of their higher resistivity.:~-. are given in table 8. Amorphous alloys measured at AB = 100 G. . "" ~ ~/~L" "-~ i0~ 125#m 102 I 103 105 FREQUENCY. for example. B. .. . At low inductions. . . The maximum dc permeability. that these results for the annealed specimens depend on the annealing history. < 100 Hz. 43 are given in table 9. . E... .. .. for a number of alloys in the as-cast and in the annealed state.... . The letter designations in the table are the same as given in the figure. _ ~ 5 0 ~.. . ~.. .518 F.. ... K -"---. -25/~m .... Results from Luborsky (1977b) for a number of fully annealed amorphous alloys are shown as a function of frequency in fig.. . ~ .... The values of MrIMs and other charactertics of the samples whose permeabilities are shown in fig. . (1976a) showed that the losses and permeability could be controlled by control of the orientation as measured. ... often calculated as BdHc. [ ] at 45 (3. It should be noted again. . .. The low frequency permeability of all of the amorphous alloys shown are less than the commercial Permalloys but higher than the FeSi.. .~'~ ~ ' ~ ~" ~ . . ... SILECTRON .. ~ ...50#m ~ ~ . by MdMs.. .. . °~ 0 I I I I I o 0 ~ u I I I I o.q. o ~. o I I I I o o ~ i 0 o o.- 0q. = o o. r.. ~.r-- . 00 o ~°'~ ~ i I I I I g.o ~ o Z 519 . .':.'0 I I000 I I0. 44. All of the alloys have been stress relieved before measuring and are representative of the alloys with the Mr/M. inductionfor amorphousalloys measuredat various frequencies. 44 for a variety of amorphous alloys at frequencies from 60 Hz to 50 kHz. At higher frequencies. GAUSS Fig. 60 HZ F / l i . Typical core loss results from Luborsky (1977b) are shown in fig. H II. Core loss vs. All samples approximately25-50/. t is the thickness. The considerable improvement in losses as the result of 10 3 E~ FesoB20 I / i~ 17-IO / " "~l= E § / / 16 10"2 I kHz /I I /.m thick. the losses are controlled predominantly by eddy currents and are given by We ¢rtB:fV/(l~fJ)u2 = (32) where f varies from f2 at lower frequencies to f312at higher frequencies. values listed in table 9.000 INDUCTION./~ is the permeability and £J the resistivity.520 F. Luborsky(1977b). ° 10"-3 i I00 K ".'~ I .E. LUBORSKY more nearly proportional to B3f. II1./. The losses than increase faster than predicted by the straight line relations shown. In many applications. 45. Results from the literature for two grades of crystalline oriented Fe-3. Results from Luborsky (1977b) for two of the amorphous alloys are shown in fig. 47. the losses of the amorphous alloys are shown at one point by their letter designations.AMORPHOUS FERROMAGNETS 521 annealing is shown in fig. Loss as a function of the product of magnetostriction and thickness for as-wound and annealed toroids. the soft magnetic material is driven to saturation.~ANNEAL ED / - 0 500 O. we present results for conventional metallic soft magnetic materials in fig. io-' % Aswou U _ c. Material prepared by Luborsky. open symbols. as obtained from commercial literature... The lower losses of the amorphous alloys are significant. X I06} X THICKNESS. Luborsky (19"/7b). the change in loss is small. Two thicknesses are shown: 25~m by the light lines and 50/~m by the heavy lines. These thicknesses are in the range of thicknesses of the amorphous alloys measured. material prepared by Allied Chemical Co.. The only data showing the thickness dependence of losses is for the FeCoSiB alloy shown. slashed symbols. For thicknesses from 21 to 35/~m. 46. to-2 o. . /~rn tO00 Fig. LO.2% Si sheet steel are shown for comparison to the Fe~B20 amorphous alloy. This is shown in fig. All of these loss results for both the amorphous and crystalline alloys show the expected frequency and flux dependence given by W ~ BOf ~. (1976a). As an aid in comparing the results of the amorphous alloys to the conventional alloys. 48 tested using both sine H and sine B excitation. depending on the magnitude and direction of the induced anisotropy as described by Luborsky et al. (33) The values of the exponents /3 and y vary in a given alloy after stress relief. 45 as a function of magnetostriction. For comparison. Loss of amorphous alloys shown here only at 1 kG for comparison. ..0 Fig... 2... 47..." .:. . (1976a)...C 0.' /}" .7 . .7.0.-" ~.' :.... Luborsky (1976b).-" o'..... Luborsky et al.6 1 0../~? / # / ~" .LECTRO.':1::" 't l// .522 103 F..'. /EG . i:/.f' I I kHz I0 -I I I0 10 2 INDUCTION....5 Wa o 2. Loss exponents for fully stress relieved amorphous Fe40N~PtdB6 annealed in various fields to produce a variety of values of loop squareness.. kG Fig.. /~....8 I 1.. SQUARE PERMALLOY ..0~ -- I.E. induction characteristics at 1 kHz for conventional crystalline commercial alloys at 25/~m (light lines) and 50gm (heavy lines).5• 0 .. /' ':''o.. SUPERMALLOY ...... 102 S.l:: //' • I0 _J ' "1".. I #':"::..... i. 46.... Two different samples shown.0 ~ o ~o 1... LUBORSKY t i / 4-79 PERMALLOY .4 Mr / M s I 0... /~./.2 I 0.. DELTAMAX . Typical loss vs.. m 229 350 Fe-3. FeCo.2 Si / / . In addition to the m a g n e t i c . induction./ 16 / 2'i ~l l ///'//S~NE o _.AMORPHOUS FERROMAGNETS 523 i L35s3 r~3o5/ SINE e I//.J . Typical characteristics for Fe-3Si tapes at various frequencies and thicknesses./"/ /~.~S N IE H ' //~ !"oNi4oP"B~ I I0 4 INDUCTION. Loss per kilogram vs. Conventional Fe-3Si sheet steel at 300/~m is compared to the new "Hi B" sheet steel and the amorphous alloys all at 60 Hz.. Rather we will describe the amorphous material parameters which are generally significant to a variety of applications. or by its dynamic or ac properties. Possible applications of a material may be determined either by its static or dc properties.(/.~305~. Thus in this section. 48.:. Luborsky (1977b). or ferrites." #. These may be found in detail from existing sources. The specific requirements of materials for these applications is also very varied. Hi-B I/. we again will not present any details of specific device requirements for the materials. Application as soft magnetic materials Conventional soft magnetic materials are used in a wide variety of applications ranging from large power transformers and generators requiring many tons of SiFe to very small transformers and inductors in hybrid electronic circuits requiring only a few grams of one of the many available grades of FeNi. ). 11. GAUSS I0 5 io-2 103 Fig."F28oj i I / 4- : s'NE" e -g . application of the very low Mr/Ms state does not now appear reasonable for this alloy. improved stability is achieved by changing the alloy composition. Even for a given alloy. Application of the high Mr/Ms state is quite reasonable since the domain orientation during most applications. high-gain magnetic amplifiers.B alloy. is the direction of the induced anisotropy. The magnetic stability has to do with the change in the induced anisotropy. also discussed in an earlier section. The worst case was taken as aging a toroid in a de saturating circumferential field beginning from the low Mr/Ms state. Typical results. and low-frequency inverters. it is expected that the changes with measurement temperature will be small.1 0 0 0 hours. at 140°C 10% reorientation of the magnetic anisotropy will take only 17 hours. For the F e . This stability has been evaluated for Fe40Ni40Pt4B6 and Fe4oNi40B20amorphous alloys in a worst case situation from the reorientation kinetics. it will take .P . and thus minimum ac losses. the properties are easily varied by changing the induced anisotropy. are best applied in high-frequency inverters or transformers where minimum losses are important. This range is also useful in signal devices such as fluxmeters and ground fault detectors where the highest permeability is desired. the high moment Fes0B20. For example. the time constants for magnetic reorientation of the Fe-Ni-B alloy are about 50 times larger (see fig. Fe-Si and the Fe-Ni at higher frequencies. extrapolated to 100*C. as thin tape. the stability of properties and cost must be considered. Samples with Mr~Ms near zero are interesting for applications in which constant permeability is desired over a wide range of 4~rM as in filter chokes or loading coils and some specialized transducers. as well as at rest. . However. Thus. However. where the square loop characteristic is needed.524 F. their higher induction compared to the Fe-Ni alloys or their lower losses compared to the Fe-Co. all will favor the use of the amorphous alloys. the lifetime is controlled by magnetic annealing. not by reerystallization. The wide range of de and ac properties provide characteristics suitable for different types of applications. as has been presented. Samples with high MJMs are particularly suited to devices such as switch cores. Samples with intermediate Mr/Ms values. For application in small electronic devices. 39) and thus should pose no problem in most applications.N i . Where the design optimization requires the lower cost of the amorphous alloys. The temperature coefficient of losses and permeability have been measured in a few amorphous alloys as reported by Luborsky (1977b). Because of the high Curie temperature.2% Si. LUBORSKY properties required. because of the differences in thickness and the lower saturation flux of the Fe-B. as also discussed. For applications in large power equipment. 49. has about ~ the sine B loss of the best quality grain oriented Fe-3. The properties available in the amorphous alloys cover a wide range by changing alloy composition and heat treatment. the amorphous alloys have somewhat poorer losses and permeabilities than the conventional Fe-Ni alloys but better than the Fe-Co and Fe-Si alloys. Under these conditions. shown for a frequency of 1 kHz in fig. the temperature coefficient of properties.E. it is not clear what the final cost/performance trade-off will be for the complete transformer. ~.58 ZIB=IO0 G I kHz o Fe40Ni40820 0. 49.. The available data from the literature and from our own work was summarized in fig.. we see that the Fes0B20 is the least stable of the alloys discussed as candidates for application.AMORPHOUS FERROMAGNETS I I I I I 525 I0~ " O~..O. .O" fl .. 13. As discussed in an earlier section in this chapter we have defined the irreversible end-of-life as the onset of crystallization. For example. For this alloy.1 ~- _¢ ¢--~ . considerably shorter than for crystalline alloys where only recrystallization. at 175°C after 550 years or at 200°C after 25 years. H. u.. . Metglas ® #2615.~ .s@ ~ 0 .. change rapidly...70 0 Fe40Ni4oPI4B 6 0. if we assume a linear Arhennius extrapolation._.. Leamy and J. 1975a.. in Metallic glasses (eds. References* Alben. and thus their loss and permeability..O~'''~ C ~" rL v . In general. The lifetimes at any temperature are.S.. It has been shown that at the onset of crystallization the coercivity of amorphous alloys.O~<>~ .O.. . Budnick and G.. as expected.. K Fig.. 12. Metals Park. crystallization will start. these properties vary with temperature about the same as for the metallic crystalline soft alloys and are much less than for the soft ferrites.¢~"t>--<>-.70 ¢ Fe4oNi4oPI4B6 0. 1977.O. Ohio) ch. confirm this.<>_ -<>-_. oxidation or phase changes limit their life. Metals. measurement temperature..J. Data sheet 12-13-75. . -" ..o~o-.J Bm=l k6 I I I I I 200 400 600 MEASUREMENT TEMPERATURE. Gilman) (American Society for *Bibliography search completed January 1977. Cargill III.I. . R. .o~... ~ o Fe80820 • 103 Mr/Ms 0. ~. Luborsky (1977b).. J..S.<>. Loss and permeability at 1 kHz of some amorphous alloys vs.o -.. .O . .'~. This lifetime appears reasonable for all but the most severe application requirements.. Allied Chemical Co.. The data define the maximum fabrication and operating time-temperature exposures.. Non-Cryst. 1966. 34. J. Clements. Passel and C. Cochrane. 2248. Becker. 1976.. 1976b. J. Giessen) (MIT Press. C. B. Appl. 366. Hasegawa. Physics of magnetism (Wiley. R. Ferris. 289. Hill. Coleman. 1963.. Appi. 1976. 35.. Phys. Eng.. H. Couch and E.C. G. 288. Cambridge. Cohen. 964. 1326. IEEE Trans. and D. LUBORSKY Chaudhari. in Amorphous Magnetism II (eds.T.F.E. 405. Stat. G. Appl.W. Levy and R. B.G. 1974. Cambridge. Grant and B. D. M.C.A.. Phys.. Metglas® #2605A. Sherwood. Cal. California Institute of Technology. 214. 1976. Chen. Hull. J. H. 29. Aucote and J.. Cohen. Chien. and R. Cambridge. L.R.J. J. AIP Conf..E. 321. Turnbull. N. and J. W.G. M. P. Chen. 1976a.D. R. Rev. and E. Lett. Hasegawa.. A.S. E. S.A. and G. E. 1972. H. Giessen) (MIT Press.A. Phys. J. Lett. 1976b. 395. section 1 (eds. and R. and C. and B. L Phys.S.. Materials Sci. Miller. Chi. S. Suryanarayana. M.. J. and R.E. Magnetics MAG-12. Turnbuli. Masumoto. Proc. 34. 83. Mass. 245. 857. Anantharaman. 23..J. M. R. 801. 9. E: Scientific Instruments 3. Sci. 41. Leamy and R. H. 1976. Materials Sci.E. Res. 1976. E. Cargill III. 12. Krause and E. M. Walter. K. Brooks. Williams. 227. G. Allied Chemical Co.S. in Rapidly quenched metals. Eng. R. Thin film phenomena (McGraw-Hill. E.. N.W. Lett. and D. J. 1976. 47.. Allied Chemical Co. 411. and C. Chen. Gyorgy.K. Sol. R. 6. Solids 13. M. Saito and T..J. 1964.11. 1971.. in Rapidly quenched metals. 1179. Brenner. section 1 (eds. 1975. 31. Metglas® #2605. 204. and R.. Proc. Chen. Data sheet 12-23-75. 561. H. Bull. G. H. 293.. [2] 19. Berry. Cargill III. Harris. A. Park. AIP Conf.S. 1976. Leonti6. 131. Gyorgy.C.C.. Phys. 23. J. A. Brenner. Data sheet 3-15-76. 988. 24. Chen. Chi. Amer.. Polk and D. 1975. 21.S. Luborsky and J. Phys. Grant and B. Mass. 161. Becker. Instrum.L. 948. Turnbuii.B. Giessen) (MIT Press.C. Davies.L. R. Arai.526 F. 1970.. Pasadena.J. Crewdson. J.) p.S.) p. H. 1969. Phys. Herd. 317. J.C.J. J.. Becker. 1973.H. Bureau Standards 44.. H. (b) 51. Electrodeposition of alloys (Academic Press.S. Davies.W. thesis. 159. H.J. Metglas® #2826. H. 1505.D. 489. Ph. Krsnik and B. 1971. New York).S. 1111. J. J. Shirae. 26. Magnetics MAG.J. Nature 189. 119. 1022. 1975. 1976. Chopra. Babi6. Scripta Met. Chien.C.H. 138. 23. Acta Met. New York) p. Amamou. Cargill III. 1977. Zuckermann. 19. C.H. in Rapidly quenched metals. Chen. Fujimori.. B. Cargill Ill. 8. Lett. AIP Conf. 1976. 676. Rev.A. 1976. 29. 1973. H.L. J. Proc. and R.M. Mass.S. Magnetics MAG-12. 1976. Rev. Pritchet. Graczyk. P. Graczyk and S. 29.L.S. Chen. Cantor. H.S.. Coleman. Hasegawa.E.S. Sigety. Turnbull. 1973. 1976 IEEE Trans.K. 41. Acta Met. AIP Conf. Nature 203. Soc. 1974. 1976a. Pritchet. 34. New York) p. 1970.J. 1974. Bennett. Phys. H. Phys. Materials Sci. Tsuya. R. IEEE Trans. H. Hasegawa) (Plenum Press. Chen. Allied Chemical Co.C. Girt. C. 1975a. G. Str6m-Olson and M. Chen. Nat. Tsuei.S. Leamy and E.M. C. 316. Glasses 17. Lett. and W. Solid State Physics 30. 1295. N. AIP Conf.S.J. Acta Met. Cahn. 344. Sol. 1961. Laridjani. AlP Conf. 1977. Proc. 267. Krishnanand. Appl. N. F. Chem.S. 1975.S.C.S. Greenholtz and R.. Data sheet 2-18-76.F. AlP Conf. Chaudhari. 28. Acta Met. Cochrane. 1976..D. and B. Proc. Chien. 1237. H. Sherwood. 1974. section 1 (eds.S. 1975b. Grant and B.D. Cargill III. 1975. G. 1970.A. Scripta Met. 1976.C. 1950. Yamada. H.. 1015. 155. Aiben. Phys. New York). Magnetics MAG-13. 24. Eng..R. 292. 933. . 1970.. T. Proc. Chikazumi. H. Phys. 1976. (a) 17. C4-269..O.. Phys. Appl. and D. 109. D.) p. Stat. Materials Sci. Axe. H. 35. K. K. 1975b. 18.L. Phys. and W. IEEE Trans. 1974. Bagley.C.. 22. Chen. 1975.. Proc. Berry. Cargill III. 377--406. Jr. Durand.J. 227281. A. Graham. Grant and B. 369. Stat. Insts. Fujimori. E. A26. Cambridge. 697. Triquet and R. H. Gilman) (American Society for Metals. 502.E. Saito... Giessen) (MIT Press. Graham. Appl.. Kazama. Phys.. 2 (ed. 1976c. 3 (ed.N. Tanner. 1323. and J. T. Hasegawa. R. Phys. T. N. Fiz. 160. Obi and S. Giessen) (MIT Press. Stat. S.J. AIP Conf. 23. 1977. N. 459. Zuckerman. Fujimori. glass and metal technology.C. 1968. Plischke and M. M. E. Proc. J.A. Amer.. J. P. 1969. Proc. Angew. LI9. and F. Gubernatis. 1974.. R. 307. Oxford) pp.M.C.M. B. Chen.J. 34. 1976. R. Sherwood and H. AIP Conf.H. unpublished.. Egami. 211. in Progress in solid state chemistry. Fujimori... Lett.S. M. Phys. B.I. Rev. 1973.AMORPHOUS FERROMAGNETS Davis. R. 1973.J. T. Willens and W. Gubanov. 1975.J. and K.. (Paris) 9. Duwez. vol. N. T. Jr. Phys. Hasegawa. Chim. 5. 1970. 1960.. M. Phys. Phys. Appl. and T. Alper) (Academic Press. Giessen) (Plenum. 34. AIME 227.D. S. Met.) p. T. R. Soc. Jones... 1975.. New York) p. K. P. P. Materials Sci. .. Suryanarayana. 1975b. New York).. Duwez. Flanders. Phys. 218. Kaneyoshi. Proc. Mass. 2. 1976. 3 (ed. P. Ann. Magnetics MAG-11. 1974. M. 362.. Japan. O'Handley.. section 1 (eds.. Arai. Obi. J. Sol. Hasegawa) (Plenum Press. Y. Handrich. H. H. and R. 1976. BS. 1425. Hasegawa) (Plenum Press. Japan. 13. New York) pp. New York) p. Trans. Ray and S. Taylor. K. AIP Conf. New York) p. IEEE Trans.. R. Plischke and M. Tohoku Univ. 298.C. H. 26. 1977. R. Flanders and C. Magnetics MAG-12.C. 323. 29. H.. J. Leamy and J.C. 15. 1976. Kanabe. 705. 1889. Jones. Cambridge. Trans. E-Ni. L.J. T. Kikuchi. Repts. 38. Y. 29. Levy and R. Jr. Harris. Phys. J. Fruchart. US Patent 3 845 805 Nov. P. 24. and R.I. 1975a. Mass. R. Hasegawa. in Developments in the structural chemistry of alloy phases (ed.. Stat. Levy and R. Flanders. and D. Giessen.C. Appl. Duwez. 1972. Tel. Duwez. Masumoto. Sol.J. 527 B. Hannay) (Plenum Press. Egami. Y.. Proc.. in Rapidly quenched metals.J. 1976.S. Willens. Res. Appl. J. Soc. New York) p. A. 1967. Fruchart. Egami.C. N. AIP Conf. Leamy. and P. R. 633. Tsuya. Lett. 8. 1970. 1967. Grant and B. 305. 1969. Obi. H. Zuckerman. H. P. in Metallic glasses (eds. 4096. 1960. 1976b. J.. 1974.. Proc. R. Tver.D. Yung. H. 42A. (Paris) 35. New York) pp. Solid State Phys.D. 1976. 281. 36. 31. Phys. 216. Luborsky. 607. in The use of phase diagrams in ceramic. and C. Metals Park. 1976. Lett. and R.H. Sci. Kavesh.A. P. Kikuchi. Wagner. Flanders and C.A. Phys. A43. J.. 1970. O'Handley and L. Soc. 1976a. R. C4-265.R.A. R. Proc. Appl. Kanematsu.I. in Amorphous magnetism II (eds. (b) 53. 275.C. 63 (in Japanese). Gyorgy.J. Phys. Lett. O'Handley.) p. B. and M.J. Sol. (a) 26. H. Phys. 198. Mendelsohn. T. Fujimori. and T.B.. Ohio 1977) to appear. P.C. in Amorphous magnetism II (eds. 32. Japan 24. and C.H. H. R. 1964. C. Levy and R. Masumoto and H. 1973. Phys. Masumoto.L. K. L.. Willens. S. 1972. R. Phys. 219. Herd. Morita. in Liquid metals (ed. 1136. 1976b. 1973. Klement. 1973. Shirae.. Obi. Foo. 220.. Durand.A. Felsch. 705. Prog. E. 29. Lett. Wu. Reiss) (Pergamon Press. vol. 1966. Dermon. 1973.C. Masumoto and N. P. Gyorgy. Durand. Giessen. Duwez. 407. K17.M. AIP Conf. 31. Rep. 98. Phys. J. Hasegawa. Materials Sci. 29. Graham. W. 1977. Hasegawa) (Plenum Press.E. R. section 1 (eds. IEEE Trans. 627.. J. C 6. K55. 1396. Flanders. 1972. H. and S. Z. Jr. Chaudhari. $. Metals 60. Appl. R.C. 393.J. Phys.. Phys. S. Giessen. 1974. in Treatise on solid state chemistry.. 128. Kavesh. 1977. Ohta. and P. 945. Harris. M. J. Saito. Kameda and T. Y. Phys.. Egami. A. in Rapidly quenched metals. and P. 103-141. Fujimori. Kavesh. 1963. 1976a. Hasegawa. J. AIP Conf. in Amorphous magnetism II (eds.J. 36. Handrich. Masumoto. T. 29. Eng.Z. Beer) (Dekker.. Lin. H. Rev. vol. Hasegawa. H.M. 28..E. Repts. (eds. S. R. J.O. Mendelsohn. IEEE Trans. J. McCary and J.S. 2.. 330. Conf. AIP Conf. Appl.E. Walter. Phys. 206. F. 139. K.J. R. Hasegawa) (Plenum Press.R. Liebermann. IEEE Trans. R. New York) p. Nesbitt and G. 1976. 1977. Passell.. (1) 9. Liquid Metals. 19.. Jap. J. Appl. Soc. 24. 953. Materials Sci.. O'Handley. Luborsky. Pan. 361. R. J. Tohoku University A26. F.C. Ohnuma. 1975. Becker and R. Massenet. Mendelsohn and E. 313. 380. Pasadena. 286. 1969. F. 1965. Vac.M. . 25. Masumoto.A. Magnetics MAG-11. 1975. and J. Mizognchi. J. 1964. N.L. unpublished. 21. Hase- Kikuchi. 1976b. J.L.C. 1976. J. J. 1.. Appl. 1977.E. T.. Bristol. L. IEEE Trans. Axe and L. Phys. IEEE Trans. Magnetics MAG-12. in Rapidly quenched metals.. and J. R. Maringer. Greenwood and J. New York) pp. 1976. Gressen) (MIT Press. 35. Nesbitt.. Sci. 1976. Lett. 1976. Phys. R. Kumar. H.W.D. Stat. R. Levy and R.C. R.C. Phys. M.. R. Giessen) (MIT Press. Kneller) (Academic Press.C. AlP Conf. Nowick.J. in Magnetism and metallurgy (eds. Phys.G. in Rapidly quenched metals. J.D. Fujimori and H. Phys. AlP Conf. Lett.E. 1976..M. 369. F.I. J. 1975. Nagel. 285. Giessen) (MIT Press..E. 1974. 273.C. 11. in Amorphous magnetism II (eds.A. Magnetics MAG-12. Shirane. 1976.E. F. R. 7. 29.. Masumoto.-P. 77. Magnetics MAG. Lett..E. Luborsky.E. Y. Watanabe and T. Levy and R. and J. and J. Kouvel. Obi and T. Metals 21.E. Grant and B. Technol. T. 1977. in Amorphous magnetism II (eds. S. G. H. Masumoto.R. 4996. Maddin.J. section 1 (eds.J.. Mobley and E.R. LeGrand. 35. Cambridge. 379. Solids 20. Proc. Levy and R. 28. H. 469. Sol. Duwez. 942. Int. 529-534. H. F. 467. Stat. T. 1463 (in English) Fran Zavodskaya Lab. O'Handley. Marzweil. 1965. Stubbs. 34. Proc. Hooper and A. Luborsky. 1973) (Nauka. Conf. 1973. Luborsky.I. Appl. 1077. Rev. Insts. and A. Birgenean and H. Ph. Magnetics MAG-12. Luborsky. 57. M. New York) pp. Ray and C. T. Luborsky. section 1 (eds.D. L. Maringer. 1974. Grant and B. Mass. Miyajima. Masumoto. 2 (Moscow Aug. McCary. Phys. Sol. Moss. Lefever.. J. Appl.H. Logan. Y. 14. 1976b.A.A. 1976.. T.E. 1968. O'Handley. K. 3648. Sci. N.N. 29. Graham..L. section 1 (eds. Trans. R. and C. S. 47. 112. 924. 611. 34. T. Vac. S. Mass.. M. 1959. H. R.A. 120. Miroshnichenko. New York) p. S. 1067. 325.V. Luborsky.. 1975. Eng. IEEE Trans.. Nagel. Naka. 1644. Walter and D. AIP Conf.) p. H. Proc.A.G. Saito. R.C. Miyajima. Materials Sci. 1975. 921. DeGraff) (Plenum.H.J. Mizoguchi. N. 209. Berkowitz and E. Japan.528 F. 523-575. J. Eng. Fujimori.E.E. Proc. Lynn. Mizoguchi. 1970.S. Montgomery. de Physique 35. Mader. Luborsky. 1976. Hasegawa) (Plenum Press. Eng.A.. in Rapidly quenched metals. in Amorphous Magnetism II (eds. in Amorphous magnetism (eds. C. Proc. I. Hasegawa) (Plenum Press. 1976a. C. R. Inst.I.I. Appl. Cambridge. Lin. Y. Sinha. Magnetics MAG-13.. Masumoto. Watanabe. Kobe. Tauc.E.A.C.. Res. 1975.S. Mook. Kimura and A..C. and R. J. A. 1973.) p. Chou.C. D. Inoe. Rev. T. 1975. New York) pp. and P. Becker. Proc. 12. 1976. M. Mader. J. D. thesis. Yamauchi and H. 1976. 25. R. Sun. R. 283. 1977a.. Cambridge. 15. Lett. C4-279. F. 5. Daver and J. in Amorphous magnetism II (eds.. vol.W.S.L Walter. Materials Sci. Levy and R. Salli. 1977a. Conf. 345-368. S... Mitera and S. and E. 46. D. N. Series 30. Bretts. 29. IEEE Trans. Geneste. Tauc. Tauc) Inst. California Institute of Technology. Walter. Phys.A. E.I. S. AlP Conf.. (a) 32. Cal. J. 1974. 25. 669. Proc. Phys. Magnetism. Ind. Lett. New York) p. R. Hasegawa. Non-Cryst.. 1976. 34.. F.L. and C. and I. Phys. and A. 1398 (1959). Waseda. and J. Tomizawa. 930. R. K. Krugler and R.) p.E.O.E. Technol. LUBORSKY J..E. O. H. 1976a. O'Handley. 1969. Ind. Smith and R. Phys. 1977b. Phys. Appl. Collings. Mobley. Grant and B. O'Handley. 29. L. 1977. Yamauchi and H. 1977b. Mass. F. Jr.J.O. Moscow). Logan. Chen. Hasegawa) (Plenum Press. F. Luborsky. Mendelsohn. O'Handley.. Obi. Luborsky. Lab. 161. J. 11.M. Giessen) (MIT Press. Luborsky. Magnetics MAG-12.AMORPHOUS FERROMAGNETS gawa. and T. R. 1406. AIP Conf. 557. 1976. Rev. Maringer and C. Stat. 37. Materials Sci. 1974.. 1976. LeGrand and F. Turnbull. Thompson. 1976. 183. thesis. 1974. and K. B13. and D. Grant. Wohlfarth. C. Hasegawa) (Plenum. and N.A. 1966.M. IEEE Trans.L. 473. S. Grant and B. D. Sherwood. 34. 1976. 47. H. Kobayashi and R. 5. Bartram. C. $1A.G..I. Mass. Yamauchi. 239.J. 1963. Luborsky. 1972. Sol. . Parsons. Tsuei. Chen. and E. and J. Instr. 603. J.C. 1972. Phys. G. Simpson.R.C. Grant and B. G. 4156. R. Yamauciii. Rev. 23. Lett. (b) 43.J. E.J. Z. 95. Phys.F.C. 47. vol. Mass. Bacon and F. ASM Fall Precongress Seminar. J.. Polk. Gyorgy. Met.G.L. E. Phys. Appl.. (a) 26. Materials Sci. Ph. Trans. Mag 3. Brambley. (b) 49. and D.O. Trans. Phys. 222. 1958. Sci. 23. Walter.E. 249. S. Stat. 541.. Levy and R. Stat. Cambridge.D. 71. 1974.. Phys. in Rapidly quenched metals.. A.W. Tsuei. K. deGraff) (Plenum. 1545. 685. C. D. 205. 1968.. Phys.C. in Amorphous magnetism (eds. Phys. 1141. 1971..~K. R. Hooper and A.E. 3. P. 164. Ferris. C4--1. Koch and S. M. Tsuei. Shimada. Grant and B. J. Magnetics MAG-11. 1974. Cambridge. 2475. and R. 1975.C. 1969. J. Phys.C.. Jr. Simpson. 34.S. Gakishuin University. C. 1975. Rado and H.L. J. Materials Sci. R. Phys. 745. Arajs. 10... Mass..S. Stat. Eng. Herman. New York) ch. Appl. Soc. A. IEEE Trans. 1975. Simpson. Rev. Phys. Phys. and D. Yamada. Sol. Eng. Clements. D.M.C. Brambley. Proc. 1338. AIP Conf.F.) p. Ozaki.D. H. D. Lin.E. section 1 (eds. F. Ray. Y. A.. Sherwood.W. 1976. 4660. R. Kavesh. Teoh and S. Giessen) (MIT Press. Turnbull. 1977. K. Swift. Shimomura. and W. 1976. and D. Takayama. Pond.G. AIP Conf. 1975. Handrich and J. Mizoguchi.W. H.) p. F. Eng. 1968. 62. Teoh. Scott. Tsuya. Phys.. Slonczewski. Stat. Sol.H. 29. Y. A. and H. Appl. Eng.P. Pietrokowsky. Materials Sci. R. and P. Richter. Leamy. Wright. Sol. Maddin. Japan 39. M. Wiesner.C. 1976.C. N. 291. Revcolevschi. Roberge. P. Phys.. Eng. Mobley.. 435. K. Walt6r. J. Sub_l)(Academic Press. Pan. 121.. W. de Physique 35. and H.. Waseda. Maddin. 1976. Appl. Trans. 1963.. 4899. (b) 68.. Giessen) (MIT Press. 1975. Schreiber. and H. 327. Norman and H. AIME 245.. 1976. 1976. Met.E. Phys. W. Foster. 1975. Yamada and T. N. Masumoto. B22. (a) 31. Shilling. Soc. D. 29. Turnbull.C.J. I (eds. Proc. and 1~ Masumoto.A. N. and R.J. in Magnetism. 1976. Proc. J. Leamy and H. Shiraga. Sol. W. Turnbull. Chen. J.B. 267. 445. Acta Met. R. Cambridge. H. Walter. Tahir-Kheli. 1969. Longworth and S.. Rao.. 1976. Contemp.C. K. and S. 485. N. 3. J. E. Schneider. 441. Shingn. 1975.W. Kojima.H. 1977.G. Y. Phys. Arai.R. 24. New York) p. H. 1976c.J. K. New York) p. Gyorgy. R. J. J. section 1 (eds. N. in Amorphous magnetism II (eds. Spaepen. D. 24.M. Sucksmith and J. section 1 (eds. 45. Met. 1975. P.E. Materials Sci. Tsuei. J. 170. Phil. in Rapidly quenched metals. 8A. in Rapidly 529 quenched metals. 325. 20. 1972. Lilienthal. 1174. K61. J. G. Materials Sci. 65. Duwez.) p. Pond. R. 1973. 1977. 393. 1980 531 . MD 20910 USA Ferromagnetic Materials. 1 Edited by E.chapter 7 MAGNETOSTRICTIVE RARE EARTH-Fe2 COMPOUNDS A. Vol. Wohlfarth © North-Holland Publishing Company.E. CLARK Naval Surface Weapons Center White Oak Laboratory Silver Spring.P. . . . . . Phenomenology of magnetostriction . . . . . . 552 5. Elastic properties of RFe2 compounds . . . . . . . . . . . . . . . . . . . . . 533 2. . . . . . . . . . . . . . . . . . . . . . . . 560 7. . . . . . . . . . . . . . . . . . Magnetic anisotropy of binary RFe2 compounds . . . . . 584 Appendix B: Temperature dependences of magnetostriction and magnetic anisotropy for single-ion models . 587 532 . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetostriction of pseudobinary RFe2 compounds . . . . . . . . . . . . . . 583 Appendix A: Magnetostriction and magnetic anisotropy of cubic and hexagonal crystals . . . . . . . . . . . . . Magnetization and sublattice magnetization of RFe2 compounds . . . . . . . . . . 557 6. . . . . . 576 9. . .CONTENTS 1. . . . . . . 585 References . . . Introduction . . . . Magnetostriction of binary rare earth-iron alloys . . . . . Magnetomechanical coupling of RFe2 compounds . . . . . . . . . . . . . . . . . 540 4. . . . 567 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535 3. 581 10. . . Amorphous RFe2 alloys . . 1963. Elastic moduli were found to be strongly influenced by the unprecedented magnetoelastic interactions. 1963. The cobalt rich R2C017 compounds (R = rare earth) possess Curie temperatures as high as 1200K. by direct compound synthesis and by rapid sputtering into amorphous alloys. Tb and Dy. Rhyne and Legvold 1965). in the heavy rare earth metals. Enormous magnetic anisotropies were also encountered in the heavy rare earth elements. However. a breakthrough in magnetostrictive materials occurred with the measurement of the basal plane magnetostrictions of Tb and Dy at low temperatures (Legvold et al. More importantly. thermal expansions are dominated by the temperature dependences of the magnetostrains.2 for Fe. Co and Fe.1. These basal plane strains are 100 to 10000 times typical magnetostrictions and still remain today the largest known ( ~ 1%).6 for Ni and 2. the parallel coupling of large orbital and large spin angular momenta yielded huge magnetic moments of 9/~s and 10/ze. Clark et al. for example. because of the low ordering temperatures of the rare earths the application of these magnetostrictive properties to devices operating at room temperature could not be achieved with the elements. In contrast to the normal Curie temperature behavior of the Ni and Co compounds. possess lower ordering temperatures and very low room temperature magnetostrictions. In 1963. Ni. the Curie temperatures of the rare earth-iron compounds increase with increasing rare earth concentration. Over wide temperature ranges. dwarfing the conventional values of 0. showed that the spin structures were much more complex than those of any of the classical ferromagnets or antfferromagnets. Both the high concentration of rare earth and the high Curie temperatures of 533 . Neutron diffraction measurements. were combined with the magnetic transition metals. The remaining Co compounds. it was widely recognized that the rare earths possessed many extraordinary magnetic properties. Only Gd. Highly magnetostrictive rare earths. 1965. Introduction By the early 1960's. The highest ordering temperatures are found for the Laves phase RFe2 compounds. plus all the Ni compounds. which are richer in rare earths. and exhibit moderate magnetostrictions at room temperature. In 1971 a search for magnetostrictive materials with high magnetostriction at room temperature was started. which is essentially non-magnetostrictive. possesses a Curie point as high as room temperature. 100 ) is discussed. sublattice magnetization and magnetic anisotropy measurements are presented in sections 4 and 5. For a broad review of the magnetic properties of the rare earth-transition metal alloys. it is important to recognize that there is no linear magnetostriction if the anisotropy is independent of the state of strain of the crystal.534 A. Measurements on single crystals are compared to those on polycrystals. In addition to the conventional static magnetoelastic property (i. Magnetization. which is applicable to the rare earth elements and the rare earth-iron compounds. magnetostriction).8. about two orders of magnitude larger than that of conventional cubic metals.E. This chapter presents an overview of the magnetoelastic properties of the highly magnetostrictive rare earth-Fe2 alloys. the reader is referred to chapters 3 and 4 of this volume and references therein. the crystal deforms spontaneously whenever to do so lowers the anisotropy energy. In section 6 the magnetostrictive properties of pseudobinary Tb-based and Sm-based RFe2 alloys are examined. polycrystals and amorphous rare earth-Fe2 alloys. the existence of magnetic anisotropy itself may be a hindrance to the technical usefulness of a magnetostrictive material.e. The effects of the strong magnetoelastic coupling on sound velocities and elastic moduli are reported in sections 7 and 8. Extraordinarily large AE effects and changes in sound velocity are observed in single crystals. both static and dynamic can be dominated by magnetoelastic effects. First. The role of intrinsic (intradomain) as well as extrinsic (domain wall induced) effects are discussed. TbFe2 possesses an anisotropy energy > 107 ergs/cm 3 and an anisotropy field > 100 kOe. Finally.~2Fe2. The expressions for the magnetostriction up to sixth order in the direction cosines of the magnetization are given in Appendix A.lll ~ )i. elastic phenomena. In fact. Elastic constants in single crystal RFe2 compounds are modified by as much as 60% by the strong magnetoelastic interaction. The objective of this chapter is to focus on the magnetostrictive RFe2 alloys. The magnetostriction of single crystal and polycrystal RFe2 compounds are compared to other magnetostrictive materials at room temperature. the degeneracy between shear waves is removed by the magnetoelastic coupling producing two shear modes whose moduli differ by 30%.Dy0. In section 3 the magnetostriction of binary rare earth-iron alloys is presented. A possible source of a startling magnetostriction anisotropy ()i. recent measurements of linear and volume magnetostriction on the amorphous form of the RFe2 alloys are presented. Non-crystalline TbxFel-x (x -.l) 3 alloys also possess comparatively high Curie temperatures and large room temperature magnetostrictions. In effect. Magnetic anisotropy plays an important role in magnetostrictive materials. In section 2 a general treatment of magnetostriction is given for the cases of hexagonal and cubic symmetry. In polycrystal and amorphous alloys. Large fields may be required to attain the large magnetostriction. in section 9. In Sm0. Low signal linear transduction properties of certain highly magnetostrictive materials are given in section 8. CLARK these compounds are responsible for huge room temperature magnetostrictions in TbFe2 and in SmFe2. the high symmetry of cubic and isotropic samples is clearly broken. . On the other hand. (2. and by An1 the change in length along [111] when the magnetization is along [111].31]. has the form Al[l = hl(~2fl2+ O~2 y/~ 2 y "3F~ z2 # ~ -2 +h4(a4~2+ 4 2 J) 2 4 2 + 2hs(otxaya2flxfly+ ayOt~a2/3y/3z+ o t ~ a ~ a 2 ~ ) + h38 [ o r h3(s . The polynomials which keep the crystal symmetry intact are identified by a. the magnetostrictive strain reduces to All! = ~2A./3i the direction cosines of the measurement direction with respect 2 2 2 2 2 2 to the crystal axes.1) Here ai denote the direction cosines of the magnetization with respect to the crystal axes. These polynomials are listed in table 1 (Bell 1954). RzT~7 and to many of the rare earth elements. The total energy must be invariant under the symmetry operations of the crystal lattice. Letting K ~'~ denote the anisotropy constants and S ''t. the symmetry polynomials . A commonly accepted expression. i. Ea. The crystal therefore deforms to minimize the total energy. the anisotropy energy.~) (2. In the following.4) E0 denotes the part of the magnetic energy which is independent of magnetization direction. utilizing five constants. can be expressed in terms of polynomials of the direction cosines which transform according to the fully symmetric representation of the crystal. including the R T z and R6Tz3 rare earth (R) transition metal (T) compounds.3alll(O~xOty#x~y 4" OtyOtz~y~z "Jr"OtzOtx~z~x). the general form of the magnetostriction for both cubic and hcp systems is derived.oo(a2/32+ a2/32 + a2/32 -13) "{. the cubic or hexagonal harmonics.3) where 0 denotes the angle between the magnetization and the measurement direction. and s = o~jd~y-t-ayO~zq-azOlx • Frequently the magnetostriction is empirically fitted by the two lowest order terms. The hexagonal expressions apply to RT3. Denoting by Aloothe change in length along [100] when the magnetization is also in that direction. The cubic expressions are appropriate for many metals.2) In the special case of an isotropic body (whether polycrystal or amorphous) AI/I = ]As(cos2 0 . Phenomenology of magnetostriction Akulov (1928) and Becker and D6ring (1939) developed simple expressions to describe the magnetostriction of cubic crystals.e. (2.MAGNETOSTRICTIVE RARE EARTH-Fe2COMPOUNDS 535 2. The linear magnetostriction described here originates because the magnetic anisotropy energy depends upon strain. It can conveniently be written E =Eo+Sa+Eme+Eeb (2. lOa. S~'4 ' . The subscript denotes the components of the same irreducible representation.a2~ .O 2 Otz a x2+ O t y + 2 = 1 a 2. + a 2r+ a2. This term.6' S~.. / 2 10 2) .a~ .:. 2 .6 ' S~ t'6 _a~_a 15 4_ a 6 __H (aX_ 2 .2 S ~ '2 ~(2a~.a2)a~a.5b) The magnetoelastic energy.. 4 .a.0/2)) a 4 ~ I ¢~" 7t a x . 2 ~(0/z(Ot X -..6 S~.to 2 2 (O/x~t'O~y 3£11~XOty)O/xO/y S~.6' S~ '6' (5a**. = X K ~.~(Ot x -.7) (.-a~-a~ 6 15 4 _ a y )2 ) _ ~ ( 25 a 2 S ~'6 2) Sa.~ )I ( O / X2. ) .-.a~) OtyOtz S~.3 _ 7 ( 2 a z _2a ~3(a~__ 2 s~.a ~)) 8~.E.4' a ~ a x o t y ... I To lowest degree in ai Ea]cubic = K " a 4 ( a x4+ a y +4a 4 .6 .~ ." (.~ 'O~xOty 8~.~.~ t ) o t z a x ( a z4 --H( az-~ .4 S [ '4 S~ '4 eGOtx a~oty 4 6 2 I I J 2 2 2 . 3x ..lS~.x -. ) ..~(a 5 .~.a~3 . )-?~ / 4.)(~.6 S~. I n the cubic system the symmetry strain components fall into the three irreducible representations given in table 2 and designated by a.5 5.-ay)) S~.. the strain components consist of two fully symmetric components. Thus taking the direct product of the symmetry strains and the direction .a~.7h a~-i~ ( a * ~ ..Olz illOlZ2 .z 2 __ ]6~ ( a 2 1 __ 2~)O. (2.a y 6 o t6 x .a4 ~ ST'2 S ~ '2 ' Ot 2 z --~ I 2~(a~ O~x~y a 2) 4 3 6 2 -~(2a..6 S~. . 2 a2~.~.-~(2a.2 S ~'2 (X/]/2)(a 2..a x .a D . C L A R K TABLE 1 Basis functions for cubic and hexagonal lattices (taken from Bell 1954) Cubic Hexagonal S a'O Sa.~'a~a~ a~aya~+22(a~+a~+a~.Y f.1 ~(az H ) ( a x4 2 2 2 ± 4 2a~-a~-a.~).l.1 5 a x~ a y 2 + 1 5 O t2x a y ~(aZ ' f ( O t2 Z--~ 1 4 --]6 I ) .Of2 y)) 1 2y 2 + a ~ ) 4(0f4 x . 2 2 2 2 2 2 or (2.5a) = K.a S~' S~ "4 4 4 6 2 2 V~((a~-ay)-7(a. designated by a 1 and a2.' S~'4 S~. arises from the strain dependence of the anisotrop3~ energy and for small strains takes the f o r m : Emo ~ E f ( a ) .?*(a 2 ~ .t.2~)OlzOly I.ll(Ot z ! 2..~D.4 azax axot v 4 4 2 a ~ . E . a2a.6' 4 6__ 2 1 2 a y2 + a~. = 1 ST.4 a~a~a~-.) a y a.~ a' x a y s~.Ot 2) (Or z .6otx ( a x4 -H(c 6t x . must be a direct product of strain components and direction cosine polynomials which transform according to the s a m e symmetry representation (Callen and Callen 1963).O/y) -.. Emo.a~' -~a..(axay + ayaz + azax) + constant and E.a 2) S~ '2 S~ "2 Sa.-~:~. y.) 4 .~2 - S~..-a~-a~) S | '2 S~ '2 8~.~. S~ "~ S ~ '6 .6 S~. in order to possess the correct transformation properties of the crystal.2 2+a4)a.536 A.3h~ . and e. In the hexagonal system.6 S[" S {.6..ZaX (O/y y __ if) (or2_ ~ ~( fX2 __ 7) I __ ~l)O~xOty t ( O l4 y+Olz_ l y ~ z2 ) O l2 y~z 4_ T OtO 4 .~.6a. and two 2-dimensional representations y and e. .K ~'2(~ 2 .I0. e .~.Be'l(~z. 2 + b 3(2( (2.~ .b~o = bo(e.x + e . .MAGNETOSTRICTIVE RARE EARTH-Fe~ COMPOUNDS TABLE 2 Symmetry strain components for cubic and hexagonal lattices Cubic Hexagonal 537 e~ e/' ~ + E~.'(-1 .IS °.7a) + B ~'~((e= .ol~.t 2 ) -. .i t.~. 1. Note: eT = ½(ex~.z 6xx + ~. i .x + e.7b) E.~. I n a s i m i l a r f a s h i o n ..) e~ e~y e~ e= * In this table the strains are defined by A x = e. E~. i.y+ ~zz ½(2~ .e y y ) S ~.(E= + ~ .~z.y) ] Em~lh~x = Z [B~1J(E= + eyy + ¢zz)S a't + B~z'~(2E= . I i i In terms of the conventional cartesian strains Eme]cubic ~l [ ( B a ' l s a ' l . ) if the strains were defined by .B Y ' l ( . c o s i n e p o l y n o m i a l s .' + B'.xSel'l + eyzS~'l)]. ~ ( ~ .y + e~zz..E= . Or for 1 =0.l . "I l i i (2.6a) (2.~ -'v ~/r3-3"' + (B°.2 (2.6b) Emeihex = • [B'~1'I6'~lS"J + B~'z'I~"2S'~'I + B v't 2 eTSV.. I + (B'~.8a) Em&o~ = b.o .I.8b) The relationships between the conventional magnetoelastic constants (Kittel 1949) a n d t h e s y m m e t r y c o n s t a n t s a r e g i v e n in t a b l e 3. t h e e l a s t i c e n e r g y . ) S ~'t I (2.:Ix = e.. t a k e s t h e f o l l o w i n g f o r m in t e r m s ..a + B ~ t'S 'i)ez~ ' + B"l(S'¢%yz + S['l¢= + S~'%.o. ) + b ~ = + b .'S°.=x + ½ex~y + ~e.~ + ~ . ) + b22(a~ -~)~= 1 a 2x--Cty)(Er~--~yy)+Ot~OtyE~y)+b4(otzOtxEzx+OtyCtz~yz).~ .~ ) ~ 1 e. + ezz) + b l ( a 2 e = + a~eyy + a 2ezz) + b2(otxayExy + otyotzEyz + OtzOtxEzx) (2.y + %z ½(2~ .¢ .t I + ExyS ~. Eme b e c o m e s Eme[cubic = ~ [ B ~ ' t e ~ S ~'t + B ~'l ~ e ~ S ~ / + B "J ~ e . "l + B "~ X ei.3b(e. 538 of symmetry strains A. T r a n s f o r m i n g to t h e c a r t e s i a n s t r a i n s Eellcubi c = 2Cll(exx 1 2 + 2 dr"e2z) + eyy Cl2(eyy4[zz -[-ezzexx + (2.t'fa2"~2J + ½c' ( ( e 0 2 + (e20 2) + 21c'((e0 2 + (el)2).10b) The relationships between the symmetry constants and the conventional elastic c o n s t a n t s a r e g i v e n i n t a b l e 3. ~£1[ 1 + lea2 22~.½ B "2 | a I a Ct3 = C~t + ~C l2-. ~ . T h e m a g n e t o s t r i c t i o n .~ = O.~C22 C44= C~ bit = B ' t ' ° . (2.[fa 1~2.b l O t 2 [ ( C l l .t'~a 1' °~2~Jt.bo[(Cll + 2c12) + c1261](c11 + 2c12)(c11 .c12) (2. alll.9a) Eellhex = 21CatI~. For the cubic case I ~ q = .10a) 2 + ~yz 2 + e~) + i 2c~(exr E~llh~x = 1 2 + e~y) + c l 2 ~ .12) ~q = .11) w h e r e t h e e~q a r e t h e e q u i l i b r i u m s t r a i n s d e t e r m i n e d f r o m 8E/~e.E.+ t.~a121..b2a~a~[ c 44.2'° c33 = c~t + 2c~2+ c~2 bl = ]B' b2 = B "2 b12 = B "''°+ 2B °2'° b21 = B ~''2 .13a) TABLE 3 Relation between symmetry and cartesian elastic constants and magnetoelastic constants Cubic c . is d e t e r m i n e d i n t h e c o n v e n t i o n a l w a y f r o m t h e d e f i n i t i o n ( K i t t e l 1949) alll = X ~i~/3~/3~ ~q (2. (2.=c~. ~ = ) 2clj(e.2 b4 = B ~'2 .el2) . + 2c33ezz 1 2 + Cl3(e=e= + ~ . = c ° +c • ct2=c~'--~c "y Hexagonal c.B ~2'2 b22= B ~2'2+ 2B "2~ b3 = B y.9b) exx~yy) (2.CzE)e2y.[ I/ + ( 1 [ ~ ) 2 + ( ~ ) 2) (2.~ 1 2 + 2c44(ey~ + e 2 ) + I(cH . CLARK Eel]cubic-'~'12Ca(Ea)2+12C'r((l[p2+(~92) + 2 lc~tt ~X2 ~.-c~2+~c~2+c ~' I a ct2=C~1--c12+'~C22 __Cy c44 = c' bo = B ~ .B . 14b) A ~'2 = (2621c13 ..b22(c11 + c i 2 ) ) / O X ~.(__ b21c33 + b22cl3)/D (2. T h e s y m m e t r y m o d e s are d e p i c t e d in fig.A a1'2(0~ 2 .bl2(Cll + c12))ID a 1.3] 21 2 2 2 2 _ 2o2 1-1 + 3AIIl(OtxOtyflxfly + OlyOgzfly~z + azOlxflzflx) (2.~ =2_ ct 2)(/3x2 _/32) + 2axay/3d3y] + 2A~'2[Olyazfly~z + OtzOtx~zflx] where A ~ 1.13)(~2 + ]~2) -. t h e r e is no m a g n e t o s t r i c t i v e c o n t r i b u t i o n to the a n i s o t r o p y . 1. ) F o r a c u b i c s y s t e m .(ctt + c12)b22)(ot 2 z .2 b l / 3 ( C H . the p r e s e n c e of m a g n e t o e l a s t i c i t y gives rise to a c o n t r i b u t i o n to the a n i s o t r o p y not included in E.C12) ~III and = -b2/3c44 Al/l[h~x = A ~"°(/32 +/32) + A a2.b40tyaz eq _ - 21(CH. Substituting e~q and .2 ~__.cl2) = 2cl3bH .a ~) e ~ = .Cl2) 539 eq -bltc33+bi2c13 ( .MAGNETOSTRICTIVE RARE EARTH-Fe2 COMPOUNDS F o r the h e x a g o n a l case 2 .13) _ - .F ~ a2'2(0[ 2 . (2.Cl2) ey~ -- c44 e= -- b40tzOtx c44 (2.0~ 2 d.(cH + C12)b12 F (2cl3b21 .11). the m a g n e t o s t r i c t i o n affects the l o w e s t o r d e r a n i s o t r o p y e x p r e s s i o n .C12) A loo = .baaxa~ eq __ -.bHc33 + b~2c~3 F ( .b 12c33 + b22c 13)(~ z D D 2 ( C l l . E x p r e s s i o n s f o r the m a g n e t o striction up to a ~ are g i v e n in A p p e n d i x A.13) _ b 3 ( a ~ .13)]32 + A "2d'^t2~.1 ) + b3(ot2x-ct~) eYY = ~ ~ D D F D D 2(c11 .2c~3.14a) where = -3bo[(Cl~ + ct2) + 3cl2bl/(cH + 2Cl~)(Cll -. W h e n the c r y s t a l s are f r e e to strain u n d e r m a g n e t i z a t i o n r o t a t i o n ( c o n s t a n t e x t e r n a l stress)..13b) w h e r e D = c33(cH + cl2) .0 = (bllc33 + b 12C13)1D A ~2'° = ( 2 b l l c 1 3 .. ( F o r a c l a m p e d lattice.b 1 2 c 3 3 + b 2 2 c t 3 ) ( o t 2 . Substituting t h e s e e x p r e s s i o n s into eq.2 = _ b412c44. w e find to s e c o n d d e g r e e in a~ Alll[cubic = A" + 2Al00(otx/3x + Otyfly + t t z p z .2 __ _ b 3 1 ( c l l cl2) A ~. Because of this. were investigated. The addition of Ni. Co and Fe to the rare earths produces compounds and amorphous alloys which in some cases have higher Curie temperatures than the elements. Tm. Er. I.b~]2c~.tll 1 F 1~ CUBIC HEXAGONAL Fig. Tb and Dy.13a) into eqs. The magnetostriction and anisotropy of the rare earths. Dy. 3. the magnetically induced strains overwhelm the conventional thermal expansion of the crystal axes (fig. in agreement with Stevens' equivalent operator calculations (Tsuya et al. 1965). 1964). and for Tb and Dy. and in others.15) where K [ = K1 + b2](cll -. however. where R = Sm.C12)-. Clark et al. (2. All of the magnetostrictive rare earths possess ordering temperatures below room temperature. only a small paramagnetic magnetostriction (A ~ H 2) exists at room temperature. much lower ones (see Taylor . Magnetostriction of binary rare earth-iron alloys The heavy rare earth elements. the intrinsic magnetostrictions ()t ~'2 (0 K)) are almost identical to each other. are huge only at cryogenic temperatures. CLARK I 1. Magnetostrictionmodes for cubic and hexagonalsymmetries.5~ A. the total energy at constant stress (~r) becomes E ~ = Eo + K ~ ( o . alloys of the type RxT~-x. 11oo t ~. Ho. ~ + ~ + ~2~2) (2..10a).' ___ tk_JJ F. Tb. To achieve highly magnetostrictive materials at room temperature. even for Tb and Dy. 2).E. e[q from eq.4. These large magnetostrictions are a direct consequence of the huge strain dependence of the magnetic anisotropy.8a) and (2. (2. Co and Fe. and T = Ni. In the hexagonal system. the lowest order anisotropy constant is not affected by the magnetostriction. J is a good quantum number. In the heavy rare earth metals. Below their ordering temperatures. display the largest known magnetostrictions (Rhyne and Legvold 1965. i . . Rhyne 1978). .~ (d) 320 380 TEMPERATURE(°K) {c) TEMPERATURE I~ Fig.6 ~ x 0.4 -0~ . .O ~ H = 7 200 OE Ola! -21 . in which the most Fe rich compound (R2Fe. taken from Rhyneand Legvold 1965). .9 -6.0. . m ! h' IM '~o . In fact.4 × i.0.~ ~0 J 3. . . I d'.4 -7. .~.2. i . . some of which are higher than their crystalline counterparts (most Co alloys) and some of which are lower (most Fe . .. Magnetostrictionof dysprosiumand terbium single crystals(Dy. The RxFel-x compounds have an anomalous Curie temperature dependence on composition x.9 0. .6 kOE (lla) DYSPROSIUM -!.2 2.2 . I ' I ' TERBIUM ' -I. . . 4.. 1971.4 %ze 2 .MAGNETOSTRICTIVE RARE EARTH-Fe~ COMPOUNDS i . . . .4 -0. i .. .4. i . I .4 O A o-s. . i i i . 200 . i i . i . .4 <>c-Am a-. Amorphous rare earth transition metal alloys produced both by rapid sputtering and evaporation techniques also possess a wide range of ordering temperatures. i .2 0 -0. . .11 2. 1965.:o 1. i .o -6. .6 kOF 411 // J y -U 41. 3.rT I . i r i .4 0 . i . I .ci I . i . 120 140 160 180 T(~lO ll) ~" .7) possesses the lowest Tc and the least iron rich (RFe2) possesses the highest. IO T.' 100 . TERBIUM ~ P ~ ." 90 1O0 120 140 160 IM 200 220 240 260 290 T (oK} m) 3. . I . i .6 < "" 0. . I . taken from Clark et al. . a . . -4.II ~ 1. . i • i . Tb.40 260 "1*0/IT. 220 2. ._.6 _ H= 13. I . all the Ni compounds have Curie temperatures below 200 K. i i i i ..6 2. i 541 . H= 10. i . . The Curie temperatures of the Co compounds span a wide range from the high Tc of 1200 K for Tb2Col7 to near 0 K for Er3Co. 2.A io 12o'1~o ~o ~ m ~ ~o* ° ... i . Also Naval Surs~Clark et al.sFeo.E. i) A. d~ S. ](. T h e f i r s t c o m p o u n d o b s e r v e d t o e x h i b i t a l a r g e m a g n e t o s t r i c t i o n ( ~ 2 x 10 -3) a t r o o m t e m p e r a t u r e w a s T b F e 2 ( C l a r k a n d B e l s o n 1972). I n v i e w o f t h i s .123 . f) See: Ferrites by Smit and Wijn (1959).62 .A~) at some large field (see references below).4Fe L6 T b C o o . J) Sato et ai. A.69 . t h e R~T~_~ a l l o y s w i t h t h e g r e a t e s t p o t e n t i a l t o a c h i e v e large room temperature magnetostrictions a r e t h e c u b i c L a v e s p h a s e R Fe2 compounds with R = Tb and Dy. denotes ~(AII-AI) at V.A~) at 14 kOe.1560 39 h h h m TbFe2(amorphous) DyFeq DyFe2(amorphous) HoFe2 ErFeq TmFe2 SmFe3 TbFe3 DyFe3 HoFe3 ErFe3 TmFe3 Ho6Fe23 Er6Fe23 Tn'hFe23 Sm2Fe~7 Tb2FerT(as cast) Tb2Fex7 DyzFel7 Ho2Fe. (1963b).211 693 352 57 . Abbundi.43 58 .E. m~Abbundi and Clark (1978). Williams (1932).7 Er2Fel~ Tm2Fe~ k h h k i h h m m m m m m m m m m m m m m m m * For the rare earth compounds. 25 kOe.36 .o4(Coo.26 .6 10~A.A. . unpublished. h~Clark (1974). Here A.[ 70 W t % Tb~ 30 Wt % F e J YFe2 SmFe2 GdFe2 d e f f f g h h h i i i i i j h 1590 1. c~Well and Reichel (1954). CLARK a l l o y s ) .5) 85 W t % Tb't 15 W t % Fe. (1976).and TABLE 4 Magnetostriction of some polycrystalline materials at room temperature* Material Ni Co Fe 60% Co 40% Fe 60% Ni 40% Fe NiFe204 Co2Fe20~ Fe304 Y3FesOn Tb2Ni17 106A.33 . ~ Koon et al. unpublished.2 . T h i s c o m p o u n d p o s s e s s e s the largest room temperature magnetostriction known to date. Miller. 4 F e i.4 65 80 336 207 73 28 95 539 Reference a b c Material TbFe2 TbNi0.110 40 .29 Reference h k YCo3 TbCo3 Y:Co17 Pr2Co~7 Tb2Coj7 Dy2Co17 Er2Com7 Tbo.9 68 25 . 1753 1151 1487 308 433 38 80 .q.25 -63 131 . denotes b) Yamamoto and Miyasawa (i965).106 . Clark and R.R. . In table 4 are gathered the room temperature magnetostrictions of some typical ferro. k~A.542 A.299 .E. A. Here A.4 0. (1974).14 -60 .55 .q . face Weapons Center TR78-88. ~)Went (1951).A~) at 25 kOe. denotes ~(Atl. e~Masiyama (1931).7 . Dahlgren. denotes ~(. < 1500 lbFe 2 OyFe2 HoFe2 lOOO ErFe2 Tm Fo2 ~r-~ 500 0 5 10 15 H(kOe) 20 25 Fig. T b . TbFe2 and SmFe2 possess the largest strains by far and are the basis of the multicomponent systems of sections 6. some rare earth--cobalt compounds and some rare earth-iron compounds. for TbFe2. ErFe2 and TmFe2 taken from Clark 1974. Thus the large magnetostriction does not fall appreciably from its low temperature value.A± = ~)ts. 1974). Contrary to expectations. where the magnetostriction of Tb and Dy are similar.~4 " . HoFe2 taken from Koon et al. Here All. In both of these compounds the rare earth ion is highly anisotropic ( S m .2 0 0 0 × 10-6. 5 and 6 the magnetostrictions of the rare earth-iron compounds are plotted vs.most prolate in form. For SmFe2. Room temperature magnetostriction of rare earth-Fe2 polycrystals (SmFe2. TbFe2. large magnetostrictions are also found in some RFe3 and R2Co17 compounds. which keeps the rare earth sublattice magnetization nearly intact at room temperature. .m o s t oblate in form) and the rare earth-iron exchange is large. 7. 4. All-A± > 2000 × 10-6. For isotropic polycrystals All. the magnetostriction of DyFe2 is much smaller than that of TbFe2 and exhibits a I I I 2500 SmFe2 2000 n~ SmFO2 kjl-k i ÷ ÷ + % . and 8. All-)t±< . DyFe2.MAGNETOSTRICTIVE RARE EARTH-Fe2 COMPOUNDS 543 ferrimagnets. DyFe2 possesses a much smaller magnetostriction than TbFe2. While the RFe2 compounds TbFe2 and SmFe2 possess the largest room temperature magnetostrictions. 3. 3.)~ denotes the fractional change in length as an applied field is rotated from perpendicular to parallel to the measurement direction. Unlike the elements. In figs. applied field. the .Fe2<l-x>Co2~ for x <0. In fig. Because of this. This is indicative of a very large magnetocrystalline anisotropy. ~>)t~00at room temperature (Clark 1974). 3). TbFe2. As will be shown in section 5. 1971).. it lies parallel to [100] (see section 4). Similar field dependences were found below room temperature in polycrystalline TbFe2 and DyFe2 (Clark and Belson 1972) and in polycrystalline DyFe2._ H0Fes TmFe30 § 10 15 20 25 30 H(k0e) Fig. the effect of replacing Fe by Co in TbFe2 is illustrated. the absence of a large magnetostriction at low fields for DyFe2 and HoFe: leads to the conjecture that AI. 1 A.<-~ '___ sOO ey r~3- 400.E. HoFe2 and ErFe2 (Koon et al. ErFe2 and TmFe2. the magnetostrictions of the remaining RFe2 compounds display rather well defined knees. the magnetization lies along the [111] whereas for the DyFe2 and HoFe2 compounds. The magnetostriction of the Sm. directly reflecting the large AH~.5. Tb. Since the Curie temperature does not fall appreciably in Tb. slow increase with magnetic field (fig... the anisotropy is indeed large at room temperature. While the magnetostrictions of DyFe2 and HoFe: are far from saturation at room temperature with laboratory fields. 4. 7. ! 3OO 2OO SmFes IO0 0 Er Fez . C L A R K I i I I 1oo0 900 60o TOO "x riFe3 Sm Fes Tb Fes Dy Fes Ho Fe3 Er Fes Tin Pes XH-X± + + __- 600 + - . Er and Tm compounds is large at low fields.. R o o m temperature magnetostriction of rare earth-Fe3 polycrystals (taken f r o m Abbundi and Clark 1978). The increasing magnetostriction with increasing field in the case of polycry~talline DyFe2 and HoFe2 is attributed to the sensing of a large AIH as the magnetic moments in the crystallites are rotated away from their easy [100] axes.544 11ooj . In the compounds SmFe2. DyFe2. 1979). Abbundi et al.6 6 × 10 -6 (Clark et al. Room temperature magnetostriction of R6Fe23 polycrystals (taken from Abbundi and Clark 1978). Czochralski and induction zoning methods (McMasters. Koon. HoFe2. ~ °tmF-e. IAm/A ~001 >> 1.1 I + I -- 6OO ~__ -" 5oo 4O0 / t "" . Williams and Koon 1975. for DyFe2. 1976. A~00= . 1978. ErFe2 and TmFe2 at room temperature. In these crystals [111] is the easy magnetization direction. AI00= 4 x 10 -6 and for HoFe2. unpublished. Strain gage measurements by Belov et al. unpublished.o--o o o o o ~ :. Room temperature field dependences of A~00are shown in fig. The compounds DyFe: and HoFe2. is uncommon.MAGNETOSTRICTIVE RARE EARTH-Fe2 COMPOUNDS 1000 I I I I I 545 900 800 7OO ~'r'~ R6 Fe. This may be due to preferred orientation of their polycrystalline samples. In these materials therefore Ai00. olblfl~ oErlFe ~ 30 I 6 I 10 I 15 ~kOe) I 20 I 25 Fig. (1975) show a more rapid decrease in magnetostriction with increasing Co concentration. on the other hand. 9. relative magnetostriction. Milstein 1976). 8. In fig. possess [100] as the easy magnetization axis.o----o----o •-o--.:. ErFe2 and TmFe2 have been prepared by Bridgman. as measured by the distortion of the cubic cell (Dwight and Kimball 1974) remains almost constant over this concentration range..n F'e23~. is sensed at technical saturation. Single crystals of TbFe:.59 to . values of/~111 a r e shown for TbFe2.ll" ~. It reveals the immense importance of grain orientation in achieving high magnetostriction in .r. 5. Such a highly anisotropic magnetostriction ratio. Tb6Fe23 and Dy6Fe23 are not completely single phase.. TII~ Fe23 I 300200 ~ Dyl Fez3 100 . In remarkable contrast to the large values of Am for TbFe2 and ErFe2. rather than Am. With the exception of Tb2Fe~7(as cast).2 00~- ROOM I I t I I 0.E._x)Coz~ (taken from • Dwight and Kimball 1974. .6 t 1 . 7.<~1001 . Room temperature magnetostriction of R2Fet7 polycrystals (taken from Abbundi and Clark 1978)..o. all samples were heat treated at 1000°C. -0 5 10 ~_ U~- "" "".546 A. 1975). 6.. "-o.O ~r~ x To~ Fig. Tb2Fet7and Dy2Fe17contain both rhombohedral and hexagonal phases. CLARK 200 180 160 140 ~* 120 x . . and O Belov et al.<~ t i + (as cast) I I Tb2 Felt Dy2 Felt H02 Felt Er2 Felt Trn2Fe17 _ / m Fel~ Er 2 60 40 15 20 25 30 H(kOe) Fig.4 o .. Curie temperature and relative magnetostriction of TbFez. a preferentially oriented polycrystal possesses the major advantage of far lower internal losses at grain boundaries.~__.<: 0 ~x. 9. 5O0 : I 5 I 10 J 15 H (kOe) i 20 I 25 Fig. As -. A m > 0..¢-. 8. in an isotropic polycrystal.-o----0-60 I I -c I -o--------o H o Fe 2 ] I -40 'x -20 . As --~0. In addition to the increase in magnetostriction constant. and in a poorly textured polycrystal.~. As.6Am.. 1975. Clark and Koon. -60 ¢. unpublished).. In an optimally oriented polycrystal. This is important in applications where a high magnetostriction at low applied fields is required... Am(T) of TbFe2 and Al00(T) of DyFe2 are contrasted (Clark et al.seo X -- 1. Room temperature magnetostriction (A~00) for single crystal DyFe2 and HoFe: (taken from Abbundi..0..5OO I' I I I I 547 2. Abbundi and Clark 1978). Room temperature magnetostriction I•lll[ for single crystal TbFe2. ErFe2 and TmFe2 (taken from Clark et al. A. Am < 0. polycrystal RFe2 materials.o___o 20~ 5 I 10 I 15 H(kOe) 1 20 I 25 I 30 Fig. In fig.{X)O _ _ TmFe2\ ErFe2~ .000 z. The effect of crystallite orientation can be two-fold beneficial. --~Am.. for ErFe2 and TmFe2.. 10. .MAGNETOSTRICTIVE RARE EARTH-Fez COMPOUNDS 2. For TbFe2. the rapid rise of [Am[ with decreasing temperature to a value approaching that of TbFe2 at 4 K is illustrated. the magnetostriction changes by a factor of 15. . however. . (1979). 1977). TmFez possesses a comparatively small magnetostriction at room temperature. At00(T) is small for DyFe2 and cannot be fit by a simple single-ion function. C L A R K ' ' ' ' I . . . Am(0) = 4400 x 10-6 for TbFe2 the largest known value for a cubic material. A fit to the data with single-ion theory (section 4) is excellent. The magnetostriction monotonically decreases with increasing temperature according to the single-ion temperature dependence (Callen and Callen 1963) (see section 4). I ^ . . The dip in the observed magnetostriction of TmFe2 at 235 K is a consequence of the cancellation of sublattice magnetizations at its compensation temperature. Am(T) is well behaved.E. See Abbundi et al. Temperaturedependenceof the magnetostrictionfor singlecrystal TbFe2and DyFe2(taken from Clark et al. This. .160 -201] 0 100 r (°K) 200 300 Fig.45 x 106]. t 4000 ~e Tb Fez 3000 Xlll O) 2000 40" 0 -40 g -80 -120 . On the other hand. This is also true for HoFe2 where IAl001is much larger [Aj00(0) = -7.548 5000 A. reflects the weak Tm-Fe exchange and low room temperature Tm magnetization. 1977). In fig. The forced magnetostriction is observed to change sign at this temperature as the Tm moment rotates from parallel to the applied field direction for T < Tcomp to antiparallel to the applied field direction for T > Tcomp. where the moments lie perpendicular to the applied field direction. 11. . 10. rather than a small intrinsic magnetoelastic coupling. At absolute zero. Over this range. '%. However. • • * e e i -2000 o • o o e • • o ° e e o • e • w • • ~:__ . .. . 12. A _1 I I I I 1_ -IOOO H 5kOe • • e i • 4 e o o o • e e e e • . taken from Rosen et al.. 11.. Magnetostriction of SmFe2 (taken from Rosen et al. • -3000 z ~ IE -4m -5OO0 I. an analysis of the temperature dependence is difficult because of a low lying J = 7 multiplet.. (1974). 12 the magnetostriction of polycrystal SmFe2. . 200 I i |I t i 300 I t T(K) Fig. 50 I 100 t 150 TEMPERATURE t 200 leK) I 250 300 Fig. .TmFe 2 . i i ' I ' ' ' ' I ~ ' ' ' I ' .-~" ( m R l ] 00 100 I . No single crystal measurements have yet been reported. Magnetostriction (A~H) of single crystal TmFe2 (taken from Abbundi and Clark 1978). -3200 \ \ x " ~ EXTRAPOLATED" -24OO >< \ T(K) -1600 -8O0 \o...MAGNETOSTRICTIVE RARE EARTH-Fe2 COMPOUNDS 549 -4000 . In fig. 1974).. .~|5/2 [. b2. . A large magnetoelastic coupling. The magnetoelastic coupling indeed is high. is plotted as a function of temperature. is also inferred for SmFe2. causes an extension of the A-B bond. the magnetization is directed along [111]. arising from the asymmetry of the rare earth 4f electron shell. CLARK broad peak in I)q . . The oblate 4f electron cloud (-e) lies perpendicular to the magnetization axis.. are effectively shorted out because of the high tetrahedral (43m) symmetry at the rare earth sites.. An atomic model for the anisotropic magnetostriction based upon the structure of the cubic Laves phase C15 compounds was proposed by Clark et al. ErFe2 and TmFe2.E. Considering only the electrostatic coulomb interaction.. the closer proximity of the 4f electron cloud on A to atoms B'.l's are allowed because two inequivalent tetrahedral sites exist in the C 15 structure which permit internal distortions along [111] directions. A~ml signifies the fractional change in length along the [111] direction when the material is magnetized along this direction. 13a. (b) MJI[100]. (1976) and Cullen and Clark (1977).e A B~ -e B' (a) (b) Fig.. In fig.. 0 and 14. The two inequivalent sites. potentially huge values of . 13. situated at 0. the distortion is illustrated for TbFe2 and other RFe2 compounds containing rare earths with oblate 4f charge distributions. 13. Model of magnetostriction in Laves phase RFe2 compounds: (a) MII[II1]. e.g. denote atoms above plane of figure. for SmFe2. than to atom B. l 4 are denoted by A (or A') and B (or B') respectively. the magnitude of which depends upon the internal A-B modulus.denote atoms below (taken from Clark et al. yielding a net positive external magnetostriction along [111]. On the other hand. 0. In fig..Ar ~ " .±l is observed between 140 K and 240 K where the easy axis of magnetization rotates from [110] to [111] with increasing temperature. This internal distortion lowers the symmetry and drives an external rhombohedral distortion (Am). In this model. C). broken circles.-..l 4. a contraction of a occurs. for compounds with rare earths possessing prolate 4f charge densities. producing the observed negative magnetostrictions (Am). The iron atoms are not shown. Open circles. A~ B i100 ] --e .Xl00. A large rhombohedral distortion thus exists [111] r. huge ?.. The resultant increase in a exceeds a small decrease in b.550 A. Conversely. 1976). Am " ~ ~ ' /':'.?. ~'~. H e r e t h e effect o f s c r e e n i n g ( F r e e m a n a n d W a t o n 1962) is neglected.1500 -3700 -3600 Am x 106(exp) room temperature - 1. It is possible to calculate the intrinsic ( T = 0 K) m a g n e t o s t r i c t i v e c o n t r i b u t i o n o f e a c h 3 + rare e a r t h ion f o r a particular c o m p o u n d (assuming its existence) given the magn e t o s t r i c t i o n o f at least o n e c o m p o u n d (e.001 0. J is the g r o u n d state angular m o m e n t u m f o r the 3 ÷ ion a n d (r 2) is the a v e r a g e radius s q u a r e d o f the 4f e l e c t r o n shell. 200B~ --300 d) -2100 - * Calculated for cubic Laves phase R3+Fe2compounds. o Koon and Williams (1977).635 -0.639 0. In table 5.772 4. RFe2 compounds R Ce* Pr* Nd* a x 102a) .643 0. Pm. t h e values o f J. a n d (r~) are given along with the c a l c u l a t e d values o f Am f o r R Fe2 c o m p o u n d s . Eu and Yb.e.696 0. W i t h the e a s y direction o f m a g n e t i z a t i o n parallel to the [100] direction.01 3.g.this compound has not yet been synthesized. T h e t h e o r y utilizes the S t e v e n s ' equivalent o p e r a t o r m e t h o d . A c c o r d i n g to S t e v e n s (1952). . is d e p i c t e d in fig. T h e e s t i m a t e d u n c e r t a i n t y TABLE 5 Magnetostriction of. b) Freeman and Watson (1962). i.20 1. the 4f e l e c t r o n c l o u d b e c o m e s equidistant to all rare earth n e a r e s t neighbors. d)Clark et al.1800 -3200 0 0 4400 4200 1600 .883 0. and t h e potentially h u g e m a g n e t o s t r i c t i o n c o n s t a n t .942 0.834 0. ErFe2 and TmFe2. (1979).613 -2100 c~ 2460d) 1260~) 185°. (1975).5.2. d o e s not appear. For R = Ce. O f the total o f fifteen lanthanide rare earths. allowing n o m a g n e t o s t r i c t i v e l y d r i v e n internal distortion via point c h a r g e electrostatic interactions. the ratio o f the intrinsic m a g n e t o s t r i c t i o n o f o n e rare earth to a n o t h e r is given b y t h e ratio o f otJ ( J . i.01 -0.0. a~Stevens (1952).726 0.785 0. f o r D y F e z and H o F e z . a.½)(r~) w h e r e ot is the l o w e s t o r d e r S t e v e n s ' f a c t o r . In table 5 are listed the rare earth e l e m e n t s in o r d e r o f the increasing n u m b e r o f 4f electrons. TbFe2).1. PrFe2 has been synthesized only under high pressure. o Clark et al.e. (1976).086 4 Pm* Sm Eu* Gd Tb Dy Ho Er Tm Yb* . T o date these internal d i s t o r t i o n s h a v e n o t y e t b e e n verified. g) Abbundi et al. o n l y a f e w f o r m highly magn e t o s t r i c t i v e R F e 2 c o m p o u n d s at r o o m t e m p e r a t u r e . L a with no 4f e l e c t r o n s a n d L u with a full shell o f f o u r t e e n 4f e l e c t r o n s are omitted.222 -0. n Abbundi and Clark (1978).10 J 5 ~ (r2) b) )till x 106(calc)* 0K 6000 5600 2000 .13 0 0 . Nd. A100.MAGNETOSTRICTIVE RARE EARTH-Fez COMPOUNDS 551 •w h e n e v e r the m a g n e t i z a t i o n points a l o n g [111].254 1. All A .72 . 13b. n o r m a l i z e d to 4400 x 10 -6 f o r TbFea. SmFe2. T h e alternate c a s e o f [100] e a s y .18 9 4 ~ 0 ~ 6 J~ 8 ~ 6 7 1. f o r TbFe2.666 0.756 0.B b o n d s are equivalent. the s y m m e t r y r e m a i n s high. ErFe2 and TmFe2.552 A. ErFe2 and TmFe2. Experimental values of AHI measured at room temperature are given in table 5 for the binary compounds SmFe2. It is clear from this work and the earlier work of Wallace and Skrabek (1964) that the rare earth and iron moments couple antiferromagnetically. 1964. if the [111] axis is easy. The calculated magnetostrictions of quadrivalent Ce and divalent Yb are zero. It is clear from the foregoing that since in many cases AH~>>A~00. Instead. Guimaraes 1971. 4. 1977. Note that the largest positive intrinsic magnetostrictions are those calculated for CeFe2. the large magnetostriction is not realized in DyFe2 since [1 Ill is magnetically hard. This is close to the observed polycrystal/single crystal . In a polycrystal in which crystallites are distributed uniformly over all directions. While both DyFe2 and TmFe2 have high incipient magnetostrictions. In this section. it is clear that the full saturation magnetization is not achieved in any of the polycrystal specimens at low temperatures. most rapidly along a direction near [211] (McMasters unpublished). DyFe2 (see section 6). and DyFe2. Magnetization and sublattice magnetization of RFe2 compounds Magnetization measurements on a large number of RFe2 binary and pseudobinary polycrystals have been reported on the literature. the largest negative magnetostrictions are those calculated for SmFe2. comparison will be made between single crystal and polycrystal data. PrFe2. However.E. Single crystal magnetizations will be used to calculate theoretical temperature dependences of the magnetostriction utilizing a theory formulated by CaUen and Callen (1963). Although the compounds are cubic and only moderate anisotropies were initially expected.866 of the aligned saturation moment (Chikazumi and Charap 1964). DyFe2. 1974. 1968. Thus only TbFe2 and SmFe2 emerge with large room temperature magnetostrictions. magnetization measurements in high fields and on single crystals have become available (Clark et al. HoFe2. Crystallites grow anisotropically. In figs. and if the magnetization lies along the [111] axis in each crystallite closest to the external field. CLARK in the absolute magnitude of All1(0) is -4. large cubic anisotropies were measured in all compounds (see section 5). Atzmony et al. Abbundi et al. 1971) and Burzo (1971). TbFe2. not all of these compounds have been synthesized. TmFe2 and YbFe2. Within the last few years. Typical preparation techniques yield samples which are far from isotropic. Extensive measurements over a wide range of temperatures have been made by Buschow and Van Stapele (1970. 1979). Ce and Yb are not found in their trivalent states.15%. Bowden et al. the magnetic moment along the easy magnetization direction is compared to data taken on polycrystalline samples for TbFe2. and the large magnetostriction of TmFe2 is realized only at low temperatures because of a weak thulium-iron exchange interaction. HoFe2.care must be taken in interpreting measurements on polycrystals. The easy directions of magnetization are consistent with those predicted by the earlier M6ssbauer measurements (Wertheim et al. the polycrystal remanent moment is 0. 1973). TbFe~. 14 through 18. PrFe2 and NdFe2 do not readily form the cubic Laves phase compounds. 1978. Magnetic moment of TbFe2 (taken from Clark et ai. ' I ' I I ' I ' I ' I ' " 120 .MAGNETOSTRICTIVE RARE EARTH-Fe2 COMPOUNDS I I I I I I 553 Tb Fe2 140 • 120 A . 14. 15. Burzo 1971). [ i 200 i ! I 300 400 T(°K) . 1978. I ~ I i I 100 200 300 400 500 TEMPERATURE (°K) Fig. 0 I 100 . . 100 SINGLECRYSTAL[Ill] POLYCRYSTAL (120 kOe) POLYCRYSTAL (AFTERBURZO) E 8o 00 20 0 . ~ POLYCRYSTAL (120 kOe) N ~ ---.. I . I 500 . ~ ..POLYC~tY~FAL (FROM BURZO) . ~ . 600 700 Fig. Magnetic moment of DyFe2 (taken from Clark et al. ^ I ° ° N \ . 1978.. I .. I L. Burzo 1971). 17..554 i 140 I i A. Magnetic moment of ErFe2 (taken from Clark 1974. Magnetic moment of HoFe2 (taken from Abbundi et al. .E.. CLARK I t I z I J I i I HoFe 2 120 100 A \ \ ~ ~ ~ ~L --e-. Borzo 1971). 16.. 1979. Burzo 1971).0' ~600 -t T(K) Fig.SINGLECRYSTAL [100] .POLYCRYSTAL - (FROMBURZO) - RO e 60 4O 200~) ' 100 ' 200 ' 3. 140 120 f l l l l J l ' l l ErFez • • SINGLECRYSTAL[ l l l l POLYCRYSTAL (120 kOe) AL (AUER BURZO) k ~ 100 6O 40 ~ 20 i l l l l l J l l 100 200 300 400 TEMPERATURE (°K) 500 Fig.0 t 40]0 ' 5. Burzo 1971). I . 1965) developed a formulation which directly relates the temperature dependence of the magnetostriction to the temperature dependence of the rare earth magnetization. magnetizations and theoretical densities for these compounds. They find A~'I(T) = A~'l(0)fl+. They are remarkably close to those adduced from nuclear hyperfine fields by Wallace (1968). In table 6 are collected Curie temperatures.832.0.61. I o 100 200 300 400 T(K) 500 600 Fig. Unlike the magnetostrictions of the transition metals Ni.04/~B) at 0 K are calculated from the single crystal magnetization measurements assuming that the rare earth moments equal gJ. the ratios are -0. When [100] is easy. the magnetostrictions of the rare earth elements follow a rather simple single-ion temperature dependence. Similar values of iron sublattice moments (1. Callen and Callen (1963. 18. Co and Fe. the corresponding calculated ratio is 0. moment ratio at 4 K for TbFe2 and ErFe2. through the relationship . 1978.MAGNETOSTRICTIVE RARE EARTH-Fe2 COMPOUNDS I I ' I ' I 555 80 TmFe 2 70 • SINGLE CRYSTAL [111] _ m POLYCRYSTAL (FROM BURZO) 60 5O ~40 Ill 10 O" i l ~ I i I . The argument x is related to the normalized magnetization m = M ] M . atomic magnetic moments./z(X) (4. No moments have been reported to date for single crystal SmFe2. only slightly higher than the calculated value. spin wave approximation and various Green's function theories (Callen and Shtrickman 1965).1) where ll+z/2 is the ratio of the hyperbolic Bessel function of order l +½ to the hyperbolic Bessel function of order 2 !. This formulation is valid in the molecular field approximation. In DyFe2 and HoFee. Magnetic moment of TmFe2 (taken from Clark et al.87. 711 s) 635 606 590. T o test the applicability of eq.75 1. and indirectly by subtracting the Fe magnetization f r o m the total magnetization. Thus.g. In a more general sense. c)Taken from single crystal data (Abbundi et al. The results are s h o w n in fig.70 5. the rare earth sublattice magnetizations.60 1. 1979) and ErFe2 (Clark 1974). unpublished) is higher than that calculated f r o m the magnetization o v e r the entire t e m p e r a t u r e range.20 !.53 M(emu/cm 3) 0K 300 K 0K nb 300 K Tc nbff ) nbv. 1978). 1968) and those obtained f r o m the total magnetization m e a s u r e m e n t s (Clark 1974). x can be defined through eq. (4. a~Taken from polycrystal data (Buschow.597 s) 560 676 a)Taken from single crystal data (Clark et al. mR'S.55 - 697.44 9.556 A. Burzo 1971). mR's.72 2.87 6.61 1. can be obtained directly b y M 6 s s b a u e r and by neutron diffraction methods.2) Since f3/2 is the familiar Langevin function. m u s t be known.0.64 - 1. we find A~"e(T) A~'°(0)m3(T) at low temperatures and A~"2(T) -.0 K DyFe2b~ HoFe2c~ ErFe2b) TmFe2a) SmFe2a) 1090 1300 1274 1120 725 410 800 810 590 280 98 400 5. CLARK TABLE 6 Magnetic moments and Curie temperatures of RFe2 RFe2 TbFe2 a) o(emu/g) 0K 300 K 120 140 135 116 74 48 88 87 62 29 10 47 p g/era3 9. (4. 19.26 4.57 1. unpublished) and total magnetization results for HoFe2 (Abbundi et al. (4. 4 and 6 in Appendix B. Similarly. F o r TbFe2 the neutron diffraction data (Rhyne.65 1.60 1. b~Taken from single crystal data (Clark 1974 Clark et al. For DyFe2 good a g r e e m e n t is found b e t w e e n the values of mDy calculated f r o m M 6 s s b a u e r m e a s u r e m e n t s (Bowden et al. ejCalculated from single crystal data assuming nbR = gJ. F o r T m F e : the neutron diffraction .60 1. 1978). however. H))].6A~"2(0)mZ(T) at high temperatures. Keffer 1955). g~Taken from polycrystal data (Buschow and Van Stapele 1971. At00 and Am.3) For the lowest order (l = 2) magnetostriction.27 3.E. good a g r e e m e n t is found between the neutron diffraction results (Rhyne. 1979). (1977) in their neutron diffraction data on TbFe2. expressing the magnetostriction in terms of the normalized magnetization m ( T . The functional d e p e n d e n c e of I1+112on m is given for l = 2. 0 Calculated from M6ssbauer spectra (see Wallace 1968).1/x. ft+l/2 (l > 1) can be considered to be "higher o r d e r " Langevin functions (Callen and Callen 1965. fall within the uncertainty cited b y B a r b a r a et al. however.2).3) to the RFez c o m p o u n d s . Both these m e a s u r e m e n t s .55 1.06 1. In molecular field theory.45 0.06 9.25 4. e.79 8. H ) A~"I(T) = A~"t(0)f~+~/2[~g-l(m(T.81 6.62 9. where /z is the magnetic m o m e n t / i o n and H is the total (effective + external) magnetic field. x = I ~ H / k T .49 2. unpublished). m = I3/2(x).28 9.79 3. (4. ~g(x) = coth x . These sublattice magnetizations. . The hexagonal rare earth elements possess the largest known magnetic anisotropies at low temperatures.. data (Rhyne. 11). The temperature dependence of the magnetostrictions were calculated from eq. . .1 7 . . . Normalizedrare earth sublattice magnetizationsin RFe2.MAGNETOSTRICTIVERAREEARTH-Fe2COMPOUNDS 1.'9 . . . i .7 o ~ j -%. 5. 19.The solidlines were calculatedfrom singlecrystalmagnetizationsminusthe iron sublattieemagnetizations(Bowden et ai. 1968)normalizedto the respectiveCurietemperaturesof the compounds.5 u~ FROMNEUTRON ~'%%a '~. ol .O Barbaraet al. . Excellent agreement between the measured temperature dependences and those calculated from the lowest order (l = 2) single-ion theory were found for TbFe2 (fig. Barbara et al. . . 1 1 . leading to incorrect magnetizations and compensation temperatures.<>Bargouthand Will 1971). . 1968. The Callen-Callen single-ion theory was found insufficient to account for the (small) h~00 of DyFe2 and HoFe2 (fig. . . . . I . . I i i i 1 ~ 1 t 0 100 200 T(OK) 300 400 Fig. Thus the currently available neutron diffraction data for TmFe2 are considered unsatisfactory.I ~ . [ . .~ --FROM MAGNETIZATION . 1977..0 ' ' ' 1 557 . . Magnetic anisotropy of binary RFe2 compounds The largest magnetic anisotropies occur in uniaxial crystals. . . The high Curie temperature compounds RCos and R2Col7 possess the .. . [ . I . (4.unpublished. (A (M6ssbauer) Bowdenet al.3 ~ . 9 and I0). I . 19.[] ~7A Rhyne...4 .. unpublished. . .3) using the rare earth sublattice magnetizations of fig. ~ . 1977) are not in agreement with the total magnetization results. . 10) and TmFe2 (fig.8 . 1975).204 Coo. CLARK largest k n o w n magnetic anisotropy energies at r o o m temperature. (1972.Fe2. DyFe2.204 .~.uO4 CoFe204 Coo. 19) and thus in the magnitude of the r o o m t e m p e r a t u r e magnetic anisotropy. The total anisotropy is a sum of both intrinsic and magnetoelastic contributions (see section 2). AKI(300)/KI(300). 1973. (1966). 1978.26¢) . Smaller anisotropies are found in the cubic RFe2 c o m p o u n d s .2Fe2. f~Abbundi and Clark (1978). g)Pearson (1960). HoFe2. J~Abbundi et al. the intrinsic anisotropies K~nt(300) and K]"t(0) were inferred. saturation is achieved below 12 kOe (see fig.550j~ ..E.8Fe2. where the magnetostriction is smaller.7600dl 2100d~ 580eJ.and ferrimagnets in table 7.5a) -43 b~ . For TbFe2. this large anisotropy sometimes persists to r o o m temperature.20%. In TbFe2. h)Perthel et al.i r o n exchange. The e a s y axes are consistent with the earlier M 6 s s b a u e r spectra m e a s u r e m e n t s (see compilation by T a y l o r 1971). anisotropy fields are in excess of 100 kOe at r o o m t e m p e r a t u r e . H o w e v e r . AK~(3OO)/Ks(300)<~ 6%. DyFe2 and TmFe2. Anisotropy constants were experimentally determined by both magnetization and magnetic torque m e a s u r e m e n t s on single crystals of the binary RFe2 c o m p o u n d s (Clark et al. Depending upon the strength of the rare e a r t h . otJ(J-½) is large. The decrease in Curie t e m p e r a t u r e with increasing atomic n u m b e r is directly reflected in the room t e m p e r a t u r e value of the rare earth sublattice magnetization mR (fig. for HoFe2 and ErFe2. According to single-ion theory (see Appendix B). Williams and K o o n 1975). (1979). ErFe2 and TmFe2 are c o m p a r e d to some typical cubic ferro. the t e m p e r a t u r e d e p e n d e n c e TABLE 7 Anisotropy constants of some cubic metals and ferrites at room temperature Metal Fe Ni 70% Fe-Co 65% Co-Ni TbFe2 DyFe2 HoFe2 ErFe2 TmFe2 10-4K.558 A.(ergs/cm 3) 45 a) Ferrite 10-4K~(ergs/cm 3) . The r o o m t e m p e r a t u r e anisotropy constants Kt of TbFe2. (1955). Subtracting these values f r o m the total anisotropies of table 7.330d) . while in TmFe2. recent m e a s u r e m e n t s have shown that they possess by far the largest k n o w n anisotropies of cubic crystals. where the intrinsic magnetostriction.818~ 260h~ 2900 1500 ajHoffman (1967). °Williams et al. b~McKeehan (1937). i)Bozorth et ai. . 20). d)Clark et al. ~)Shih (1936). (1978).53f~ Gao.3Zno. In table 8 are shown the calculated contributions to the anisotropy f r o m the magnetoelastic coupling. as obtained f r o m AK1 =-Szc~A~. MAGNETOSTRICTIVE 100 RARE EARTH-Fe2 COMPOUNDS - I : 559 F / I , _. I _- _ I _ - I ;, - I li ~ so -."71oo~ _ 12 ,, . . . . . . . . . . . | - 11o 7-' ...... _.....y.--m -~ G ~I~ , TmFe2 I , I . I , I , I , I -~ .~I ~ 20- - - - - ' : / ~ J 2 I 4 I 6 8 10 12 14 16 H(kOe) 0 __._J I 0 2O 40 6O i 80 l 100 I 120 H(kOe) Fig. 20. Magnetic m o m e n t o f TbFe2 and TmFe2 at r o o m t e m p e r a t u r e (taken f r o m Clark et al. 1975, A b b u n d i and Clark 1978). TABLE 8 Intrinsic, K~at, a n d m a g n e t o e l a s t i c , AKt, c o n t r i b u t i o n s to the m a g n e t i c a n i s o t r o p y ( e r g s / e m 3) AKI(300)* × 10-4 -970 - 1330 - 350 - 7.5 - 20 - 9.7 K~"(300) x 10-4 -6300 2450 590 - 310 - 43 AKI(300) K~nt(300) 0.21 - 0.14 - 0.01 0.06 0.22 K~"t(0)** x 10 -s -5.2 4.7 2.7 - 5.4 - 3.8 RFe2 SmFe2 TbFe2 DyFe2 HoFe2 ErFe2 TmFe2 * Calculated f r o m 29c44A2., taking c44 = 4.87 x 10" d y n e s / c m z f r o m Rinaidi et al. (1977). ** E x t r a p o l a t e d to T = 0 using single-ion theory. of the lowest order (intrinsic) anisotropy constant in cubic crystals is given by K~'4(T)/K"4(0) = t9/2[,~t~-l(mx)] or (5.1) (5.2) Kj(T)/KI(O) = fg/2[-o~-I(mR)] whenever [K21 < l11 KII. 5~ "1°9" ...... A.E. CLARK I. . . . . . . . I. . . . . . . . 1ffi-5.4 X 108 19/2[,~ 1(mR) ] "108 7[To K ~ D HIGHFIELD MAGNETIZATION DATA o MAGNETIC ~ ~ O EDATA .107 200°K .loe ....... , ........ zo "1 ., ?,O~K,, lo":' ,\ zo-3 ^ 19/2[,~"1(mR)] Fig. 21. Magnetic anisotropy KI of ErFe2 vs. single-ion theory (taken from Clark et al. 1974). 109 los t~ .e f.i 107 106 105 0 100 200 300 400 500 600 T(K) Fig. 22. Anisotropy constant KI for DyFe2 and TmFe2 as a function of temperature (taken from Clark et al. 1978). The solid curves are calculated from single-ion theory. MAGNETOSTRICTIVE RARE EARTH-FeqCOMPOUNDS 561 Figure 21 shows that the experimentally observed anisotropy of ErFe2, in which AK/K is negligible, conforms rather well to the simple theory, as given by eq. (5.2). The temperature dependence of the anisotropy constants (Kl) for DyFe2 and TmFe2 are plotted in fig. 22. The anisotropy spans three decades. Again satisfactory agreement between experiment and theory is found. With one adjustable constant, K~nt(0), the fit to the data is within 20% over the entire temperature range. The values of K~nt(0) calculated from eq. (5.2), utilizing higher temperature measured values and the sublattice magnetizations mR from section 4, are given in table 8. All anisotropy magnitudes exceed 2 x 10s erg/cm 3 at T = 0 K and agree with each other within a factor of two. Higher order anisotropy terms also contribute to the total anisotropy energy, particularly at low temperatures. Evidence for their existence can be found from spin reorientation diagrams of pseudobinary RFe2 compounds (Atzmony et al. 1973, 1977; Atzmony and Dariel 1976) and from torque magnetometry measurements in the Tb~Hol-xFe2 system (Williams and Koon 1975, 1978). Temperature dependences of the anisotropy constants are in general complex and require the inclusion of the large magnetoelastic contribution (Koon and Williams 1978). The binary RFe2 compounds TbFe2, DyFe2, HoFe2, ErFe2 and TmFe2 have only one easy direction at all temperatures. However anisotropy compensation and spin reorientation can be achieved with suitable rare earth alloying into compounds of the form ~,t~)o¢2) .Fe2 ( x + y = 1). Spin reorientation diagrams and anisotropy measurements for some pseudobinary RFe2 compounds are discussed in section 6. ~ X ~ y • • • • • 6. Magnetostriction of pseudobinary RFe2 compounds In the hexagonal rare earths, the lowest order anisotropy and magnetostriction arises from the same degree of spin operator (l = 2). In contrast, in the RFe2 compounds, because they are cubic, the anisotropy arises from l = 4 terms and the magnetostriction from l = 2 terms. This makes it possible to tailor compounds with optimum magnetostriction and anisotropy properties simultaneously. For certain magnetostrictive materials applications, high strains at low fields are necessary. In these cases a low anisotropy is important in order to maximize domain wall mobility and easy domain rotation at low fields. Table 9 shows the signs of A, K ~'4 and K ~'6 for the binary RFe2 compounds taken from the signs of the Stevens' equivalent operator coefficients. Using this table, pseudobinary compounds can be constructed in such a way as to minimize the magnetic anisotropy while still maintaining a large positive (or negative) magnetostriction. It is preferable to alloy binary compounds with the same magnetostriction sign but with opposite signs of anisotropy. Ternary compounds yielding large positive magnetostrictions at room temperature must contain Tb. Hence acceptable anisotropy compensating systems are Tbl-xDyxFe2, Tbi_xHoxFe2 and Tbl-xPr~Fe2. Experimental spin reorientation diagrams for Tb~-xDy~Fe2 and Tb~-~HoxFe2 are shown in fig. 23. The region of 562 A.E. C L A R K TABLE 9 Polarity of ~, K ~'~ and K Q,6 PrFe2 a) A -K ~*, K I + K 2 / I I K a'6) K 2 SmFe2 0 TbFe2 + -I- DyFe2 + + - HoFe2 + + q- ErFe2 - TmFe2 -{- YbFe2 a) + - + + - ") The binary PrFe2 and YbFe2 compounds are not readily synthesized. spin reorientation and anisotropy compensation are clearly identified from 0 K to 300 K. Ternary compounds possessing a large negative magnetostriction at room temperature must possess Sm. However Yb, the only suitable element with the correct sign distribution, is not available in a trivalent state. Fortunately, the ratio of A/K is much larger for Sm than for the heavy rare earth compounds. I i 300 ,,- 200 [1111 IO0 I TbFe 2 Im 0.2 0.4 0.6 0,9 DyFe 2 300 " • • • /A • lOOI 1110] . . ,t I 0.6 4 0.8 \ % HoFe 2 TbFe2 0.2 0.4 Fig. 23. Spin orientation of Tbl_xDyxFe2 and Tb,-xHoxFe2 systems (taken from Atzmony et al. 1973). Filled circles, triangles and squares correspond to [111], [!I0] and [100] axes of magnetization respectively. Open triangles correspond to intermediate directions. M A G N E T O S T R I C T I V E R A R E EARTH-Fe2 C O M P O U N D S 563 Hence certain ternary alloys, such as Smm-xDyxFe2 and Sml-xHoxFe2, are attractive candidates for anisotropy minimization. The Tbt-xDyxFe2 system has been investigated in detail. In fig. 24, are shown the magnetostrictions at room temperature of polycrystalline samples of Tbm-xDy~Fe2 for H = 10kOe and H =25kOe. Near x =0.7, the magnetostrictions at these fields exhibit a peak, reflecting the near zero magnetic anisotropy at this concentration. Figure 25 illustrates how the single crystal magnetostriction constant Am varies with Dy concentration. Am was determined by X-ray techniques, utilizing a method developed (Dwight and Kimball 1974, Clark et al. 1975) to accurately determine the magnetostriction at the point of spin reorientation. When [111] is easy, a large rhombohedral distortion (Am) occurs contributing to a large X-ray splitting of the (440) and (620) lines. When [ 100] is easy, only a tiny distortion is realized (AJ00-- 0) and X-ray splittings are not observed. The concentration at which the magnetostriction disappears clearly identifies the point of anisotropy minimization. At the spin reorientation Am = 1600x 10-6. The extrapolated value of A m f o r DyFe2 is 1260 x 10-6. The magnetostriction of single crystal Tb027Dy0.,Fe2 has been measured through the anisotropy compensation region (Abbundi and Clark 1977). A spectacular "turning on" of a huge rhombohedral (magnetostrictive) strain by a rise in temperature occurs. At low temperatures, MI[[100], and no significant 3,000 I f I I Tbl. x 9Yx Fe2 I I I I = 25 kOe / H =10 kO. 2,000 ,,.,< 1,000 I Tb Fe2 I I .2 i I .4 I I .6 i I .8 i I 9/Fe 2 X Fig. 24. Magnetostriction o f Tbl_xDyxFe 2 at room temperature (taken from Clark 1974). 5~ 280,,[_ I " ~ , A.E. CLARK ~ ~ , ~ ~ 2 4 0 0 ~ ~ Tbl_ x Dyx Fe 2 2000 - ~ . _ ~ . T" 1200 800 40O Tb Fe2 I I 0.2 I I 0.4 I I 0.6 I __~__d 0.8 1,-, 1 _ Dy Fe2 Fig. 25. Am of Tb~-xDy~Fe2at room temperature. Open circles are Am; solid circles denote region where no spontaneousA~,,exists (taken from Clark et al. 1976). magnetostrain exists. Rather abruptly, at the anisotropy compensation temperature, magnetization rotation takes place and a large rhombohedral distortion (Am) develops. The effective linear thermal expansion coefficient at = dhm/dT reaches 110 ppm in this region (see fig. 26). The region of the anomalous thermal expansion can be shifted in temperature by application of an external magnetic field. The fields required for magnetization saturation through the compensation region are shown in fig. 27. In fig. 28, the room temperature saturation magnetostriction measurements of Koon et al. (1974) for Tbl-xHoxFe2 are shown as a function of composition x. Since the anisotropy of Ho is smaller than that of Dy at room temperature, compensation occurs at a larger value of x than in the Tb~-xDyxFe~ system. In Tb~-xHo~Fe2, compensation occurs near x = 0.85 as indicated by the anisotropy measurements of Williams and Koon (1975). At this concentration, h~ll = 500 x 10-6 (Koon and Williams 1977). Figure 29 shows the effect of the addition of PrFe2 to TbFe2. Here the magnetostriction remains very high, but complete anisotropy compensation cannot be reached. Beyond 20% substitution, non-cubic phases appear. In multicomponent pseudobinary systems, such as TbxDyyHozFe2, TbxDyyPr~Fe2 and Tb~DyyHozPrwFe2, values of x, y, z and w can be selected to achieve maximum magnetostriction with the simultaneous minimization of two or more anisotropy constants. Williams and Koon (1977) have successfully determined the ahoy composition of the (Tbo.3Dyo.TFe2)x(Tbo.l~-Ioo.s6Fe2)l-~pseudobinary for simultaneously minimization of the t w o lowest order anisotropy constants. They found low anisotropy for x---0.32 and calculated a still lower anisotropy for Tb0.20Dy0.22Ho0.ssFe2. For this compound, A, = 530 x 10-6. The three lowest symmetry anisotropy constants K4, K6 and Ks, calculated from a least square fit to torque data, are illustrated in fig. 30. MAGNETOSTRICTIVE RARE EARTH-Fe2 COMPOUNDS 565 0 H =10 kOe ~.,j ~" ~ ' ' ~ ~b x -500 / / ':~"e -1000 -/ • / / i I 240 ,7' 220 n , I 260 I I 280 I I 300 l 320 T (K) Fig. 26. Thermal expansion along [Ill] in single crystal Tbo.z?Dyo.?3Fe2(taken from Abbundi and Clark 1977). ~f/| f~ ~ |1 , I Tb27 ~ DY.73 I ' Fe2I ' I ,,~oo "'-~ 0 I 200 i mlP'l 300 o I 400 i 500 600 T (K) Fig. 27. Fields required for magnetic saturation along the principal directions in single crystal Tb0.2¢Dy0.73Fe2(taken from Clark et al. 1978). 5~ 500 400 A.E. CLARK =. 300 x 200 100 I I B 1 o 2-I -2 .7 I .8 I .9 1.0 x~ Tbl.xHoxFe2 Fig. 28. Magnetostriction, As, and magnetic anisotropy of Tb~-xHoxFe2(taken from Koon et al. 1974, Williams, private communication). 3,000 ~ I i I I I i (I-L - . _ ~ _ ~ 2,000 ~ ~ ,wo,,.e , ~ -a- ...... "'Tbl.x Cox Fe2 ~ ~ , ~ Tb1-x Prx F02 1,000 Sm l:xYbxFe2 1 I ! I I ",,. ,I i ~i I1 ! -[ I I 0.1 --0.2 0.3-- X 0,"4 0.5 0.6 Fig. 29. ~H~ of some Tb~_xR~Fe2and Sm~_~RxFe2 alloys. Open symbols are I~H~[; solid symbols denote region where no spontaneous A~,, exists (taken from Clark et al. 1977). M A G N E T O S T R 1 C T I V E RARE EARTH-Fe2 C O M P O U N D S i 4.0 o 567 I I B.0 3,.( /~s : : : 5.0 c~ v 2.0 V-v f 1.0 2-0 0.0 0.1 X 0,,2 0,3 D.O Fig. 30. Anisotropy constants x4, x6 and xs for the compound (Ho0.s6Tb0.n4Fe2)n_x(Dy0.TTb0.3Fe2)x (taken from Williams and K o o n 1977). Values of the magnetostriction for some quaternary compounds are listed in table 13 of section 8. In fig. 29, the absolute value of Am is plotted vs. x (0 < x <0.4) for the two Sm alloys Sml-xDyxFe2 and Sm~-xHo~Fe2. In these systems, both Am and K~ compensate, as can be seen from the sign distribution in table 9. However, because of the relatively small anisotropy of SmFe2, only small additions of Dy and Ho are needed for spin reorientation and anisotropy minimization. X-ray measurements show that reorientation occurs near x = 0.12 for Smj-xDyxFe2 and near x = 0.3 for Sm]_~Ho~Fe2. The values of magnetostriction at these concentrations are large and negative. In both alloys, JAm[ > 1200 x 10 -6. RFe2 bimetallic strips composed of highly magnetostrictive alloys of both positive and negative polarity can exhibit huge flexural strains. The extent of the motion depends upon the magnetostrictions, strip length and strip thickness. 7. Elastic properties of RFe2 compounds Room temperature sound velocities, densities and moduli are listed in table 10 for polycrystalline TbFe2, ErFe2, YFe2 and TbFe3. The moduli are midway between those of the soft rare earth elements and the stiffer magnetic transition metals, such as F e and Ni. The moderate magnitudes of the moduli and the huge magnitudes of the magnetostrictions combine to yield huge magnetoelastic forces and energies for these compounds. Values of As, E,L and the energy density, l 2EA 2 ~, are shown in table 10. They are compared to those of elemental Ni, a typical magnetostrictive material. The quantity EAs is a measure of the pressure exerted by a constrained bar of the material which is magnetized to 568 A.E. CLARK TABLE I0 Elastic and magnetoelastic properties"~ TbFe2 v~(m/sec) v,(m/sec) p(g/cm3) E x 10-I° (newton/m2) As × 10 6 EAs x 10-7 (newton/m2) EA~/2 x 10-3 (joule/m3) 3940 1980 9.1 9.4 1750 17 145 ErFe2 4120 2180 9.7 12.1 -229 2.8 3.2 YFe2 4340 2720 6.7 12.7 TbFe3 4230 2320 9.4 13.1 693 9 32 Ni 21b) -31 ¢) 0.7 0.1 a~Clark et al. (1973b). ~J"Nickel", The International Nickel Co., Inc., (1951). c)Went (1951). saturation. The energy density, JEA 2 2 ,, represents the amount of magnetic energy which can be transformed to elastic energy per unit volume of the material. For TbFe2 this energy is about 1000 times that of earlier magnetostrictive materials, such as Ni. Rosen et al. (1973, 1974) have determined the Young's modulus and the shear modulus ultrasonically for the ternary Tbl-xHoxFe2 system and for SmFe2 as a function of temperature. Their values are illustrated in fig. 31. Clearly defined depressions in the moduli occur where easy axis rotation takes place. (Refer to the spin reorientation diagram of fig. 23 and the magnetostriction data of fig. 12.) Young's moduli for a large number of binary RFe2 compounds as a function of temperature are given in fig. 32 (Klimker et al. 1974). Unprecedented changes in elastic moduli with magnetic field (AE effect) have been observed in the highly magnetostrictive RFe2 compounds. In figs. 33 and 34 are plotted the relative changes in Young's modulus with field, E n - E0, normalized to the modulus at zero field E0. zaE effects are huge for the highly magnetostrictive TbFe2 and Tb03Dy0.7Fe2 compounds. Conventional A E effects, i.e. reductions in the modulus from their intrinsic high field values, have been generally associated with domain wall motion (see Bozorth 1951). H o w e v e r , in the RFe2 compounds, the moduli continue to change far above technical saturation. Thus the major source of the field dependences cannot be attributed to the motion of domains, but to an intrinsic softening of the lattice due to local atomic magnetoelastic interactions. In this section we shall derive an expression for the softening in the shear modulus, c44, by the second order contribution of the large magnetoelastic coupling, b2. It was shown in section 2 that a magnetostrictive system, composed of magnetic anisotropy, magnetoelastic energy and elastic energy components leads to the equilibrium strains ~ q = -- (b2/c°)otiotj (7.1) MAGNETOSTRICTIVE RARE EARTH-Fe2 COMPOUNDS I ~.. t t ) i i 4.5 569 11 X°o.sTbe.2F°2 ,~ E J ,o 9 ,oo.,,,,.=,,)\ "'-.~,. ~ ~.o 3.5 Hoo.6Tbo.4F 8 .oo s T ~ ~ . . . . ..__~'~___ 3.0 7 6 i i t i i ) 2.5 5.6 ~_ _ ~ , ~ . 5.2 ~ 2.0 ,.~/4.4~ 4.O I ~. \ %% ~ ", SmFe2 ,, - ,.~ 1.4 "t \,,</ I 50 I 100 I I 150 200 250 TEMPERATURE (?K) ,o I 300 350 '"I 2.8 0 V I Fig. 31. Temperature dependence of Young's modulus, E, and shear modulus, G, for Tbl_xHoxFc2 and SmFe2 (taken from Rosen et al. 1973, 1974). 12.4 i I i i I ¢N 12.(J E ~ 11.E "o ~ 11.2 o ~ IO.E =J 10.~ 8,4 E r F e 2 ~ 6.0 5. 0 i 50 CeFe2 I I I~"----""~ i 100 150 200 250 300 TEMPERATURE (OK) Fig. 32. Temperature dependence of the Young's moduli for the RFez compounds (taken from Klimker et al. 1974). 570 A.E. C L A R K 1.6 -1.4 I I ' I I -I.2 --1.0 AE 8T 0 ~7 w 6 6 .4 .2 0 , I I , I 2 t 1 3 ~ 4 I 5 H [k0e) Fig. 33. Y o u n g ' s m o d u l u s and a E effect at room temperature for Tb0.3Dyo.TFe2, AE = E n - Eo (taken from Clark and Savage 1975). and to an effective anisotropy constant Ki K i = K I - (b~/2c ° ) (7.2) whenever b2"> b l. (The superscript ,,0,, is added to c44 to label the "intrinsic" stiffness.) Thus as a function of the magnetization cosines, ai, the total energy at constant stress (including magnetoelastic and elastic terms) becomes simply E o- ~ t 2 2 OtyOtz Kl(axOty+ 2 2 + axOty )2 2 + constant (7.3) The dependent variables, the strains, have been eliminated. Only an effective anisotropy constant remains. In like manner the effect of the magnetoelastic interaction on the elastic moduli and sound velocity can be readily calculated. Here, instead of the strains, eq, being the dependent variables, the magnetization direction cosines, at, are the dependent variables and the elastic strains are the independent variables. To determine c44 we consider an arbitrary exy strain, produced, for example, by an ultrasonic transducer, and calculate the equilibrium values of ax, ay and az. This exy strain can be visualized as a shear wave polarized in the x [100] crystalline direction and propagating in the y [010] direction. In the following we: (1) assume b2-> bl, and (2) introduce the effect of an external field applied along x, such that the moment is nearly parallel to x (ax = 1). For this case, the total energy expression [eq. (2.4)] becomes ~(eyz + ezy ) + elastic t e r m s in exx.6) T h e equilibrium v a l u e a~.MAGNETOSTRICTIVE RARE EARTH-Fe2 COMPOUNDS 571 55 5O 45 ErFe2 1300K) 35 6 ErFe2177K1 30 q o 0 Z 0 4 3 HoFe2 (T/K) ILl Z O .2 (2Kj + M H ) 2 xy.~ 0 2 DyFe2 (T/K) 10 ~ ¢~: (T/K) C.-~K ) 0 5 10 15 20 25 MAGNETIC FIELD H (kOe) Fig. -o -5 HoFe2 ( :.5) From they a eq = 0. 34. eyr and e~.7) .(a2a~+a2a2+ eq 2 2 .H M a x + b2axOtyexy + ! ~o_2 Otzax) 2t.~. Magnetic field d e p e n d e n c e of the m o d u l u s change (EH(taken f r o m Klimker et al. b2 (7.44exy eq 1 0 eq2 eq2x + b2(aya~ey~ + a~axezx) + 2c. it f o l l o w s (to l o w e s t order) (7.q can be a p p r o x i m a t e d f r o m eq. 1974). (7. (7.5) using the relation2 = 1 -C~y.4) T o d e t e r m i n e the equilibrium v a l u e s of cti. 2 (7.. it f o l l o w s that o~eq eq = xa y 2 K I + M H e~y. Eo)/Eo of the RFe2 c o m p o u n d s E=K. the torque is s e t equal to z e r o . F r o m the z c o m p o n e n t o f the t o r q u e . c o m p o n e n t . 2 Thus ship: c~x ot~q = 1 1 2 1 1 b2 e2 .2 0% = . 3Dy0. which are in excellent agreement with the static measurements reported in section 3. (7.]\I+ I~H/2K.e. eq.E.i. 35.10) is valid for Hll shear polarization. H must be replaced by H + 4.10) 2K1 + MH" b2. The change in modulus is of the same order as 6 4 2 [ 5 I 10 H (kOe) I 15 I 20 25 Fig.3 x 109 erg/cm 3 and K1 = . In fig. H as measured by Cullen et al.3 × 106 erg/cm 3. In fig. l/(ch-c.4) E=~(c44 2Kt~MH)e2xy-MH.c°-c~= c°( 1-K~(K.c~) -1 vs. magnetic field for Tb0. H.9) becomes 1 Ac44-. Here H is applied parallel to the shear polarization. (7./Ki. i.)" minimum c44 occurs when Kj = I 2 2b2/c~. (7. the reduction in the intrinsic modulus is . Equation (7. (1978) in Tb0. The large b2 has a profound effect on c44 and the corresponding sound velocity.rM.9) The at the condition of magnetic isotropy (Ki = 0). 1978). In terms of the measured anisotropy. where eddy currents play a significant role.3Dy0. Note that in metals. p.TFe2.9) it is possible to determine both b22 and Kt graphically. For the c44 mode.e. For the case of H _1_ p.572 A.TFe2 (taken from Cuilen et al. there is no magnetoelastic effect to lowest order (ax = 0) and the elastic modulus c44 remains stiff. .8) For large of the modulus can almost be complete. the effective elastic constant is c _c o 1 0 b2 (7. the softening (7. 35 is plotted (c ° .~) vs. K i.5 5 % . the coupled (HIIp) and uncoupled (H _1_ p) moduli are plotted vs. CLARK Substituting for axeqay eq and for ag q into eq. They find Ib21 = 2. From eq. The reciprocal of the difference in shear modulus. 36. The coefficient of ½ex2y. (7. p. Thus by rotation of the magnetic field. Experiments on Tb0.~ P IfH \ C44 . 1978).0 i (C!rC12)/2 .7Fe2by Rinaldi et al. the modulus itself. Shear moduli c~ and ½(cll.) Note that c ° >½(cll. Ultrasonic echo patterns taken for fields at various angles. (1977) are given in table 11. 0. the elastic anisotropy can be nullified and even inverted.cn) for Tb0.c n ) > c ~ at low fields.. magneticfield strength. Experimentally. the (degenerate) shear mode in the isotropic polycrystal breaks up into two modes. the coupled modulus is higher than the uncoupled modulus. the modulus rises smoothly from the lower strongly coupled value to the higher uncoupled value. Here. 36.?Fe2vs.7Fe2 by Rinaldi et al. Elastic isotropy can also be achieved for lower fields applied along intermediate directions. for this case. In contrast. The magnetic field was applied parallel and perpendicularto the shear polarizationdirectionP (taken from Cullen et al. The uncoupled elastic constants as measured ultrasonically on Tb0.MAGNETOSTRICTIVERARE EARTH-Fe2COMPOUNDS u. with respect to the direction of polarization of the . In-depth studies of the magnetoelastic behavior of the shear moduli and the sound velocity have also been made in the polycrystalline RFe2 compounds at room temperature. one polarized normal to the field and the other perpendicular (Cullen et al. (1977) have shown that as a field H is rotated from H H P to H _l_p.'. 2 5 10 15 20 25 H(kOe) Fig. with the application of a very low applied magnetic field. 1978).3Dy0.u I I I I 573 PIN 4.3Dy0. the ½(c11-c12) mode. for which the appropriate magnetoelastic coupling is bl. Thus elastic isotropy can be achieved with H[Ip at a sufficiently large applied magnetic field. instead of a continuous change in shear modulus with field direction. (In fact. has a small magnetoelastic contribution. two independent sound modes propagate whose intensities depend only upon field direction.3DY0. This cannot be attributed to the lowest order magnetoelastic effects considered above. (1977.27Dy0.87 DyFe2 TbojDyo.70 4. unpublished). The magnetic field dependences of both shear waves were measured in polycrystalline Tb0. Echo pattern for shear waves propagating perpendicular to the applied field H in amorphous TbFe2. Two clearly separated modes 2nd ECHO l ][ 3rd 4th ECHO ECHO I II ] II 0 =90 c 75 ° 60 ° 45 ° 30 ° 150 0o t Fig. a single train of echoes is observed with those for 0 = 0° reflecting the slower velocity. The changes in the amplitudes of the peaks as the angle 0 between the direction of H and the polarization is varied indicate the presence of two normal modes with polarization parallel and perpendicular to H (taken from Cullen et al. CLARK TABLE I 1 Elastic constants of R Fe2 compounds* (x 10-" dynes/ cm 2) CI1 I(Cl1 -- Cl2) C~4 4.TaFe2. For 0 = 0° and 90°. 1978).89 3.THo0jFe2 and amorphous TbFe2 (a-TbFe2) by Cullen et al. At intermediate angles. .81 * Taken from Rinaldi et al. The isotropy of the amorphous sample with respect to shear waves is broken by the magnetoelastic coupling. are shown in fig. a superposition of the two patterns is observed.574 A.1 3.E. (1978) (see fig.ssDy0aEFe2. 37 for amorphous TbFe2.TFe2 14. 37. indicating the simultaneous propagation of two shear waves. Sm0. impinging sound wave. Sm0. c44 is a strong function of field. 38).58 14. c~4 denotes the pure (uncoupled) elastic modulus (see text). 12Fe2.. as well as the crystal symmetry. In a magnetostrictive system with b~ and b2 non-zero.ooO' eoOOOOOOoOOW I I o00 eO I to0400ore 1... The velocity of the slow modes could not be saturated even at 25kOe.8 I ~ ~ 1..3Dyo.6 /o ° js I E G 1. determine the normal modes. were obtained.4 OOeO 1.MAGNETOSTRICTIVE RARE EARTH-Fe2 COMPOUNDS 575 2"2f(a ) ++.. may not occur. By plotting the velocities of the fast mode vs.THoo./~0.0~ f~ * I tl _. The magnitude and direction of the applied field. H plots are given in table 12. 1978).71 0 | ========================== i . In the preceding single crystal work it was assumed that b 2 ~ bl. 1. • H J_p) in (a) Tbo. Sound velocity as a function of applied field H for H parallel and perpendicular to the polarization p (O HI[p. (b) Smo. the intrinsic (uncoupled) elastic shear moduli.3Fe2 and (d) a-TbFe2 (taken from Cullen et al.TFe2. 38..2: )o o° I I I 1 ./(d) 1.4 2. the customary break in the shear degeneracy by the cubic crystal symmetry into the well known normal modes with polarization along the crystalline axes.+++~+++++++++++++~ 2.0 (C) ooooQeoooOOOOOeeOO i I I eo0o4ooo4.6 t • • ooOOoo° Oo oO oOO I oo. . However. 1.. The values obtained in this way. along with the values of bp calculated from the slope of (/~0_/~)-i vs. I/H. were observed. . i L 5 10 15 20 APPUEDFIELOH (kOe) l 25 Fig. (c) Smo. b~ 4 0 .agDyo. • . This pulling of the polarization away from the crystal axis has been demonstrated in Tb0.TFe2 Smo./z0 in 1011dynes/cm2 and bp in 109 ergs/cm.9 0. the expressions for the shear velocities and moduli as a function of field angle 0 and magnitude H are given by Rinaldi and Cullen (1978). In fig.3 1. Magnetomechanical coupling of RFe2 compounds Because of their large magnetostriction the rare earth-Fe2 compounds have potential as high power transduction elements.3Dyo.THo0.E. /~0.4-[(l(C q.C ' ) 2 q . b~. for polycrystalline RFe2 at room temperature (Ms is in emu/cm3. For the general case of b~ # 0 and b 2 ~ 0 . and magnetoelastic coupling.576 A. 3 x 109 ergs/cm 3 and assuming b~ = 0. If B = 0.73Fe2.2 . 0 is the angle of the applied field with respect to the [001] direction. the field angle 0 for Tb0. (1978).9 b~ 1. When B ~ 0 . 8.C ) +. For propagation along [1]0] they find I) 2+~_ ½(C + C t) .12) where • is the angle of the polarization with respect to the [001] axis. CLARK TABLE 12 Uncoupled elastic moduli.b ] cos 20/HMsp C .4 3. taking b2 = .1b2.3Fe2 a-TbFe2 Ms 780 360 145 390 ~o 4. In this section the low signal linear properties of these compounds will be examined. Note that the large change in ~ occurs over a small change in 0 near 0 = 4 5 ° for H = 8 kOe.)* RFe2 Tbo.3 3.C) 2 + B 2)112] (7. (1978). 39 are plotted the values of • and v vs.ssDyo.27Dy0.3Dy07Fe2 by Cullen et al.b ~ sin 2 OJHMsp (7.12Fe2 Sm0.5 * Taken from CuUen et al.11) B = bib2 sin 0 cos O/HMsp. the two conventional transverse shear waves are polarized a l o n g [100] and [110] directions with velocities C 1/2 and C '~/2. = I 2(cll o _ c°2)]p .4 0.(~(C' .B2] 1/2 where C = c°~[p .5 2. the polarization is determined by the strength of B according to the following expression tan 4+ = B/[½(C' . . (8. defining the permeability at constant strain /~" and the compliance at constant induction s ~ (blocked conditions). stress and magnetic field (see for e x a m p l e Berlincourt et al.3 577 2.d21sHI~T)I~ T SB = (1 -. p e r m e a b i l i t y / ~ r and coupling d through the following equations = sliT + dH B = d T +l~rH. (8. the orientation of the magnetization for [110] propagation in Tb0.2a) (8. B. T and H symbolically r e p r e s e n t c o m p o n e n t s of the strain.The magnetization is in the (110) plane at an angle 0 from the [001l.d2[sHI~T)T + (d]l~T)B. Eliminating T and H respectively f r o m eq. the fraction of stored mechanical (elastic) energy which can be c o n v e r t e d to magnetic energy.TFe2. F o r a m a g n e t o m e c h a n i c a l vibrator with no loss or radiation.2 . (8. or c o n v e r s e l y .8 30 ° 0 00 10 ° 20° 30 ° 40° 8 500 60 ° 70° 800 90 ° Fig. Calculated dispersion and direction of polarization of one of the shear normal modes vs. k 2 denotes the fraction of magnetic energy which can be c o n v e r t e d to mechanical (elastic) energy per cycle. 1964).4) in t e r m s of moduli c ~ l/s (8.k2)Ea = k2Em~. it follows that /~" = (1 .o.9 o x :> 1.1b) H e r e ~. 1978).1a) (8.d 2 / s n l ~ r ) H e = sU(1 . (8.1) B = (dlsU)~ +/~T(1 -. 39.1 0 ~. k. Writing eq.4) . 2.3) (8.3Dyo. The single m o s t i m p o r t a n t low signal transducer p a r a m e t e r is the magnetomechanical coupling factor. magnetic induction. 2.0 1. T h e relation b e t w e e n k 2 and the conventional linear properties of a m a g n e t o m e c h a n i c a l l y coupled s y s t e m can be obtained startir/g with the definition of the compliance s H.d21sHI~T)s H.2b) Thus.MAGNETOSTRICTIVE RARE EARTH-Fe2 COMPOUNDS 2. H = 8 kOe (taken from CuUen et al. For a mechanically driven s y s t e m (1 . the permeability is reduced f r o m its intrinsic value /z r w h e n e v e r energy is transferred to the elastic system. .H.. Likewise.~t.r .d2/SI-ItZT)CB. whereas Qy. Qz. the quality factor at constant voltage drive. Q factor and relative permeability/t.E.- s-~ = (8.5 110 100 0. The m a x i m u m fraction of magnetic energy which can be t r a n s f o r m e d is ~/x n 1 Trr2 .6) Similarly the m a x i m u m fraction of elastic energy which can be t r a n s f o r m e d is ~C e -. i 5000 i0 0. 40.c. F o r a torroid k33 = k. 1. Energy is transferred w h e n e v e r the m o m e n t is rotated f r o m its equilibrium value by an applied stress. f.578 Cn = (1 -.3Dy0.7 0. 50 . includes both mechanical and electrical losses. is reduced to a lower value c ~ when energy is transferred f r o m the elastic to the magnetic system.4 0. quality factor Q and permeability/~ for Tb0. i~ T ~ d2 kZ" 12l ~ TH 2 (8.3 ~r 90 80 70 60 0.2 50 40 30 20 .' . (1975) to determine the complex i m p e d a n c e for the low permeability RFe2 alloys as a function of frequency. of Tb0. e 1 B_2 I. e U 2 ~LT --/X~ . . c B. . The m a g n e t o m e c h a n i c a l coupling k33.3Dy0. A successful method was developed by Savage et al.~/~ 11 .2 cB _ C H = de k2" 12CBe2 = . A material coupling factor k33 is defined which is g e o m e t r y independent.5) In effect.?Fe2as a function of bias field. includes only mechanical losses (taken from Savage et ai.TFe2 calculated this w a y are shown ' I ''"1 ' ' ' I ~'~1 ' ' 0. the quality factor at constant current drive. 100 500 I 1000 . At constant strain the m a x i m u m energy is stored in the elastic system. . Coupling factor k33. the intrinsic (uncoupled) elastic stiffness. 1975).7) The magnetomechanical coupling k is conventionally obtained b y measuring the c o m p l e x i m p e d a n c e of a coil containing the magnetostrictive material. . A. CLARK (8. for a slender rod k33 -= ( w / X / 8 ) k .1 BIAS FIELD (Oe) Fig.6 i150 140 130 120 0. and the other microscopic. neglecting loss terms k 2 = 1 . Above technical saturation. i 4000 Fig.t = (cn/p)lie/. from eq. 41 are plotted the resonant and antiresonant frequencies of a 10 cm thin rod of Tb0. Note that the permeability is low.g. a necessary consequence of a highly magnetostrictive polycrystal. as seen in fig. 1975).7).(fn/fB)2. allowing the storage of energy in the magnetic system.~Fee (taken from Savage et al. I 17 14 i-- C O K ~ ' T ~ "CONSTANT FIELD 12 11 ~ i 1000 . I i i . in a highly magnetostrictive polycrystal both fa and f n depend strongly upon applied magnetic field. due to the atomic interaction between the magnetic moment and the local strain field within the domain. This induced redistribution due to the pressure field causes a reduction in the modulus.8) Also. BIAS FIELD (Oe) i 2000 . In most conventional materials. The change in fB and f u with magnetic field reflects the moduli change (AE effect) discussed in section 7. . one macroscopic. Resonant frequency (at constant induction and constant field) vs.TFe2 driven magnetically. (8. The resonant frequency differs from the antiresonant frequency at each bias field by an amount related to the coupling. the bar executes motion at frequency f n = vn/. Thus.jDy0. At resonance (maximum change in magnetic induction with fixed magnetic drive H). The amount of rotation depends upon the externally applied field and ' I . 41. due to domain wall motion. The Coupling factor is high when the field is between 100 and 500 Oe. bias field of a 10 cm bar of Tb0. r 3000 .t = (CB/p)I/2/A. The domain free material at technical saturation is stiffer. e. 41. The change can be divided into two parts. Ni. an externally imposed elastic stress rotates the moment slightly from its aligned condition.3Dy0. L whereas at antiresonance B executes minimum oscillation and the bar vibrates at fB = vB/. (8. the major contribution arises during the magnetization process by a redistribution of the domains.MAGNETOSTRICTIVE RARE EARTH-Fe2 COMPOUNDS 579 in fig. In fig. 40 as a function of magnetic bias. It is solely magnetoelastic in origin. 42. Eddy current losses. . become important for high frequency applications. _ 0. x for the ternary Tb~-xDyxFe2 and Tb~-xHoxFe2 alloys.5 I 0.0 Fig. Timme 1976).3 0.6 I ~ I I I - 0. calculated from f n for Tb03Dy0. In table 13. 1975.6 for Tb0. In fig.26Dy0.xRxFe2 I 0. . is much larger than that of Ni and Fe. The modulus and AE effect at constant field.E. are listed the magnetomechanical coupling factors for a number of rare earth-Fe2 materials along with those of a few typical magnetostrictive materials.. Further increases in k33 are observed in the quaternary TbxDyyHozFe2 system. c a. 42.6 x-~ I I 0. With the addition of DyFe2 and HoFe2 to TbFe2. At room temperature. its value. while comparable to that of the rare earth elements. which exist in metallic transducers.74Fe2 and k33 ~ 0.2 0.7Fe2 is plotted in fig. The largest coupling factors are found in grain oriented RFe2 alloys. The increase in modulus is about 150%.44 for Tb0. the values of k3a increase to a peak k33 = 0.2sHo0.9 1.:sFe2. In fig. Only when the magnetic system is blocked (H-~oo) is it possible to keep the energy totally within the elastic system and obtain the stiff modulus.7 0. CLARK any magnetocrystalline anisotropy. for Tbl-xDyxFe2 and Tbl-xHoxFe2 (taken from Savage et ai. k33. 0.5 k33 - o. 43 electrical resistivity measurements for TbFe2 are plotted as a function of temperature. 33.8 Tbl. k33 is plotted vs.7 0.5~ A. Magnetomechanical coupling. o Ferebee and Davis (1958).62 0.1620 .lsHoo. R h y n e e t al.35 0.73Fe2(oriented) 0. unpublished.~TFe2(oriented) Tbo. W h i l e t h e i n t r i n s i c a l l y h i g h m a g n e t i c a n i s o t r o p y o f t h e r a r e e a r t h p e r s i s t s to r o o m t e m p e r a t u r e .31 0.59 0.5% Ni (NiO)o. e)Yamamoto and Nakamichi (1958).73Fe2 Tbo.22HOo.53-0. L i k e t h e a n i s o t r o p y . T b F e 2 h a s a l a r g e u n s a t u r a t e d m a g n e t o s t r i c t i o n a n d D y F e 2 h a s a s p o n t a n e o u s . k)Timme.4 0 0 K .o27 (FeO)o.MAGNETOSTRICTIVE RARE EARTH-Feq COMPOUNDS TABLE 13 Maximum magnetomechanical coupling factor and magnetostriction kss ~q~ x 581 106 Am x 106 -23 8 160 -40 - Reference a. (1977).sFe2 Tbo.61-0. h)Savage and Clark.2100 -. 4 5 in a m o r p h o u s TbxFe~-x.35 0. c e.12Fe2 Smo. T h i s is a t t r i b u t e d to t h e c o m b i n a t i o n o f high a n i s o t r o p y a n d t h e a b s e n c e o f c r y s t a l s t r u c t u r e .1370 710 1620 h h i i i i h j j k h a)Bozorth and Hamming (1953). l a r g e m a g n e t o s t r i c t i o n s a r e f o u n d in t h e a m o r p h o u s s t a t e ( C l a r k 1973).o3Fe2 SmFe2 Smo. f g Ni 13% AI 87% Fe 5 0 % C o 5 0 % Fe 4. w h i c h is c o m p a r a b l e to t h e l a r g e s t m e a s u r e d v a l u e f o r S m . 0 Clark (1956).60 0. unpublished. c d.60-0. Consequently coercivities of only ~100Oe are observed at room temperature. A m o s t s t r i k i n g f e a t u r e o f t h e s e a l l o y s is the l a r g e c o e r c i v i t y a t l o w t e m p e r a t u r e s ( C l a r k 1973.66 0. C u r i e t e m p e r a t u r e s r a n g e f r o m b e l o w r o o m t e m p e r a t u r e t o .ssDyo.36 -51 70 30 -30 - TbFe2 Tbo.sDyo.35Hoo. (1978) h a v e r e p o r t e d m a g n e t o s t r i c t i o n s g r e a t e r t h a n 2 0 0 × 10 -6 f o r 0 .27Dyo. b)Hall (1959).9j3(CoO)o.7Fe2 a n d D y F e 2 a r e s h o w n in fig. 1972).3Dy0.27Dyo.35 0.ssFe2 Tboa9Dyo. T h e m a x i m u m e n e r g y p r o d u c t c a l c u l a t e d f o r a m o r p h o u s T b F e 2 at 4 K is 29.51 0.C o a l l o y s .23Dyo. J)Savage and Clark (1977).74 - 2450 1840 1620 1130 820 810 .5 x 106 G O e .5% C o 95.76 0. o See Davis (1977).o~(Fe203) 0. o Savage et al.23Hoo.2oDyo. Tb0. t h e t h e r m a l e n e r g y is t o o h i g h to i n h i b i t m a g n e t i z a t i o n reversal. T h e r o o m t e m p e r a t u r e m a g n e t o s t r i c t i o n s o f a m o r p h o u s T b F e 2 . 2 5 < x < 0 .sFe2 Tbo.35 0.7Hoo. 1974). a) Hall (1960). 9.42Fe2 Tbo. 44.55 0.c b.51 0. F o r e s t e r e t al. Amorphous RFe2 alloys S p u t t e r e d a l l o y s o f c o m p o s i t i o n R Fe2 a r e b o t h s t r u c t u r a l l y a n d m a g n e t i c a l l y a m o r p h o u s ( s e e R h y n e e t al. 500 . 240 260 2~ 300 50 40 30 Tb Fe 2 20 10 . 200 . unpublished).. 200 100 ~ ~ _ .582 A.- r . CLARK TIK) 60 160 180 . Tb0.~Fez and DyFez at room temperature (taken from Clark 1973. 220 .- l i l l 400 z 300 ~ ~ TbFe z 0 1"b.. . I 100 120 140 ~g. . 43.3Dy0. 0 I 20 . I 40 i I 60 i l 80 TIK) i I ~ I .7Fe2 00y Fe 2 .3 Dy .i. Resistivity of ~ 2 vs. see Clark 1 ~ . Magnetostriction of amorphous TbFez. temperature (taken ~om Sav~e. .E. 44.o loo[-5 10 15 20 H (k Oe) 25 Fig. the magnetostriction of amorphous DyFe2 increases rapidly with decreasing temperature (fig. ) derive their magnetostrictive effects from the large anisotropic 4f charge density of the R 3÷ ions. for amorphous DyFe2. . unpublished). .< 3O0 x 2OO 100 I I . The strong magnetoelastic coupling also manifests itself in huge magnetically 800 I I I I I 700 DyFe2 AMORPHOUS 6OO 500 "~ . Thus in polycrystailine materials.tm/A~001-> 1) characterizes many of these compounds. An unusual magnetostriction anisotropy (I. Similar to the RFe2 compounds. . Summary The RFe2 alloys (R = Sm Tb .and ferrimagnetic cubic materials. . the highly magnetostrictive amorphous alloys can also exhibit a large forced magnetostriction at room temperature. Unlike crystalline DyFe2.oo . 45). the large intrinsic zero temperature magnetostriction is preserved more-or-less intact up to room temperature. Tc > r o o m temperature.. I I T ('K) Fig. The high anisotropy of the 4f electron cloud and high Curie temperatures lead to huge cubic magnetocrystalline anisotropies at room temperature as well as large magnetostrictions. where dMdT < 0. the magnetostriction and magnetomechanical coupling is strongly dependent upon crystailite orientation. I0. This difference is accounted for by the difference in Curie temperatures.R exchange interactions.MAGNETOSTRICTIVE RARE EARTH-Fe2 COMPOUNDS 583 magnetostriction near zero. For amorphous TbFe2.. In TbFe2 and DyFe2 the anisotropy is over an order of magnitude larger than that of conventional ferro. temperature (taken from Abbundi and Clark. Because of strong Fe-Fe and F e . Tc < room temperature. Magnetostriction of amorphous DyFe2 vs. 45. J. one function in the strain space and the other in the space of the magnetization. (a) Cubic: Al/l = A ~ ' ° + A~'4{0~4-t" 0~4-t. The proper expression for the magnetostriction for a particular symmetry can be determined by taking the direct product of the basis functions of the same irreducible representation. Tamagawa and K. can be synthesized to exhibit a wide assortment of magnetic properties."L 4 22[ax+ 4 + a ~ _ 3d .S. Using orthogonal functions has the advantage that the coefficients of the lower order terms do not change as higher order terms are added. Callen.R. Special thanks are due to E. Williams. The author is particularly grateful to N. R. whose assistance made this chapter possible.2 / 32 . Because of the cubic symmetry of the Laves phase RFe2 compounds (unlike the hexagonal heavy rare earth elements).5~ A.g.C. the coefficients of these terms possess characteristic temperature dependences (Callen and Callen 1963). the lowest order anisotropy and magnetostriction possess different sign sequences as R is changed from one element to another. Thus pseudobinary RFe2 compounds. Aa00and A111. Acknowledgements The author would like to thank his many co-workers: H. (Bell 1954). They are derived from the cubic and hexagonal basis functions of table 1. C.2{~2/~2+ ~ . the integrals vanish for l' > 6. For th"e rare earths. In addition. This huge "AE effect" reflects the IAm/Alool> 1 anisotropy.4~ . but are also orthogonal. Timme and A. within first order perturbation theory we can expect terms to exist up to sixth degree. J. (4f[ Vc[4f). Expressions for the magnetostriction and magnetic anisotropy to sixth degree in the direction cosines of the magnetization are given below.E. Belson. E.Otx4_ 5} 6 { OL2 4"}[ a " xOL 2 ya 2 z ~.E. Koon. where R is composed of various rare earths. Cullen. Abbundi for critically reading the manuscript. Abbundi. e.M._L ay 10d +A.~[~x+ 1 4 a4+ ~4] 6 2 2 2 2 . where l = 3. + ~ /23 z .2 2 . the required integrals are of the form: J" ~4fV~ g'4f dO.. N.J. R. Callen and R. While in many cases it is possible to fit the experimental data with the lowest order magnetostriction constants. Appendix A: Magnetostriction and magnetic anisotropy of cubic and hexagonal crystals In computing the crystal field matrix elements for the rare ~ r t h ions. Savage. CLARK induced moduli changes. In this way magnetostriction and magnetic anisotropy expressions are generated which not only manifestly reflect the crystal symmetry. Sato.T. Miller for many valuable discussions and for permission to include their work prior to publication.W.3 ~} + x 7• + ~ /43 ~ 4 {~x/3~ 4 2 + a . Rhyne. H. ~ +{A2a.l l t t z + ~ ] a x O t y f l x f l y +C. Aioo=]A "2 and Am = ~A"2....+ 4 2 15a]ot~.0tyi~y + CItZ~ z 2 2 ..}. of section 2 (see Callen and Callen 1963).I.3(~x+ a ~ + ~D] 2 J..P..~." 4 ~ 2 _t_ .)/3zfly}..~_~ -Jr-/t 2' I. 4..76~ 3.2+x... 4 .231/ 6 .6' ( a ~ 2 4 6 2 1 5 a x a y .} + It ~_.~2 t o ~ .t..s ) .0 ~laz+ 33)} +x~'{~z~A~-lO~+5~4)~. h .76__2_t_-.3[a..~.15a~a~+ + h 2a.~.10s}. N o t e for l---2.15 4 .1)+~..(~.2 6~ 2 l t t t z .. (b) Hexagonal: A I / I = { A ~ .71)a~ay3~By+ C. + ayO~zl3yl3z+ a~d3~#A + A"4{(a~ .t3.O~ + ~_ lOot~ay ~ ~+ a ~..~.6 { a : % a z ... + a6 A3~.6'(01~6__ 15Og4xO~2q_ 1 5 0 t x2 a4 y .t~x + o.6-2 1..t 2 2.. ~ta6: 6 15~. {/~ y.~ K ~'~ and K2 = K ~'6.4/^.13x~.P.- + K.I I ( 0 t x p x "1." + x ~...~... + o~] 1.~ .ffZ A I ~ ...6J'F~.4 tl..1 1 ( a x a y + aya~ + a z a x . o + ~ .$_ 2 ~-~1} IlO~z "~ 110~ z .P. ~. [. .ii[~x3x + ay/3y + z#z .6'{016 15ot~ot. 2 2 2 J- 2 2 2 2 2 2 1 _1_ The conventional cubic anisotropy constants KI and/(2 are related to the s y m m e t r y constants by Kt = .5.2 (a~-3)+.:+ o:.la IlOtz llOt~z./~+~:.(~z_b+ .x"2{~xO~.~ 22 22 "].} +.Oty)}/3~ %6 4 (ax .~( a ~ .~-~ 1. K ~.._ X y.~ 2 2 3 a~ay]a~y[3d3y + C.i l t t z .6{0/6 .. 4 ( a 2 __ 7~ ) +x +.K a'4.~'(~_ ~)} 2 +s(~_6~+ ~ 2 +{x.6'{[a~+ a y4 .O +A2a.I. Appendix B: Temperature dependences of magnetostriction and magnetic anisotropy for single-ion models The magnetostriction and magnetocrystalline anisotropy of a magnetic system derive from spin operators which have the functional form of the basis functions found in table 1.. t ' I Z .31)} + .Ot 6 y ) } ( f l x2 + / 3 y )2 2 1 ~ a..)} + {~ .4~ 5 2 _.IzT35-P a 6 (or: 6 2 +AI" 4 "1.. 2 .a~+~)} .a~}.~... 4 2 4 2 4 .)(:~. Ea = K a ' 4 {axay+ 2 2 2 2 11 2 z + OtzO£x-O/yOt 5[ +K a.MAGNETOSTRICTIVE RARE EARTH-Fe2 COMPOUNDS 585 +a %6 6 2 6 2 2 1 6 {. Ot~z . The temperature ..5__ 231) .llCt z 7.. 525J(J + 1)J~ - for I = 2.6 J ( J + 1) + 3 J : ( J + 1)2) + 294J~ 5J3(J + 1)3 + 40J2(J + 1)2 .) ~ I9/2(x) --.E. spin waves. 46.J ( J + 1))-~ fs/2(x) = (3/x 2 + 1) .30J(J + 1)Jz 2 + 25Jz 2 . [1312 vs.0 •6 m A 2 0 Fig. random field approximation. these averages can be expressed in terms of the moment (Jz) itself. In the limit of large J.60J(J + 1)). C L A R K dependences of these quantities depend upon the thermal averages of these operators over the allowed energy states. Thus a calculation of temperature dependences require the quantum statistical averages of such quantities as (Stevens 1952) (J~-J(J + 1))..l / x + ctnh x = m (J~z . These (single-ion) theories include not only molecular field theory. the normalized magnetization. in the molecular field approximation. .e.(31x) ctnh x (35Jz4 • • . these averages take the simple form of the following hyperbolic Bessel functions (J~) --> ~ ( x ) = .586 A.( 1 0 5 / x 2 + 4 5 l x + 1) - (105/x 3 + 10/x) ctnh x A 15t2 10"1 19t2 10"2 A 10"3 113/2 1o ~ 10-5 / 1. ! = 4 and I = 6 respectively. Normalized hyperbolic Bessel f u n c t i o n s [sl2. Callen and Shtrickman (1965) have shown that for a large number of theories of ferromagnetism. other Green's function decoupling) in which the quasiparticle levels are equally spaced and ordered like Jz quantum states.315J(J + 1)j4z + 735J~ + 105J2(J + 1)2Jz ~ . but those collective excitation theories (i. (35J 4 . Ign and m. and (231J 6 . and H. C 1-672.. Hamming. Appl. and R. Rev. Bowden. and M.R. Van Stapele.B. Rev. Atzmony. Buschow. and S. D. 1964. A. Nikitin. Ferromagnetism (Van Nostrand. S. B7. R. and S.N. Proc. 1939. G. 1968. and H. 1965.) I. Clark. E. S. The parameter "x" can be eliminated from these relationships.E. 1976.M.S. B. E. 89. 1788. Clark. . 1971.R. C (Proc. C 1-675. In fig. 5. Met. J. 578. 1970. Rev.. (by W. O. Angew. La Forrest. Mod. Munich. Belson.. Naval Surface Weapons Center. 1969. VA 22448. Callen. Rev. Clark. 1973. Pshechenkova. • Kim. Phys. I. 1971.P. E. E. J. 311. U. Taratynov. D. Jaffe. Phys. 1977. Tech. Savage. B13. Becker. D. Proc. 18 (American Institute of Physics. Clark.M.E. A455. 1973. D. Mag.(11-945[x 5 + 1210/x 3 + 21Ix) c t n h x. E. Bauminger. Callen. Phys. Proc. Rev. Phys. E. DeSavage.) --> f13/2(x) ~-. 50. Callen.. AIP Conf. Guimares and R. H.S. R. Bunbury. Physica 86-88B. Lett. Bell. Clark. Williams.. Mag.. J. Curran and H. 41. 155. IA.E. 1977.F. Rev. A. Appl. IEEE Trans. Phys. I9/2 a n d f~3/2 a r e p l o t t e d vs. Offer. 100. 129. New York) p. Lett. Belov. 11. and H.E. 4066. Lehenhaum.. Phys. de Physique 32. 3565. A. CaIlen. yielding express i o n s o f t h e f o r m fl+l/2[~-~(m)] f r o m w h i c h eq. Rev. 1979.J.. V. Clark.I. 1951. Shtrickman. M. Dariei and G. Mason ed. and A. N.V. T h e h y p e r b o l i c B e s s e l f u n c t i o n is a g o o d a p p r o x i m a t i o n f o r t h e h e a v y r a r e e a r t h i o n s w i t h l a r g e J.(11 "945/x 6 + 47251x 4 + 210Ix 2 + 1) 587 . 1015. Appl. IEEE Trans.P. Phys. St. 865.C. Phys. LeMaire. P. R. Siaud and J. 50. Bozorth. 1671. AIP Conf. W.. Dublon. Callen. no. 1977. Center.B. and V. Clark. Oak Ridge) p. No. K. 1376.A. New York). 1974. 32. Sept. Yelyutin. R. 3.D. Int. G. Appl. 4006. Chikazumi. and A. on Mag~netism ICM-79. 46. Rev. Physical Acoustics.P. E. Katayev. Atzmony. Clark and N. Phys. Phys.. Dariel. USA. Schweitzer. Surovaya. Charap. 972. Rev.. 11th Rare Earth Research Conf. 39. J. Koon. t h e r e d u c e d m a g n e t i z a t i o n . A. 1953.3) a n d eq. 1975. Physik 52. 26. Berlinconrt. 1954. and W. Bozorth and B. Phys.) (Academic Press. Phys. 1964. Atzmony. (U. 3642... Abbundi. Barbara.W. Bargouth.G.E. A.1) f o l l o w d i r e c t l y . R. 127. 1963. New York). A. New York) p. R. Buschow. 99. Phys. Tilden. Van Stapele. Burzo. and H. Akulov.A. Also Proc.A. J.C. MAG-8. Z. is/2. Ferromagnetismus (Springer. F r o m this figure t h e t e m p e r a t u r e d e p e n d e n c e s o f t h e m a g n e t o s t r i c t i o n a n d a n i s o t r o p y c a n b e d i r e c t l y r e l a t e d to t h e t e m p e r a t u r e d e p e n d e n c e o f t h e e m p i r i c a l l y d e t e r m i n e d m a g n e t i z a t i o n . Bozorth. 4220. Callen and H. L. 1971. J. 5 (American Institute of Physics. 1519. The temperature dependences found in this way are independent of the details of the magnetic model. Also NSWC/WOL/TR 78-88. 1498.E.T. New York). R. Soc.E. Will. A l l e x p r e s s i o n s a r e n o r m a l i z e d to o n e at T = 0 K . and R. (5. Callen.. V. 389. BS. Snyder. (4. and G. Phys. INF. D. Clark. Z. 1928. Giraud. 1963b. 1975. and A. Phys. 1965. 139. 642. Berlin). D. Dariel. G. Bozorth. Physics of Magnetism (Wiley. Dahlgren. Doring.B. Phys. Phys. M. K. R. Abhundi.P. G.. and R. 34.E. Conf. K.. BI5.P. 1978.I. J. Appl. A. on Sonics and Ultrasonics SU-22. J..E.MAGNETOSTRICTIVE RARE EARTH-Fe2 COMPOUNDS (231J6z. Metallogr. MAG-13. 1296. B. 1972. m. J. Solid State Comm. Solntseva.. Nowik and S. S. 49. DeSavage. R. IEEE Trans.M. M. Phys. de Physique 32. 1979. References Ahbundi. 1955. 1963. Phys. A. 477. Coleman. 50. Abbundi and W. p. A. Tamagawa and E. 574. 49. Holland and K. N. Appl. Tohoko Univ. R. Clark... and S. K... J. J.. J. 816. Phys. Clark. Phys. Watson.C. MAG-11. 1974. 1936.D. IEEE Trans.C. no. Williams and F.. 1952. and W. J. J.W. Cullen and K. Gschniedner. Blessing. Sci. 1965. and H. College of Liberal Arts. K. 1976. 42A..E. Cullen. Stevens. Sato. J. Powers. Handbook on the physics and chemistry of the rare earths. G. Belson. no...H. 169. Legvold. Hottman. 136. Dariel. Ferebee. Freeman. 10. AIP Conf. 1976. Koon. J. Phys. Acoust. 37A. J. Proc. Schindler and F. 51. Proc. 1977. 1962. J.. Adv.. J. A.E. Masiyama.. Carter..J. 1978. 45. Taylor. A. 50. Crys. A. eds.N. A. Y.. IEEE Trans. Koon. Lett.E. Callen and N. 551. Alstad and J.R. Savage. 1958. 376. 1978. Keilig. Rev. 138. New York) p. 1973a. England. Conf. R. Clark and J. Proe. D. Clark. New York) p. Alperin. B15.. See K. 335. 4672. Klimker. 254.E. 22.. 1948. MAG-13. Sept. Phys. Rev. Belson. Rev. 29 (American Institute of Physics. Gillmor. Kittel.A. Also Phys. 7. Rosen. on Rare Earths and Actinides. Physica 86-88B. 1973. 2791. Phys. Lett. 1973. 542. and L. Pickart and H. E. Also NRL Rel~ort 8064. J. A. 24 (American Institute of Physics. Phys. Rhyne. Williams. Atzmony and M. no.. J. S.. C.E. 551. Wijn. AIP Conf. Amsterdam). Proc. B9. Proc. Abbundi. R. 160. 355. Keffer. 1965. Florida. CLARK Report 8137. NRL . Klimker. 2058. Rev. J.M. Schindler. 3677. Moscow. 1955. 2968. Acta. A. 1963. 19. Soc. Washington. 160S.. Schelleng and N. B30. Lubitz. and R. 151. Callen.A. 1976.. N. Naval Research Laboratory. Clark. J. Appl. A. 5389. 1975.588 A.. Phys. Phys. Phys. and C. 1977. DeSavage and R. Milstein.E. K.. C. Koon. 413. Rev. Cullen.. Lett. Mag. J.E.F. A. 1977.. 670.E.. Rhyne. 1949.V.E. 1966. Phys. Blessing. M. TMS-AIME 218. Phys.P. BI0. S. H. Koon. U. 59.C. 1956. 1960. 1960.P. 1966. J.E. Soc.R. Angew Phys. F. 1976. McKeehan. Kimball. 1972. Phys. 1967. Adv. Davis. 2366. 1931. Dwight.. L. Rev. AlP Conf. 4510.T. and C. Rep. C. Phys. N. J. 1961.D. N e w York) p. Rev. 747. R. H. Workshop on Magnetostrictive Materials. A. vol. J. Clark. J.R. J. 192. Perthel.G. Phys. 1978. O. IEEE Trans. 1937.) (NorthHolland. 30. 2 (K. Koon and C. Rhyne.E. J. Guimaraes. Rhyne. Sato. Appl. 509.. 1977.. New York) p. A. A. and A.W.. 209. J. Phys. 30. A. 44. 1977.. S. Rev. S. O. New York) p. 1960. Clark. 592.. dissertation. Durham. Phys. Phys. Phys. Phys. Jr. Soc. 18. U. 1971. 465. Am. Tamagawa. Ph. 1311. H. Rinaldi. Dariel and U.C. R.M. G. Rinaldi. 1978. Taylor. H. no. 29. Clark..C. Rev. Hall. Phys. and A.C.M. Forester. Tamagawa.W. N. Clark. Cullen and G. Phys. 29 (American Institute of Physics. 577. M. Elbinger. Trans. Rev.. 1974.. Koon. 1974. Rinaldi and G. Appl. Proc.T.E. Gscheidner Jr.M. 1959. Savage. Phys. Mod. 1562. C..C.A507. Status Solidi 17. J. 930. Ferrites (Wiley. Clark. Callen. McMasters and E. Clark. S. in Physics 20. and C. Conf. 73.. BS. R. Phys. Atzmony. Cullen. 1978.. July 1977. McMasters. Bozorth. and C. N. H... Rev. Pearson. 1517. Rosen. 459. H. Eyring. Brit. Schelleng and P.. Carter. M. 2913. N. Dariel. 1973b. Appl. 21. Shih. O. 1977. 106. Mag. 65. M. 1977. Vittoria. Int. Davis. Klimker. 1974. 10 (American Institute of Physics. B10.S. B. and R. J. 31. 39. Mag. Rev. Phys. Phys. 1971. and J. 49. McMasters and H. S. 1692. Rosen.M. p. Cullen. Appl. Hall. J. Clark. Smit.C.T. Acoust. 127. D. Rev. U. Appl. /kiP Conf. Lett. Williams. 20. 1355. Appl. on Magnetism ICM-73. J. 749. Savage. 61A.F. Rev.. Belson and N. Crystal Growth 43. H. Acoust. 100. C. A. Z. Phys. Am. 268. H. 1978. 1959. Clark. volume IV. Strakna. Naval Research Laboratory. A216. Am.S. 541. Phys. 33. Rhyne. A. 1978. 1974. 1974. R. MAG-14. 20.J. Orlando.. Toyama University 9. Atzmony and M. Savage. Timme. Legvold. Soc. Phys. Williams. 1975. 49. 1971.. H. Lett. Rev. J. Wallace. 3.. Proc. 151. 1975. and N. 3. Int. Prog.E. W. 27. AS. 1965.J. N. BI1. New York) p. 228. Radium 15. Reichel. 589 1964. Yamamoto. 1964. Milstein. J. 1978. of Phys. Koon. 1958. 250. W. V. Physica 8688B. New York). 1977. C. 1978. 1932. 1954. Phys.. Yamamoto. Williams. Sci. and N. A. Solid State Commun.E. Williams. and E. Technol.. J. Jaccarino and J. 1964. Conf. Clark and R. Solids 39. Williams. and Physical Society.. S. 1973. Instrum. 1951. 14. Wernick. 98.. and N. 22. Phys. 4360.E. Rare Earth Research II (Gordon and Breach. Weil. 81. 675. 1968. and T. Wallace. 431. W. M. Tohoku Univ. Phys. Rev. Koon. Phys. 823. Koon and J. L. Williams. Rare Earth Sci. Koon. Williams. Wallace. M.R. and K.. Sci. on Magnetism. C. A135. N. London) p. Soc. C. Miyasawa. Bozorth. 725. J. Nottingham (Inst. Nakamichi. I. Wertheim. Skrabek.. G.MAGNETOSTRICTIVE RARE EARTH-Fe2 COMPOUNDS Tsuya. C. Chem. Phys. J. and R. Rare earth intermetallics (Academic Press. Japan 2. Physica 17. Rev. Rev. Went. . Rep. 520521 annihilation operator 197 antiferromagnetism 348. 327. 203 621 band structure 307. 264-266. 325. 323.507-514 compensation in rare earth compounds 561 compositional 510 constant strain. 45. 331. 311. 200. 80. s e e electrical resistivity core losses 518-523 correlation in metals 13 corrosion resistant coatings 453 Coulomb interaction 12 Coulomb term 197 creation operator 197 critical exponents 28. 199 conductivity. 559 mono-atomic directional 524 in rare earth compounds 311.SUBJECT INDEX actinides 415 activation energy for crystallization 478-479 alloys of rare earths 243. 499 bernal model 477 Bloch functions 206 Bohr magneton 188.312. 515. 104. 317.344. 203 calorimetry 469 centrifugal quenching 462 chemical bonding 482 chemical clustering 75 chemical deposition 460 chemical disorder 467 cluster glass 73. 126. 510. 51 . 501. 50. 268 angular momentum orbital 188 spin 188 total 188. 482 boiling points of rare earths 186 Born-Oppenheimer approximation 198 bottleneck effect 103. 345. 344 critical field dependence 318 coercive force 514-517 coherent potential approximation 335 coherent scattering domains 469 collinear spin structure 340. 329.341. 382 compositional anisotropy 510 compositional inhomogeneities 454 Compton profile 64 computer simulations 138. 119. 455. 515 strain induced 514 annealing 454. 197 amorphous alloys 354. 329 compensation point 342. 382 antiphase domain 236 applications 523-525 apw (augmented plane wave) 198. 132 Brillouin zone 199. |03. 318. 113. 517. 82. 364. 315. 356 band theory 482. 510. 345 in rare earth-Fe2 compounds 557 single-ion temperat~e dependence 585 strain-magnetostriction 454. 150 conduction electrons 185. 134. 581 anisotropy 38. at 540 diatomic directional 511 directional order 511 exchange 514 local 507 magnetic 507-514 magneto-elastic contribution 540. 133. 29. 203 Arrhenius plots of crystallization 478 atomic volume of actinides 421 of rare earths 186 augmented plane wave (APW) 198. 87 coercitivity 314. 194. 341 commensurability 326. 79. 39. 262 of rare earth-Fe2 compounds 580 electrical transport 424 electrodeposited 453. 241 crucible melt extraction 465 crystal field 185. 341. 151. 81. 323. 125. 15. 8 diatomic directional ordering 511 diffusion 456 directional order anisotropy 511 directional order kinetics 512-514 directional order relaxation 481 disordered alloys 360 dispersion relation 500 distances (interatomic An-An) 424. 5. 125. 121. 122. 525 crystal structure 302. 188. 520 elastic constants 46 elastic moduli magneto-elastic softening 572 rare earth compounds 567 electrical resistivity 51. 331. 317 walls 314. 460 electroless deposition 460. 234. 329. 24 Debye temperature of Dy 226 of Er 235.622 SUBJECT INDEX structure 314. 225 critical point 240. 19.476--481. 502 electrons delocalized 417 5f 418 itinerant 418. 78. 137. 229. 7. 238 of Y 259. 246.253 of Pr 247 of S m 256 of Tb 220 of T m 236 Eddy current loss 518. 319. 98-100. 307 for Er 210 for Pr 210 for rare earth compounds 298. 105.205. 323.) of rare earths 189. 429. 108. 317. 431 displaced hysteresis loops 79. 364. 193 Curie temperature 1I. 74. 470 of Ce 242 of Dy 225. 55. 226 of Er 234 of Eu 214 of Gd 217 of Ho 230. 255 of Pr 249 of Sc 259 of S m 256 of Tb 222 of T m 237.514 wall pinning 514 double piston 461 double roll casting 464 drum casting 463 dynamic response of domain walls 515 AE effect 514. 260 of Yb 259. 317. 192. 90-94. 216. 197. 58. 244. 382. 208-210. 266. 97. 118 divalent 187. 579 easy magnetic direction 185 in rare earths (table) 189 of Dy 224 of Er 234 of Gd 216 of Ho 228. 102. 262 of Lu 260. 396 of rare earths 186. 123. 107. 229 of Nd 251. 231 of La 261 of Lu 259. 568. 103. 84. 146. 252 Curie-Weiss law and constant 12. 362.315.344 point charge model 307. 225. 313. 330. 317. 16. 121. 249. 331 crystallization 469. 243. 476-480 activation energy 478-479 arrhenius plots 478 stability 455. 268 delocalised electrons 417 density 455. 260 of Nd 253. 262 of Sc 260 of Sm 257 of Tb 222 of Tm 238 of Yb 260 degeneracy 208 de Gennes factor 188. I00.203 domains 505-507 • dynamic response 515 . 14. 339 wall motion 314. 438 localized 418 critical field 220. 433. 325. 16. 152. 113. 113. 23. 470-473 of rare earths 186 density of states 4. I09. 323.524. 152. 201. 115. 187 of actinides 419 Curie points (T. 144. 134. 237. 319. 236 of Eu 215 of Gd 219 of Ho 232 of La 260. 192. 363. 248. 193. 140. 151. 197. 141. 5. 352. 317. 123. 139. 149.SUBJECT INDEX electron diffraction 457.206 Hall effect 53. 104.146. 87. 19. 330 filament casting 463--465 first order transition 329. 313 indirect 185. 332. 83 623 g-factors 34. 123 hard coatings 453 hard magnetic materials 344 heat capacity. 152 ferromagnetism in rare earths 185 field emission 61 field induced transition 226. 313. 7. i12. 90. 349 electron spin polarization 304. 313. 6. 57. 304. 351 4f conduction electrons 304. 335. 337. 190. 334 induced moment 339. 120. 351. 82-85. 206 for Eu 204 for Gd 201 for La 202 for Tm 207 for Yb 205 ferromagnetic resonance 103. 340 form factor 329 free jet spinning 466 freezing temperature 78. 314. 335. 356 3d conduction electrons 334. 332. 327. 120. 124. 83-85. 335. 213. 48. 91. 317. I!0. 117. 319 Land6 g-factor 34. !17. 91. 15. 128. 118. 75. 27 high pressure 337 Hund's rules 185 Hund's rule interaction 12. 134. 82. 324. 23. il8. 96. 228. 313. 329. 9. see a l s o exchange 190 helical ordering 185. 119.205. 324. 332. 199. 354 . 514 biquadratic. 188 Gennes. 313. 347 interaction energy 511 interference function 468 interlayer turn angle 219. ! 1 Fermi surface 4. 90. 224 intermediate valence 313. 307. 205. 320. 9. 242. 336. 350 internal friction 514 irreversibilities 79. 80. 345. 6. 8. 334 magnetic semiconductor 313 RKKY 77-79. 152. 333. 350. 122. 201. 7. s e e specific heat Heisenberg exchange. 316. 110. 132. 113. 201. 438 Jahn-Teller effect 323. 132. 340. 89. 346. 339. 147. 355 Kondo effect 73-75. 305. 325 enhancement 82-85. 418. 330. 125. 332. 121. 192. 121. 8. 138. 63 5f electrons 418 Fermi-Dirac statistics 10. 102. 352. 121. 332. 354. 128. 35. 188 lanthanide contraction 187 lattice constants of rare earths 186. 146--151 gun quenching 460 Hamiltonian 190. 139. 98. 5. 326. 266. 199 for Eu 204 for Gd 200 for La 202 for Yb 205 energy levels of Eu 199 of Gd 199 entropy 96-98. 79. 190. 356 electron paramagnetic resonance 103. 87. 433. 424 splitting 4. 468 electron donor character 454 electron microscopy 469 electron negativity 299. 340. 112. 62. 197 excess magnetic moment of Gd compounds 263 exchange anisotropic 316. 81. 107. 187 lattice distortion 314. 198. 145. 324 liquid state 25 local anisotropy 507 local environment effects 345. 55. 117. 148. 268 generalized susceptibility 191 Giant moments 73. 88. 335. 206 helimagnetic order 346 high magnetic field effects 26. 122. 316. 102. de-factor 188. 197. i16. 137. 85. 89. 355. 136. 148. 152 frustration 79. 137.355. 322. 327. 307. 322. 88. 35. 133. 109. 16 hydrogen absorption 359 hyperfine fields 22. 339. 192. 135 itinerant electrons 10. 197. 104-110. 340. 14. 339 Embrittlement 455 energy bands 4. 337. 105. 87. 99. 505 hysteresis loss 518 impurity scattering 206 indirect exchange see also exchange 185. 201. 304. 335. 331 Knight shift 306. 304. 89. 272. 91-93. 219. T1 431 intermetallic 433 Laves phases 439 metamagnetics 440 plumbides 431 pnictides 429 silicides 431 stannides 431 ternary 433. 87. 540 for Er 289 .for Pr 290 . 364. 247 of Sm 256 of Tb 220 of Tm 236. 124 magnetostriction 35. 138. 118. 124. 278 of Y compounds 272. 382. 121. 216 of Ho 228. 98. 584 equations 285. 20. 281. 273. 253 of Pr 246. 281 of La compounds 243.353 magnetic families 424 Magnetic moments. 234. 142. 355 long range magnetic order 80 losses 518--523 core loss 518-523 Eddy current loss 518. 285 magnetic entropy 197 of Dy 226 of Er 235 of Eu 215 of Gd 219 of Ho 232 of Sm 257 of Tb 222 of Tm 238 magnetic dilution 316. 36. 229. 82. 126. 283 . 584 magnetization compensation. 21. 276. 345 of rare earth compounds 533 f magnetomechanicai coupling of rare earth compounds 576 magneto resistance 82. 281. 520 hysteresis loss 518 temperature dependence 524 L-S coupling. 225. 277 of Nd compounds 276. 28.283 of Lu compounds 272. 195. s e e Magnetization magnetic ordering of compounds 425 anti-ferromagnetic compounds 442 borides 421 carbides 432 chalconides 427 germanides 431 with Ga. 279283 of Yb compounds 269-271 spin dependence 192. 193 table for rare earths 189 magnetic phase diagram. 277 of Tb compounds 274-278 of Tm compounds 274. 34. 354 local moments 304. 278. 42. 382 magnetic semiconductors 313 magnetic stability 524 magnetic structures 364. 279. 271-274 of Ho compounds 274. 102.for Tb 287. 84. 434 magnetic ordering temperature of Ce compounds 243 of Dy compounds 274. 82. 540 - localized electrons 418 localized spin fluctuations 74. 112. 339. 63. 119. 277. 109. 507-514 constants 2~. 501-504 cubic crystals 539.494 of Dy 189 of Er 233 of Eu 213 of Gd 215. 284. 114. 351. 229 of Nd 251. 221. 237 of rare earths (table) 189 of rare earth-Fe2 compounds 552 magneto-caloric effect 51 magneto-elasticity 43. In. s e e spin-orbit coupling magnetic anisotropy 194. 110. 282 of Eu compounds 269-271 of Gd compounds 263-266. 122. 276. s e e susceptibility magnetization 19. 121 local moment formation 336. 211 magnetic susceptibility. 27.624 SUBJECT INDEX of Sc compounds 272.. 283 of Pr compounds 276. 104. 482-. 152. 110. 102. 286 giant 219 hexagonal crystals 539.for Gd 287 for Ho 288 . 217. 324. 280. 143. at 548 rare earth-iron compounds 540 f single-ion temperature dependence 585 symmetry modes 539 table of coefficients 286 temperature dependence of coefficients for Dy 288. 329. 278-280 of Er compounds 274. 96. s e e magnetic ordering temperature magnetic phase transitions 329. 109. 117. 195. 285. 105. 152 operator equivalents 209 optical properties 56 orbital angular momentum 188 overlap of f-bands 625 pair correlation function 467 paramagnetic curie temperature. 228. 487 moleculair field model 138. 339. 504-505 intermetallics 321. 151 inelastic 317. 344. 109. 354. 242-244. 267 piston and anvil 461 planar spiral 195 plasma jet spray 463 plasma losses 64 positive muon depolarization 85.SUBJECT INDEX magnetothermal effect 314. 128. 137. 17 melt extraction 465 melting points of rare earths 186 melt quenching 460 metallic radius of rare earths 186. 34 neutrons polarized 324. 126. s e e a l s o rare earths compounds 186. 101. 103. 251 of rare earths (table) 189 neutron diffraction 211. 353 magnon 196 magnon dispersion relations 316 of Dy 227 of Er 235 of Gd 218 of lip 230. 151 permanent magnets 344 permeability 517-518 phase diagram 241 phase separation 456 phase transition crystallographic 324 electronic 324 field induced 324. 357. 348. 326. 328. 329. 326. 137. 132. 30. 467. 87. 357. 114. 344. 319. 345. 87. 458. 329 see also photoemission spectroscopy. 358 N6ei point 121. 151 positron annihilation 64 preparation techniques 421. 133. 113. 82. 347. 102. XPS 57 f phonon 196 physical properties of rare earths. 345.457-466 centrifugal quenching 462 chemical deposition 460 crucible melt extraction 465 double piston 461 double roll casting 464 drum casting 463 electrodeposited 453.346 metamagnetic 320. 131. 143. s e e susceptibility Pauli paramagnetism 185 pendant drop melt extraction 465 percolation limit 73. 125. 324. 340 mictomagnetism 73. 329 techniques 29. 102. 103. 187. 330 hell-ferromagnetic 321. 130. 326. 128. 137. 220. 356. 317. 345. 358 transition metal compounds 344. 328. 344. 84. 346. 127. 332.355 nuclear orientation 101. 324. 358 rare earth compounds 321. 356. 468 on Dy 224 on Er 233 on Eu 213 on Gd 215 on Ho 228 on Nd 251 on Pm 254 on Pr 249 on Sm 255 on Tb 219 on Tm 236 neutron scattering 106-108. 106.102. If4. 360 magnetovolume effects 352. 354. 79. 357 Knight shift 306. 333. 357. s e e Curie temperature paramagnetic susceptibility. 80. 150. 325. 221. 355 relaxation 327 spin echo 329. 494. 134. 236. 149. 440. 460 filament casting 463--465 free jet spinning 466 gun quenching 460 melt extraction 465 melt quenching 460 pendant drop melt extraction 465 piston and anvil 461 plasma jet spray 463 ribbon casting 463--465 . 314. 80. 146. 152. 142.224. 190. 322. 351. 231 of Tb 223 many body effects 15. 354. 499 mono-atomic directional ordering 511 Mfssbauer spectroscopy 98. 340. 345 NMR 101. 187 metamagnetism 323. see also magnetization 188. 142. 20. 501. 329. 323 small angle X-ray scattering 454. 89. 332. 121. 83--85. 117. 228 of Er 235. 552 transition metal 334. 382.510. 87. 112. 87. 319. 106. 143. 138. 114. 193. 146. 109. 139. 128. 14. 87. 78-80. 148. 345 in rare earth-Fe2 compounds 561. 61 preparation techniques ( c o n t ' d ) roll casting 464 rotary splat quenching 462 splat quenching 454 torsion catapult quenching 462 vacuum deposition 458--459 pressure effect 43. 134. 117. 245 of Dy 226. 326. 113. 76. 140. 223 of Tm 238 of Y 260 spectroscopic state of rare earths 189 spin densities 34 spin disorder resistivity 264 spin fluctuations 16. 213. 151 spin orbital momentum 188 spin--orbit coupling 185 spin polarization 185 spin polarized photo'emission 60 spin reorientation 329. 149. 520-521 crystallization 469. 396 magnetomechanical coupling 576 magnetostriction 533 f magnetization 189 f. 236 of Eu 214. 64. 113. 113. 128. 337. 314. 500 splat quenching 454 sputter deposition 459 stability 455. 125. 17. 260 of Sm 257 of Tb 222. 496 on N6el temperature 265 on magnetization 488--491 probability distribution 113. magnetic and electrical properties 439 specific heat 47.626 SUBJECT INDEX singlet ground state 185. 122. 137. 112. 91. 120. 100. 150 quenching 208 quadrupole interactions 324 quadrupole splitting 505 radial density 191 radial distribution function (RDF) 467 RAPW (relativistic augmented plane wave) 198. 382 amophous transition metal 354 relaxation 119. 476--481. 145. 138. 118 remanence-to-saturation ratio 517 residual resistivity 206. 329. 55.562 spin wave dispersion coefficient 500 spin waves 11. 364. 143. 455. 134. 136. 21. 143. 149. 205 ribbon casting 463--465 rigid band model 482--484 RKKY. 31. 150. 349 of Ce 244. 98. 339. 19. 467 soft X-ray spectroscopy. 351. see electrical resistivity reviews 186. 476--480 diffusion 456 directional order 512-514 embrittlement 455 magnetic 524 phase separation 456 stress-relief 454 structural relaxation 456. 139. 149. 202. 121. 198. 246. 23. 266 resistivity. 30. see also exchange 77-79. 335. 215 of Gd 219 of Ho 232 of La 262 of Nd 253 of Pr 249 of Sc 259. 424 roll casting 464 rotary splat quenching 462 samarium structure 187 saturation magnetization.355. 104. 482--491 saturation magnetostriction 501-504 scaling 87 short range order 313. 141. 315. 317. 94-96. 115. 525 annealing 454. 15. 82. 29. 439 spin glass 73. 121.524. 152. 195. 515. 118. see also XPS 60 solid solutions. 131-134. 117-126. 517. 17. 89. 311. 87. 203 rare earth compounds anisotropy 557 elastic properties 567 intermetallics 297. 330 single crystals production 422 single ion anisotropy 221 . 107. 119. 121. 362. 18. 480--481 Stoner criterion 14 Stoner energy gap 5.491 on Curie temperature 265. 97. 142. 136. 135 relaxation time 205 remanence 79. 469. 112. 304. 342. 213 X-ray analysis 457. 10.517-518 of Ce 243. 321 anomalous magnetostrictivily induced 564 thermoelectric power 55. 469. 100. 132. 515 stress induced order 514 stress relief 454 structural anisotropy 510 structural relaxation 456. 81-83. 9. 152. 14 Stoner model 10 strain-magnetostriction anisotropy 454. 135. 12. 330 transuranium elements 420 tunnelling 61 ultrasonic experiments 125. 88-92. 134. 27. 151. 93. 467. 126 vacuum deposition 458--459 variational treatment 198 volume magnetostriction 44 wave-vector 197 weak moments 73. 191. 349. 12. 112-118. 32. 107. 510. 480--481 structure of amorphous alloys 467--481 structure collinear 429 superconduction compounds 321. 29. 322. 83 wear resistant coatings 453 wigner-seitz radius 190 work function 64 (X-ray photoemission 6Of. 136. 24.487 superzones 206. 197 transition metal compounds 382. 94. 423 superconduction transition temperature 268 superparamagnetism 87. 25. 359. 322 thermomagnetic history 117 total angular momentum 188. 468 Zeeman energy 190 XPS spectroscopy) . 123. 139-141. 137. 351. 74. 124. 221 surface diffusion 456 susceptibility l I. 133. 131. 109. 13. 317. 244 of Dy 225 of Er 234 of Eu 213 of Gd 216 of Ho 229 of La 258 of Lu 258 of Nd 252 of Pr 248 of Sc 258 of Tb 221 of Tm 237 of Y 258 of Yb 258 627 temperature dependence of losses 524 of magnetization 497-501 of permeability 524 tesseral harmonics 209 thermal expansion 45. 26. 128. 319. 144-148. 125. 98.SUBJECT INDEX Stoner excitations 11 Stoner-Hubbard parameter 4. 396 transport properties 313. 132 AgNi 75. 420.77. 243. !14. 115. 125. 80. 21. 487 Co-P-B-AI 471. 81 CuCr 75. 490. 382. 49. 493. 513 Co-Ni-P-B-AI 489. 494 Co-Ni-Si-B 489. 127. 81. 19.81 AgFe 75. 396. 629 63. 81 AuV 75. 58. 399 Be-R 326. 492. 77. 81 . 81 AgV 75. 116 AuCr 75. 468. 508 CoUSez7 436 Co-V 495 Co-V-P-B 488.81. 498 Co-Pd-Si-B 489. 116. 420. 396 CrUS3 436 CrUSe3 436 Cu 206 CuCo 75. 423 CmAs 430 CmN 430 Co 3. 558 Co-Mn 495 Co-Mn-P-B 495 Co-Ni 488. 382 Ce-Ternary compounds 357. 136. 420. 20. 420. 125.81 Ag-R 323. 303. 501. = non-magnetic metal. 513 Co-Si 483. 366. 367. 488.92. 375. 142 AuMn 75. 135. 126 CuMn 75. 492 Co-Au 454 Co-B 490. II.479. 45. 34. 490. 41. 375. 495 Co--R 334. 399 AI-R 314. 77. 77. 81 CuFe 75. 137. 81.81. 113.476. 365.R 323. 495 CoFe204 542. 357. 23.MATERIALS INDEX *R = rare earth metal~ M. 118. 494. 420 AgCo 75. 14. 133 AuNi 75. 8. 81. 503. 12. 115. 29.81 AgMn 75. 120--122. 115. 123--131. 423 AmFe2 438 AuCo 75. !13. 492 Co-Si'-B 477. 81. 39. 471. 268 Ce-Tb 275 Ce-M. 125. 398 Am 418. 53. 48.503. 244.43. 81 A u .8 ! AgCr 75. 75. 80. 27. 503 Co-Cr 495 Co-Cr-Si-B 489. 82. 478. 423 Cd-R 330. Md = d-transition metal Ac 418. 141. 35. 376. 136. 483. 52. 460.36. 115. 128-132. 498 Co--P 454. 513 Co-Cr-P-B 488. 81. 495 Co-Ni-Fe-P 460 Co-Ni-P-B 493. 487. i16. 137 CuNi 75. 423 Cm 418. 126 AuFe . 81. 396 Cf 418. 508 Co-P-B 486. 499. 132. 397 B-R 312.364-381 Ce-Md 334. 381 Ce-Gd 275 Ce-La 242. 542 Co-AI 483. 77. 377 Bk 418.84 (CuNi)Fe 84 C u V 75. 44. 364-381 Er-M~ 334. 488. 487. 489. 498.490. 188. 479.272.Fe. 490.502. 364. 521. Er 499. 547. 40. 516 Fe-Co-Si-B 471. 63. 501 Fe-Ni-P-B-Si 471. 495 Fe-Cr-P-B 488. 503. 212. 32. 491. 489. 483. 29. 505. 420 Eu 184.23. 494. 496.. 515. 493. 520 Fe-Cr 488. 30. 517. 519. 276-280. 505. 489. 491. 525 Fe-Ni-B-Si 489. 490. 490. 288. 504. 483. 503.501 Fe-Ga-P 492. 486. 272. 524. 230. 493. 211. 478. 541 Dy2Cov7 542 Dy-Er 264-266. 456. 508. 505. 357. 494. 488. 489. 519 Fe304 542 Fe-P 471. 494. 547. 501. 503.494. 495 Fe-Co--B 473. 503. 208. 503 Fe-Ni-Cr-P-B 471. 276. 486. 504. 498. 497. 523. 503.479. 522. 559. 34. 397. 509. 53. 513.44. 493. 524. 504.513. 492. 382-395 Eu-Ternary compounds 357. 509 Fe-Mn 495 Fe-Mn-P-B 488. 58. 498. 501. 199. 515. 488. 493. 495 Fe-Co-P-C 471. 508. 553. 489. 280 Dy-M. 493. 494. 569 ErFe3 542 Er. 486.~ 542 Er. 12. 502. 497. 497 Fe-P-B 485. I I. 47. 520. 487. 224-228. 490. 480.486.. 14.480. 509. 509. 272-274 Er-Ho 264-266. 508. 474. 479. 514. 519. 479. 264-269. 396-399 Es 418. 489. 509. 490. 490. 475. 574 DyFe3 542 DyzFei7 542 Dy--Gd 264-266.512. 471.399 Deltamax 522 Dy 184-195. 278 Er-Tm 266. 279 Dy-La 268 Dy-Lu 266 Dy-Tb 264-266.46. 487. 19. 494. 514 Fe-P-B-AI 471. 519. 474. 189. 364.493. 278 Dy-Y 279. 504 Fe-P-B-C 471. 6. 501. 382-395 Dy-Ternary compounds 357. 498. 503.523 Fe-Ti-P-C 480 .483. 43. 496 Fe-Mn-P-C 480 Fe-Mo-B 471. 519.475. 494. 272-274 Dy-Ho 264-266. 495.474 Fe-Ni-P-B-AI 470. 188. 495.523. 381 Dy-Md 334. 503. 62. 498. 396-399 184-186. 501. 484. 493. 508. 501. 45. 542 Fe-AI 483. 509 Fe-B 474. 478. 507. 212-215. 490. 490. 511. 239. 569. 273.479. 509.502. 520 Fe-P-C 454.279 ErFe. 39. 520 Fe-Co-Ni-P 503 Fe-Co--Ni-P-B 501 Fe-Co-P-B-A! 478. 274.. 264-269. 186. 303.630 MATERIALS INDEX Cu-R 303. 239. 495. 519 Fe-Si 456. 502. 514. 364-381 Eu-Md 3~4. 222. 521. 21. 303. 513. 517. 513. 495. 499. 519.Fet7 542 Er-Gd 264-266. 500. 27. 52. 517 Fe--Co-P-B 487. 471. 396.. 493. 473. 517. 483. 496 Fe--Cr-P-C 480. 36. 199. 192-194. 501. 503. 508.502. 48. 478. 396--339 Fe 3. 7. 542. 264-2269. 506.493 Fe-Ge-P 492. 199. 468. 554.502.490.472. 480. 203. 509 Fe-Ge 490. 498. 486. 502. 280. 282 Er-Y 282 Er-Mn 303. 279 DyFe2 542. 501. 509. 35. 489. 477. 20.474 Fe-Mo--P-B-AI 470 Fe-Ni. 189. 475. 479. 281 Er-La 268 Er-Lu 266 Er-Tb 277. 492 Fe-As-P 492. 504. 512. 382-395 Er-Ternary compounds 357. 209-212. 516 Fe-Ni-Co 513 Fe-Ni-P-B 469.. 502.496. 520. 519. 517. 492. 268-27 ! Eu-La 268 Eu-Yb 269-271 Eu-M.. 37. 525 Fe-C 469. 511. 480. 509. 525 Fe-Ni-P-C 474. 516. 520. 498. 498. 277282 Er2Cot7 542 Er-Dy 264--266. 503. 492. 487. 49. 233-236. 508. 508. 513 Fe-Ni-B 473. 483 Fe-Co 488. 492. 488. 83. 215. 189. 274 Gd-Y 262-264. 397 Hg-R 331. 271. 272-274 Ho-La 268 Ho-Lu 266 Ho-Tb 277. 238. 268. 84. 285. 272. 382-395 Lu-ternary compounds 357.364-381 Lu-Md 334. 221. 396-399 Ge-R 319. 268. 271.212.364-381 La-Md 334. 188-193. 281 Ho-Y 281 Ho--Mn 303. 272-274 Gd-Er 264-266. 559. 283. 206. 272-274. 372. 378 Mn-P-C 468 Mn-R 334. 206. 364-381 Nd . 258. 199. 569 Gd-Ho 264-266. 201. 382 Ho-Ternary compounds 357. 195. 382-395 La-ternary compounds 357. 272 Gd-Sm 275 Gd-Tb 264. 188. 278 Ho-Tm 266. 364-381 Ho. 275. 271. 84 (Mol-xPdx)Fe 170. 188. 569 HoFe3 542 HoFe23 542 Ho2FeI7 542 Ho-Gd 264-266.272 Lu-Ho 266 Lu-Tm 266 Lu-Mn 303. 277 Lu-Dy 266 Lu-Er 266 Lu-Gd 262-264. 396 Hydrides-R 359 631 In-R 319. 236. 368. 239. 286. 280. 258.239. 188.MATERIALS INDEX FeU2Ss 437 Fe-V 488. 257. 276 L a C e 242-244. 171. 242. 83. 271. 208. 222.381 Ho 184--186. 211. 170 MoMn 75. 284 Nd-Pr 283 Nd-Tb 275. 219. 275 Gd-Lu 262-266. 382-395 Gd-Ternary compounds 357. 281 HoFe2 542. 266. 271. 275 La-Ho 268 La-Nd 268. 547. 83. 265. 257. 276. 303. 198-202. 272-274 GdFe2 542. 388. 192-195. 276 Nd-M. 201. 211-219. 266. 268 La-Dy 268 La-Er 268 La-Eu 268 La-Gd 262-264. 394 184. 495 Fe-V-P-C 480 Fe-R 334. 398 MoCo 75. 261-264. 268. 397. 396 Ir-R 349. 264-269. 244.272. 271-276. 271-273 Gd-Yb 262-264 Gd-M.272. 269. 283. 284 La-Sm 268 La-Tb 268. 275. 272-274 Gd-Th 262-264 Gd-Tm 266. 280. 272-274 Gd-La 262-264. 84 MoFe 75. 172 184-186. 554. 232. 397. 239. 262-269. 189. 189. 271.334. 186. 276 Nd-Gd 275 Nd-La 268. 226. 272. 390. 275. 271. 260-264. 396-399 Lr 418 Lu 184--186. 188. 240.202. 228-232. 303. 276 La-Tm 268 La-Yb 268 La-M. 268. 396-399 La Md 418 Mg 262-264 Mg-Gd 262-264 Mg-R 326. 398 Fm 418 Ga-R 317. 217.272 Gd-Mg 262-264 Gd-Nd 275 Gd-Pr 275 Gd-Sc 262-264. 251-255. 279 Ho-Er 264-266. 396 Gd 184-186. 288 Ho-Dy 264-266. 284--287 GdAI2 120 Gd--Ce 275 Gd-Dy 264-266. 83 MoCr 75.364-381 Gd-Ma 334. 369. 277-281. 303. 112. 88. 468. 290 Pr2Cot7 542 Pr-Gd 275 Pr-Nd 283 Pr-Tb 275. 83. 83. I01-103. 37. 165 PdNiCo 101 (PdNi)Fe 84 Pd-Ni-P 472 PdRh 112 (Pdl_xRh~)Co 173 (Pdj_xRhx)Fe 85. 173. 102. 27. 103. 102. 52. 31. 101. 149. 29. 101. 382-395 Pr4ernary compounds 357. 84 PtFe 75. 396. 148. 499. 170 Pt-Ni-P 472 Pt-R 349. 83. 32.475. 43. 90. 107-110.239. 109. 103. 145. 471. 11. 88. 240. 20. 40. 94-98. 112. 23. 133 Pd-Mn-P 472 PdNi 84. 188. 98. 240. 133. 39. 145. 161-164 (PdMn)H~ 85. 97. 479. 21. 153-155 . 101.373 PdAg 112 (Pd~_xAgx)Co 171 (Pd~_xAg~)Fe 85. 167-169 PtFeMn 174 PtMn 75. 201. 110-112. 105. 469. 146. 35.239. 101. 113. 498 Ni-R 334. 394. 48. 392. 85. 34. 110. 25. 399 No 418 Np 418. 148. 112. 142. 396 Pu 418.Cu . 14. 149.-148. 106. 166. 517. 152 (Ni3_~Gal+x)Fe 84. 120. 44. 396-399 PtCo 75. 478. 145. 83. 101. 173 Pd-Si 454. 364-381 Pr-Md 334. 111. 275. 88. 100-108. !10.478. 59. 133. 88. 133 PdFoMn 172 PdMn 75. 490 Ni-V 495 Ni-P-B 487 Ni-Si-B 477. 91. 171 (Pdl_~Agx)Mn 171 (PdAgRh)Fe 172 PdCo 75. 478. 133. 53. 133. 149. 472 PdSnCo 101 Pd-R 349. 542. 174 (PdI_~PL)Fe 172. 90-94. 36. 396 Permalloy 456. 97. 91. 83. 145. 103. 522 Pm 184. 56.152 Ni-B 460 Ni--Cr 495 NiFe2Ot 542 Ni-Mn 495 Ni-P 460. 19. 276 Pr-Mn 303. 104.Si 472 PdFe 75. 82. 88. 420 Pb-R 321. 96-98. 420. 479. 84. 186--189. 45. 518. 4. 420. 110. 167 PtCoFe 174 PtCr 75. 149 (Pdl-xCux)Co 172 Pd . 246-250. 479 Ni-P-B-AI 471. 101. 12. 101-103. 423 PuAs 424 PuAsSe 436 PuAsTe 436 PuBej3 442 Nd-Md 334.632 MATERIALS INDEX PdCoFe 172 (PdCo)Hx 85 PdCoNi 172 PdCr 75. 148. 63. 82. 106. 94. 142. 49. 83. 155-161 (PdFe)Hx 85. 83. 109. 110. 106. 90. 112. 98. 254 Pr 184-186. 106. 111. 396-399 Ni 3. 382. 90. 83. 82. 88. 96-101. 568. 101. 112. 105-110. 57. 423 NpAl2 438 NpAl3 438 NpAs 442 NpAs2 442 NpAsS 435 NpAsSe 435 NpAsTe 436 NpB2 432 NpB~ 442 Np-C 432 Np2C3 432 NpCo2 442 NpF¢2 438 NpIr2 442 NpMn2 438 NpNi2 438 NpOs2 438 NpOs2-~Rux 438 NpP 442 NpPd 442 NpPt 442 NpRe2 438 NpS 442 NpSb 442 NpSn3 442 Pa 418. 105. 189. 581 (Ni3_~AII+~)Fe 84. 109. 382-395 Nd-ternary compounds 357. 107. 169. 82. 128. 148. 103. 266. 280. 209. 262.7~Fe2 563. 547. 574. 225. 420. 364--381 Sm-Md 334. 278 Tm-Y 282. 254-257. 189. 272278. 188. 211. 570. 276. 555. 208. 272-274 Tb--Ho 277. 230. 364-381 Tm-Md 334.379. 188. 84 RhCr 75.239. 83. 84. 276 Th3P4 424 Th3Sb4 424 TI-R 319. 559 TmFe3 542 Tm6Fe23 542 Tm2Fet7 542 Tm-Gd 266.276 Tb--Sc 264. 264-269. 284--287. 83. 285 Tm-Dy 266. 83. 83. 174 RhMn 75. 423 Th3As4 424 ThCo5 438 Th-Fe 345. 278 Tb-Y 264 Tb-M~ 303. 276. 303. 391 184-186. 382-395 Sin-ternary compounds 357. 236--239. 581 Tb-Er 277.MATERIALS INDEX PuD2. 84 RhFe 75.212. 371. 189. 396 Square Permalloy 522 Supermalloy 518. 272. 276. 274 Tm-Ho 266. 522 Sm 184. 278 Tbo. 370 Tm 184. 278 Tb-La 268. 382-395 Tm-ternary compounds 357. 277-280. 396-399 Th 262-264. 231. 240.5 438 .27Dyo. 282 TmFe2 542. 382-395 Tb-ternary compounds 357. 264. 275 SmFe2 542. 276 Tb-Nd 275. 423 UAL2 439 UAs 424. 396 U 418. 275. 211. 541 TbCo3 542 Tb2Col7 542 Tb--Ce 275 Tb-Dy 264-266. 353 Th-Gd 262-264 Th-Tb 275. 420. 192-194.73Fe2 563. 271. 283 Tm-M. 579. 186-189.74 426 PuFe2 438 PuGe2 432 PuH2+~ 426 PuN 442 PuP 424 PuPd3 442 PuPt 438 PuPt2 438 PuPt3 442 PuRh3 442 Pu3S4 442 PuSb 424 Ra 418 RhCo 75. 276. 271. 442 UAs2 442 U3As4 424 UAsS 434 UAsSe 434 UAsTe 434 UBi 442 UBi2 424 U3Bi4 430 UBiTe 434 UCo5. 193. 398 Silectron 518. 568 Tb Sc 633 Tb2Fel~ 542 Tb-Gd 264. 219-223. 210. 281 Tra-La 268 Tm-Lu 266 Tm-Tb 272.399 Ru-R 349. 186. 418. 275. 265.272 Sc-Tb 264. 84 RhNi 84 (P. 276. 391. 276 Tb2Nil7 542 Tb-Pr 275.hNi)Fe 84 Rh-R 349. 266. 276 Tb--Tm 277.27Dyo. 522 184-186. 239. 277 Tb--Th 275. 268. 574. 396-399 Sn-R 321. 279 Tm-Er 266. 192. 199. 364-381 Tb-Md 334. 257-260. 207. 274.373. 264-269. 199. 278 Tbo. 565. 569 SmFe3 542 Sm2Fet7 542 Sm--Gd 275 Sm-La 268 Sm-Mn 303. 277 S i R 319. 266. 581 TbFe3 542. 277 Sc-Gd 262-264. 549. 565. 203. 186-189. 262. 303. 396-399 ZnMn 82 Zn-R 328. 124 Y . 257-259. Luh-xB4 432 VFe 84 VMn 84 184-186. 279-283 YCo3 542 Y2Co17 542 Y-Dy 279. 430 UPb~ 442 UPd4 442 UPS 434 UPSe 434 UPTe 434 UPt 438 US 427. 303. 379. 276. 262-264.634 UCu5 442 fl-UD3 UFe2 438 UGa 442 UGa2 432 UGa3 442 U2Ga3 432 ~x-UH3 fl'UH3 UHg2 442 UGe 432 U3Ge4 432 Uln3 442 UMn2 442 UN 442 U2N3 442 UNCL 435 U2N2Bi 434 U2N2Sb 435 U2N2Te 435 UNi2 438 UOS 442 UOSe 442 UOTe 442 UP 442 Up2 442 U3P4 429. 430 USbSe 434 USbTe 434 USe2 442 UTe 428 U2Te3 442 UTI3 442 Ux(Y. 569 Y3FesOw2 542 Y-Gd 262-264.364--381 Yb-Me 334. La. 396-399 Yb 184. 283 Y-M. 277. 280 Y-Er 282 YFe2 542. 206. 428 USSe 435 USTe 435 USe 428 USeTe 435 USb 442 MATERIALS INDEX USb2 442 U~Sb4 429. 257-260. 268-271 Yb--Eu 269-271 Yb-Gd 262-264 Yb-La 268 Yb-M.271-273 Y-Ho 281 Y-Tb 264 Y-Tm 282. 271273. 267. 364-381 Y-Me 334. 382-395 Y-ternary compounds 357. 380 ZrMn 82. 382-395 Yb-ternary compounds 357. Documents Similar To E.P. 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