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Handbook on the Physics and Chemistry of Rare Earths, volume 20 Elsevier, 1995 Edited by: Karl A. Gschneidner, Jr. and LeRoy Eyring ISBN: 978-0444820143
Handbook on the Physics and Chemistry of Rare Earths VoL 20 edited by K.A. Gschneidner, Jr. and L. Eyring © 1995 Elsevier Science B.V. All rights reserved
PREFACE Karl A. G S C H N E I D N E R , Jr., and L e R o y E Y R I N G
These elements perplex us in our rearches [sic], baffle us in our speculations, and haunt us in our very dreams. They stretch like an unknown sea before us - mocking, mystifying, and murmuring strange revelations and possibilities.
Sir William Crookes (February 16, 1887)
This volume, which completes the second decade of volumes in this series, is focused on physical aspects of metallic compounds. Research efforts on metallic rare earth compounds started in earnest about 50 years ago and received a significant boost with the discovery of the RCo5 permanent magnets about 12 3(ears later. In this time much has been learned about the structure as well as the electrical, magnetic and thermal properties of ~2500 binary rare earth metallic compounds. But considering the possible true ternary compounds, and possible pseudo-binary ternary alloys formed by mixing two binary compounds, we have just begun to scratch the surface of the wealth of knowledge these yet-to-be discovered materials will bring to mankind. The information contained in this volume will be but a few footsteps in our journey to unravel the mysteries hidden in these unknown materials. Hopefully, the four chapters will serve as useful guides in our quest for this new knowledge. The first chapter (135) in this volume, by Onuki and Hasegawa, deals with the Fermi surfaces of rare earth (Y, La, Ce, Pr, Nd, Sm, Gd and Yb) intermetallic compounds. Initially, the reader is introduced to the relevant theories required to describe the electronic behavior of the electrons near the Fermi surface, and then to the basic experimental techniques to study these surfaces. The main portion of the chapter is devoted to a comparison of the experimental results with the band structure calculations for a large number of compounds. The authors have found some systematics in the observed behaviors, and have grouped the compounds into several different classes: i.e. non-4f behaviors, including some cerium compounds; valence fluctuation compounds; Kondo regime materials; and magnetic materials with magnetic energy gaps etc. They also note that the more complicated the crystal structure the larger the discrepancy between theory and experiment. Next, Gasgnier examines the world of thin films of rare earth metals, alloys, and compounds in chapter 136. The three main topics are the pure metals themselves, metallic
vi
PREFACE
alloys and compounds, and metalloid compounds. Many of the metallic elements exhibit a "valence" change when they change from the vapor to solid or vice-versa and this has some strong influences on the physical properties, especially the vapor pressure. Another major problem is the easy way which the rare earth metal films can become contaminated especially by the strongly electronegative non-metallic elements, i.e. H, N, O. The reported results are critically examined by Gasgnier. Included in his coverage are the results on metallic alloy/compound thin films include permanent magnets, R-Ni and R-Co hydrogen storage alloys, modulated and multilayered structures, and superconducting materials. The metalloid films include those with the chalcogenides, bismuth, lead and their combinations. The third chapter (137) in this volume, by Vajda, is devoted to hydrogen in metals and their binary compounds RH2 and R H 3 . One of the critical problems is the purity of the starting rare earth metal itself because phase relations can be greatly affected by impurities. Therefore, Vajda devotes some time discussing the preparation of specimens and the phase diagrams. The interesting structural properties, kinetics and thermodynamic behavior, as well as electronic, magnetic and thermal properties are reviewed. The occurrence of H-H pairs in zig-zag chains along the c-axis in the heavy lanthanides and Sc and Y terminal solid solution alloys is one of the unusual structural behaviors observed in these materials. The formation or annihilation of these pairs lead to some interesting kinetic effects and phase transitions during heating and cooling. Also examined is the profound influence of hydrogen on the magnetic properties by the mediation of RKKY interaction in these materials. The final chapter (138) of this volume, by Gignoux and Schmitt, is an update on the magnetic behaviors of lanthanide intermetatlic compounds. This chapter builds on the review of Kirchmayr and Poldy in chapter 14 of volume 2 of this Handbook series. When one examines chapter 138, it will immediately be apparent that a great deal of science and technology has occurred in the past 15 years in the magnetic behaviors of lanthanide compounds. Gignoux and Schmitt divide their chapter into two main parts: one is devoted to 3d magnetism where both the 3d metal and the lanthanide element contribute to the magnetic behavior; and the second is concerned with lanthanide magnetism by itself. In the first group the major emphasis is on systems which exhibit collective electron metamagnetism. In addition, magnetocrystalline anistropy, and topological frustration and magnetic instability are reviewed. The section devoted to compounds with the lanthanide as a magnetic atom, deals with materials which exhibit metamagnetic processes from different origins. It is found that the majority of these compounds order antiferromagnetically with complex magnetic field vs. temperature phase diagrams. This is due to the long range and oscillatory nature of the RKKY exchange interaction.
CONTENTS
Preface Contents
v
vii
Contents of Volumes 1-19
ix
135. Y. 0nuki and A. Hasegawa Fermi surfaces of intermetallic compounds
1
136. M. Gasgnier The intricate world of rare earth thin films." metals, alloys, intermetallics, chemical compounds . . . . 105 137. P. Vajda Hydrogen in rare-earth metals, including RH2+x phases 138. D. Gignoux and D. Schmitt Magnetic properties of intermetallic compounds
Author Index
425
Subject Index
457
vii
293
207
CONTENTS OF VOLUMES 1-19
V O L U M E 1: Metals 1978, 1st repr. 1982, 2nd repr. 1991; ISBN 0-444-85020-1 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
Z.B. Goldschmidt, Atomic properties (free atom) 1 B.J. Beaudry and K.A. Gschneidner Jr, Preparation and basic properties of the rare earth metals 173 S.H. Liu, Electronic structure of rare earth metals 233 D.C. Koskenmaki and K.A. Gschneidner Jr, Cerium 337 L.J. Sundstr6m, Low temperature heat capacity of the rare earth metals 379 K.A. McEwen, Magnetic and transport properties of the rare earths 411 S.K. Sinha, Magnetic structures and inelastic neutron scattering." metals, alloys and compounds 489 T.E. Scott, Elastic and mechanical properties 591 A. Jayaraman, High pressure studies: metals, alloys and compounds 707 C. Probst and J. Wittig, Superconductivity: metals, alloys and compounds 749 M.B. Maple, L.E. DeLong and B.C. Sales, Kondo effect." alloys and compounds 797 M.E Dariel, Diffusion in rare earth metals 847 Subject index 877
V O L U M E 2: Alloys and intermetallics 1979, 1st repr. 1982, 2nd repr. 1991; ISBN 0-444-85021-X 13. 14. 15. 16. 17. 18. 19. 20.
A. Iandelli and A. Palenzona, Crystal chemistry ofintermetallic compounds l H.R. Kirchmayr and C.A. Poldy, Magnetic properties of intermetallic compounds of rare earth metals 55 A.E. Clark, Magnetostrictive RFe2 intermetallic compounds 231 J.J. Rhyne, Amorphous magnetic rare earth alloys 259 E Fulde, Crystalfields 295 R.G. Barnes, NMR, EPR and M6ssbauer effect: metals, alloys and compounds 387 E Wachter, Europium chalcogenides: EuO, EuS, EuSe and EuTe 507 A. Jayaraman, Valence changes in compounds 575 Subject Index 613
V O L U M E 3: Non-metallic compounds - I 1979, 1st repr. 1984; ISBN 0-444-85215-8 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
L.A. Haskin and T.P. Paster, Geochemistry and mineralogy of the rare earths 1 J.E. Powell, Separation chemistry 81 C.K. Jorgensen, Theoretical chemistry of rare earths 111 W.T. Carnall, The absorption and fluorescence spectra of rare earth ions in solution L.C. Thompson, Complexes 209 G.G. Libowitz and A.J. Maeland, Hydrides 299 L. Eyring, The binary rare earth oxides 337 D.J.M. Bevan and E. Summerville, Mixed rare earth oxides 401 C.P. Khattak and EEY. Wang, Perovskites and garnets 525 L.H. Brixne~ J.R. Barkley and W. Jeitschko, Rare earth molybdates (VI) 609 Subject index 655 ix
171
x
CONTENTS OF VOLUMES 1-19
V O L U M E 4: N o n - m e t a l l i c c o m p o u n d s - I I 1979, 1st repr. 1984; ISBN 0-444-85216-6
31. 32. 33. 34. 35. 36. 37A. 37B. 37C. 37D. 37E. 37E 37G. 38. 39. 40.
J. Flahaut, Sulfides, selenides and tellurides 1 J.M. H~chke, Halides 89 E Hulliger, Rare earth pnictides 153 G. Blasse, Chemistry and physics of R-activated phosphors 237 M.J. Weber, Rare earth lasers 275 EK. Fong, Nonradiative processes of rare-earth ions in crystals 317 J.W. O'Laughlin, Chemical spectrophotometric and polarographic methods 341 S.R. Taylor, Trace element analysis of rare earth elements by spark source mass spectroscopy 359 R.J. Conzemius, Analysis of rare earth matrices by spark source mass spectrometry 377 E.L. DeKalb and V.A. Fassel, Optical atomic emission and absorption methods 405 A.P. D'Silva and V.A. Fassel, X-ray excited optical luminescence of the rare earths 441 EW.V. Boynton, Neutron activation analysis 457 S. Schuhmann and J.A. Philpotts, Mass-spectrometric stable-isotope dilution analysis for lanthanides in geochemical materials 471 J. Reuben and G.A. Elgavish, Shift reagents and NMR of paramagnetic lanthanide complexes 483 J. Reuben, Bioinorganic chemistry: lanthanides as probes in systems of biological interest 515 T.J. Haley, Toxicity 553 Subject index 587
VOLUME 5 1982, 1st repr. 1984; ISBN 0-444-86375-3 41. 42. 43. 44. 45. 46.
M. Gasgnier, Rare earth alloys and compounds as thin films 1 E. Gratz and M.J. Zuckermann, Transport properties (electrical resitivity, thermoelectric power and thermal conductivity) of rare earth intermetallic compounds 117 EP. Netzer and E. Bertel, Adsorption and catalysis on rare earth surfaces 217 C. Boulesteix, Defects and phase transformation near room temperature in rare earth sesquioxides 321 O. Greis and J.M. Haschke, Rare earth fluorides 387 C.A. Morrison and R.P. Leavitt, Spectroscopic properties of triply ionized lanthanides in transparent host crystals 461 Subject index 693
VOLUME 6 1984; ISBN 0-444-86592-6 47. 48. 49. 50.
K.H.J. Busehow, Hydrogen absorption in intermetallic compounds 1 E. Parth~ and B. Chabot, Crystal structures and crystal chemistry of ternary rare earth-transition metal borides, silicides and homologues 113 P. Rogl, Phase equilibria in ternary and higher order systems with rare earth elements and boron 335 H.B. Kagan and J.L. Namy, Preparation of divalent ytterbium and samarium derivatives and their use in organic chemistry 525 Subject index 567
VOLUME 7 1984; ISBN 0-444-86851-8
51. 52. 53.
P. Rogl, Phase equilibria in ternary and higher order systems with rare earth elements and silicon K.H.J. Buschow, Amorphous alloys 265 H. Schumann and W Genthe, OrganametalIic compounds of the rare earths 446 Subject index 573
CONTENTS OF VOLUMES 1-19
xi
VOLUME 8 1986; ISBN 0-444-86971-9 54. 55. 56. 57.
K.A. Gschneidner Jr and EW. Calderwood, Intra rare earth binary alloys: phase relationships, lattice parameters and systematics 1 X. Gao, Polarographie analysis of the rare earths 163 M. Leskel~t and L. Niinist6, Inorganic complex compounds I 203 J.R. Long, Implications in organic synthesis 335 Errata 375 Subject index
379
VOLUME 9 1987; ISBN 0-444-87045-8 58. 59. 60. 61.
R. Reisfeld and C.K. Jorgensen, Excited state phenomena in vitreous materials 1 L. Niinist6 and M. Leskel~i, Inorganic complex compounds II 91 J.-C.G. Biinzli, Complexes with synthetic ionophores 321 Zhiquan Shen and Jun Ouyang, Rare earth coordination catalysis in stereospecific polymerization Errata 429 Subject index 431
395
VOLUME 10: High energy spectroscopy 1988; ISBN 0-444-87063-6 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72.
Y. Baer and W.-D. Schneider, High-energy spectroscopy of lanthanide materials - An overview 1 M. Campagna and EU. Hillebrecht, f-electron hybridization and dynamical screening of core holes in intermetallic compounds 75 O. Gunnarsson and K. Sch6nhammer, Many-body formulation of spectra of mixed valence systems 103 A.J. Freeman, B.I. Min and M.R. Norman, Local density supercell theory ofphotoemission and inverse photoemission spectra 165 D.W.Lynch and J.H. Weaver, Photoemission of Ce and its compounds 231 S. Hfifner, Photoemission in chalcogenides 301 J.E Herbst and J.W Wilkins, Calculation of 4f excitation energies in the metals and relevance to mixed valence systems 321 B. Johansson and N. M~trtensson, Thermodynamic aspects of 4f levels in metals and compounds 361 EU. Hillebrecht and M. Campagna, Bremsstrahlung isochromat spectroscopy of alloys and mixed valent compounds 425 J. R6hler, X-ray absorption and emission spectra 453 EP. Netzer and J.A.D. Matthew, Inelastic electron scattering measurements 547 Subject index 601
VOLUME 11: Two-hundred-year impact of rare earths on science t988; ISBN 0-444-87080-6 73. 74. 75. 76. 77. 78. 79.
H.J. Svec, Prologue 1 E Szabadv~ry, The history of the discovery and separation of the rare earths 33 B.R. Judd, Atomic theory and optical spectroscopy 81 C.K. Jorgensen, Influence of rare earths on chemical understanding and classification 197 J.J. Rhyne, Highlights from the exotic phenomena of lanthanide magnetism 293 B. Bleaney, Magnetic resonance spectroscopy and hyperfine interactions 323 K.A. Gschneidner Jr and A.H. Daane, Physical metallurgy 409 S.R. Taylor and S.M. McLennan, The significance of the rare earths in geochemistry and cosmochemistry 485 Errata 579 Subject index 581
xii
CONTENTS OF VOLUMES 1-19
V O L U M E 12 1989; ISBN 0-444-87105-5 80. 81. 82. 83. 84. 85. 86. 87.
J.S. Abell, Preparation and crystal growth of rare earth elements and intermetallic compounds 1 Z. Fisk and J.E Remeika, Growth of single crystals from molten metal fluxes 53 E. Burzo and H.R. Kirchmayr, Physical properties of R2Fel4B-based alloys 71 A. Szytuta and J. Leciejewicz, Magnetic properties of ternary intermetallie eompounds of the RT2X2 type 133 H. Maletta and W. Zinn, Spin glasses 213 J. van Zytveld, Liquid metals and alloys 357 M.S. Chandrasekharaiah and K.A. Gingerich, Thermodynamic properties ofgaseoas species 409 W.M. Yen, Laser spectroscopy 433 Subject index 479
V O L U M E 13 1990; ISBN 0-444-88547-1 88. 89. 90. 91, 92,
E.I. Gladyshevsky, O.I. Bodak and V.K. Pecharsky, Phase equilibria and crystal chemistry in ternary rare earth systems with metallic elements 1 A.A. Eliseev and G.M. Kuzmichyeva, Phase equilibrium and crystal chemistry in ternary rare earth systems with chalcogenide elements 191 N. Kimizuka, E. Takayama-Muromachi and K. Siratori, The systems R203-M203-MtO 283 R.S. Houk, Elemental analysis by atomic emission and mass spectrometry with inductively coupled plasmas 385 P.H, Brown, A.H. Rathjen, R.D, Graham and D.E. Tribe, Rare earth elements in biologicalsystems 423 Errata 453 Subject index 455
V O L U M E 14 1991; ISBN 0-444-88743-1 93. 94. 95. 96. 97.
R. Osborn, S.W. Lovesey, A.D. Taylor and E. Balcar, Intermultiplet transitions using neutron spectroscopy 1 E. Dormann, NMR in intermetallic compounds 63 E. Zirngiebl and G. Giintherodt, Light scattering in intermetallic compounds 163 E Thalmeier and B. Liithi, The electron-phonon interaction in intermetallic compounds 225 N. Grewe and E Steglich, Heaoyfermions 343 Subject index 475
V O L U M E 15 1991; ISBN 0-444-88966-3 98. 99. 100. 101. 102. 103. 104.
J.G. Sereni, Low-temperature behaviour of cerium compounds 1 G.-y. Adachi, N. Imanaka and Zhang Fuzhong, Rare earth carbides 61 A. Simon, Hj. Mattausch, G.J. Miller, W. Bauhofer and R.K. Kremer, Metal-rich halides 191 R.M. Almeida, Fluoride glasses 287 K.L. Nash and J.C. Sullivan, Kinetics of complexation and redox reactions of the lanthanides in aqueous solutions 347 E.N. Rizkalla and G.R. Choppin, Hydration and hydrolysis oflanthanides 393 L.M. Vallarino, Macroeycle complexes of the lanthanide(llI) yttrium(IIl) and dioxouranium(VI) ions from metal-templated syntheses 443 Errata 513 Subject index 515
CONTENTS OF VOLUMES 1-19
xiii
M A S T E R INDEX, Vols. 1 - 1 5 1993; ISBN 0-444-89965-0 V O L U M E 16 1993; ISBN 0-444-89782-8 105. 106. 107. 108. 109.
M. Loewenhaupt and K.H. Fischer, Valence-fluctuation and heavy-fermion 4fsystems 1 I.A. Smirnov and V.S. Oskotski, Thermal conductivity of rare earth compounds 107 M.A. Subramanian and A.W. Sleight, Rare earthspyrochlores 225 R. Miyawaki and I. Nakai, Crystal structures of rare earth minerals 249 D.R. Chopra, Appearance potential spectroscopy of lanthanides and their intermetallics 519 Author index 547 Subject index 579
V O L U M E 17: Lanthanides/Actinides: Physics - I 1993; ISBN 0-444-81502-3 M.R. Norman and D.D. Koelling, Electronic structure, Fermi surfaces, and superconductivity in f electron metals 1 111. S.H. Liu, Phenomenological approach to heavy-fermion systems 87 112. B. Johansson and M.S.S. Brooks, Theory of cohesion in rare earths and actinides 149 113. U. Benedict and W.B. Holzapfel, High-pressure studies - Structural aspects 245 114. O. Vogt and K. Mattenberger, Magnetic measurements on rare earth and aetinide monopnictides and monochaleogenides 301 115. J.M. Fournier and E. Gratz, Transport properties of rare earth and actinide intermetallies 409 116. W. Potzel, G.M. Kalvius and J. Gal, M6ssbauer studies on electronic structure of intermetallie compounds 539 117. G.H. Lander, Neutron elastic scattering from actinides and anomalous lanthanides 635 Author index 711 Subject index 753 110.
V O L U M E 18: Lanthanides/Actinides: Chemistry 1994; ISBN 0-444-81724-7 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129.
G.T. Seaborg, Origin of the aetinide concept 1 K. Ba|asubramanian, Relativistic effects and electronic structure of lanthanide and actinide molecules 29 J.V. Beitz, Similarities and differences in trivalent lanthanide- and actinide-ion solution absorption spectra and luminescence studies 159 K.L. Nash, Separation chemistry for lanthanides and trivalent actinides 197 L.R. Morss, Comparative thermochemical and oxidation-reduction properties of lanthanides and actinides 239 J.W.Ward and J.M. Haschke, Comparison o f 4 f a n d 5felement hydride properties 293 H.A. Eiek, Lanthanide and aetinide halides 365 R.G. Haire and L. Eyring, Comparisons of the binary oxides 413 S.A. Kinkead, K.D. Abney and T.A. O'Donnell,f-element speciation in strongly acidic media: lanthanide and mid-actinide metals, oxides, fluorides and oxide fluorides in superacids 507 E.N. Rizkalla and G.R. Choppin, Lanthanides and aetinides hydration and hydrolysis 529 G.R. Choppin and E.N. Rizkalla, Solution chemistry ofactinides and lanthanides 559 J.R. Duffield, D.M. Taylor and D.R. Williams, The biochemistry of the f-elements 591 Author index 623 Subject index 659
xiv
CONTENTS OF VOLUMES 1-19
VOLUME
19: L a n t h a n i d e s / A c t i n i d e s : P h y s i c s - II
1994; ISBN 0-444-82015-9 130. 131. 132. 133. 134.
E. Holland-Moritz and G.H. Lander, Neutron inelastic scattering from actinides and anomalous lanthanides 1 G. Aeppli and C. Broholm, Magnetic correlations in heavy-fermion systerr~." neutron scattering from single crystals 123 P. Wachter, Intermediate valence and heavy fermions 177 J.D. Thompson and J.M. Lawrence, High pressure studies - Physical properties of anomalous Ce, Yb and U compounds 383 C. Colinet and A. Pasturel, Thermodynamic properties of metallic systems 479 Author Index 649 Subject Index 693
Handbook on the Physics and Chemistry of Rare Earths Vol. 20 edited by K.A. Gschneidner, Jr. and L. Eyring © 1995 Elsevier Science B.V. All rights reserved
Chapter 135 F E R M I SURFACES OF INTERMETALLIC C O M P O U N D S Yoshichika Onuki
Department of Physics, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan Akira Hasegawa
Department of Physics, Faculty of Science, Niigata University, Niigata 950-21, Japan
Co~e~s List of symbols and abbreviations 1. Introduction 2. Theory of energy band structure 2.1. Relativistic effect in the lanthanide atoms 2.2, Luttinger's theorem on the Fermi surface 2.3. Relativistic band theory 2.3.1. Kohn-Sham-Dirac one-electron equation 2.3.2. Self-consistent, symmetrized relativistic APW approach 2.3.2.1. APW matrix elements in a symmetrized form 2,3.2.2. Determination of eigenvalues and eigenfunctions 2.3.2.3. Electron density function 2.3.2.4. Self-consistent calculation 2.4. Determination of the density of states, the Fermi surface and the cyclotron effective mass 2.5. Mass enhancement factors 3. Transverse magnetoresistance and de Haasvan Alphen effect 3.1. Transverse magnetoresistance 3.2. de Haas-van Alphen effect
1 2 8 8 11 12 14 16 16
19 20 21
22 24 26 26 27
4. Experimental results and comparisons with band calculations 30 4.1. Fermi surfaces in the simple cubic Brillouin zone 30 4.1.1. RB 6 30 4.1.2. LaAg and YZn 38 4.1.3. RIn3 40 4.1.4. RSn 3 52 4.2. Fermi surfaces in the bcc Brillouin zone 59 4.2.1. RX 59 4.2.2. RAt 2 67 4.3. Fermi surfaces in the hexagonal Brillouin zone 70 4.3.1. RG% 70 4.4. Fermi surfaces in the tetragonal Bfillouin zone 74 4.4.1. RRu2Si 2 and RRu2Ge2 74 4.4.2. CeCu2Si2 81 4.5. Fermi surface in the orthorhombic Brillouin zone 82 4.5.1. RNi 82 4.5.2, RCu 2 87 4.5.3. RCu 6 90 5. Conclusions 95 Acknowledgement 98 References 98
List of symbols and abbreviations a
lattice constant
AF1,2
antiferromagnetic states
2 APW c C dHvA e EF Ef Eex Ei F FFT FS g
Y. 0NUKI and A. HASEGAWA
KKR LAFW
augmented plane wave phase velocity of light specific heat de Haas-van Alphen electronic charge Fermi energy f level exchange splitting energy eigenvalue of ~pi de Haas-van Alphen frequency fast Fourier transformation Fermi surface g factor for the spin of the conduction electron Land6 g factor magnetic field critical field for the metamagnetic transition Planck constant divided by 2~ effective H including the exchange field current total angular momentum z-component of J wave vector magnitude of k Boltzmann constant magnitude of wave vector along the field direction Fermi vector along the three principal axes (i = 1,2, 3) Korringa-Kohn-Rostoker linearized augmented plane wave
LDA LMTO m0 mb
local density approximation linearized muffin-tin orbital free electron mass band mass
gj H Hc h Hex J J J~ k k kB kH kv~
m* m~ Mosc MBZ
N(EF) ne nh RKKY S T Tc TD TK TN TQ U v vF v±
V(r) V 7 7b )~ ~'m ~,p /tB #x~[p(r)]
Ap/p a(r) z wc
effective mass cyclotron effective mass oscillatory component of magnetization magnetic Brillouin zone density of states at E F number of electron carriers number of hole carriers Ruderman-Kittel-Kasuya-Yosida extremal cross-sectional area of the Fermi surface absolute temperature Curie temperature Dingle temperature Kondo temperature N6el temperature quadrupolar ordering temperature Coulomb repulsive force velocity of an electron Fermi velocity velocity component perpendicular to the Fermi surface or cyclotron orbit external potential hybridized coupling constant electronic specific heat coefficient 7 calculated from the band model mass enhancement factor ~, due to electron-magnon interaction ), due to electron-phonon interaction Bohr magneton exchange-correlation potential magnetoresistance, Ap/p = [p(H)-p(O)]/p(O) local spin density at r scattering lifetime cyclotron frequency
1. Introduction T h e l a n t h a n i d e c o m p o u n d s are u s u a l l y t r e a t e d in m a g n e t i s m b y a n f - l o c a l i z e d m o d e l , b u t s h o w v a r i o u s i n t e r e s t i n g p h e n o m e n a s u c h as v a l e n c e fluctuations, gap states, K o n d o lattice, a n d h e a v y electrons. T h e s e o r i g i n a t e f r o m t h e 4 f e l e c t r o n s i n t h e l a n t h a n i d e c o m p o u n d s , w h i c h are e i t h e r b o u n d to t h e l a n t h a n i d e a t o m s or delocalized, i n d i c a t i n g
FERMI SURFACESOF INTERMETALLICCOMPOUNDS
3
an itinerant nature. The 4f electrons in the atom are pushed deep into the interior of the closed 5s and 5p shells because of the strong centrifugal potential l(l + 1)/r 2, where l = 3 holds for the f electrons. This is why the 4f electrons possess an atomic-like character in the crystal. On the other hand, the tail of their wave function spreads to the outside of the closed 5s and 5p shells, which is highly influenced by the potential energy, the relativistic effect and the distance between the lanthanide atoms; this results in hybridization of the 4f electrons with the conduction electrons. These cause the various phenomena mentioned above. The Coulomb repulsive force of the 4f electron (or the intra-atomic correlation energy) U at the same atomic site is so strong, for example U ~ 5 eV in Ce compounds, that occupancy of a same site by two 4f electrons is usually prohibited. The 4f partial density of states determined by resonant photoemission experiments shows a maximum below the Fermi level which corresponds to the binding energy or the level of the 4f electrons El. For example, the distance from this 4f level to the Fermi level is 7.0 eV and 1.2 eV in SmCu6, 5.5 eV in NdCu6, 3.5 eV in PrCu6 and 2.4eV in CeCu6 (Ishii et al. 1987). The tail of the 4f partial density of states extends to the Fermi level even at room temperature in CeCu6 and also slightly in PrCu6, while no trend of 4f states is observed around the Fermi level in NdCu6. Near the Ce or Yb end of the R series, the 4f level thus approaches the Fermi level in energy and the 4f electrons hybridize more strongly with the conduction electrons with the kinetic energy Ek. This f-hybridized coupling constant is denoted by V. A theoretical treatment for such a system is called the periodic Anderson model (Anderson 1961). The parameters Ek, V, Ef and U predominantly control the dynamics of the system. These values depend actually on the crystal structure. The relation between the magnetic ordering temperature and the distance between the Ce (or U) atoms is known as a Hill plot (Hill 1970). When U is strong and/or V is ignored, the freedom of the charge in the 4f electron is suppressed, while the freedom of the spin is retained, representing the 4f-localized state. Naturally, the degree of localization depends on El, where larger Ef helps to increase the localization. This situation is applied to most of the lanthanide compounds in which the RKKY interaction (Ruderman and Kittel 1954, Kasuya 1956, Yosida 1957) plays a predominant role in magnetism. Therefore, the mutual magnetic interaction between the 4f electrons occupying different atomic sites cannot be of a direct type, such as in 3d metal magnetism, but should be indirect, which occurs only through the conduction electrons. In the RKKY interaction, a localized spin Si interacts with a conduction electron with spin s, which leads to a spin polarization of the conduction electron. This polarization interacts with another spin Sj localized on ion j and therefore creates an indirect interaction between the spins Si and Sj. This indirect interaction extends to the far distance and damps with a sinusoidal 2kv oscillation, where kv is half of the caliper dimension of the Fermi surface. When the number of 4f electrons increases in such a way that the lanthanide element changes from Ce to Gd or reversely from Yb to Gd in the compound, the magnetic moment becomes larger and the RKKY interaction stronger, leading to
4
Y. ONUKI and A. HASEGAWA i00
"~"1
,
,,,,,,,i
'
'
'''"'1
'
_X=
0.50 . . . . . . . . . . . . . . . . . . . . _ -o.73
0
~ ' ~ 1
~
,
',,,,q
,
,
CexLal-xCu6 J//b-axis .
.
.
.
.
~
~
.
o 50
-
,/
9 0 ......... 0.01
0,1
1
Temperature (K)
10
100
Fig. 1. Temperature dependence of the electric resistivity in CexLa~_xCu6 (Sumiyama et al. 1986).
magnetic order of which the ordering temperature roughly follows the de Gennes relation, (gj-1)2j(j + 1). Here gj and J are the Land6 g factor and the total angular momentum, respectively. Contrary to what happens at large U, higher V tends to enhance the hybridization of 4f electrons with conduction electrons, thus accelerating the delocalization of the 4f electrons (Koelling et al. 1985). The delocalization of 4f electrons tends to make the 4fband wide. When Ef > V, we have still better localization and expect the Kondo regime in the Ce (or Yb) compounds. The Kondo effect was studied for the first time in a dilute alloy where a ppm range of the 3d transition metal is dissolved in a pure metal of copper. Kondo (1964) showed that the third-order scattering of the conduction electron with the localized moment of the transition impurity diverges logarithmically with decreasing temperature, and clarified the origin of the long standing problem of the resistivity minimum. This became the start of the Kondo problem, and it took ten years for theorists to solve this divergence problem at the Fermi energy (Wilson 1975). The many-body Kondo bound state is now understood as follows. For the simplest case of no orbital degeneracy, the localized spin S(T) is coupled antiferromagnetitally with the spin of the conduction electron s(+). Consequently the singlet state {S(i") • s(J,) + S(1)" s(T)} is formed with binding energy kBTK. Here the Kondo temperature TK is the single energy scale. In other words, disappearance of the localized moment is thought to be due to the formation of a spin-compensating cloud of the conduction electron around the impurity moment. Kondo-like behavior was observed in the ianthanide compounds, typically in Ce and Yb compounds (Buschow et al. 1971, Parks 1977, Falicov et al. 1981). For example, the electric resistivity in CexLal-xCu6 increases logarithmically with decreasing temperature for all the x-values (Sumiyama et al. 1986), as shown in fig. 1. The Kondo effect occurs independently at each cerium site even in a dense system. Therefore, this phenomenon was called the dense Kondo effect.
FERMI SURFACESOF INTERMETALLICCOMPOUNDS
5
The Kondo temperature in the Ce (or Yb) compound is large compared to the magnetic ordering temperature based on the RKKY interaction. For example, the cerium ion is trivalent (J = 5/2), and the 4f energy level is split into three doublets by the crystalline electric field, namely possessing the splitting energies of A1 and A2. The Kondo temperature is given as follows (Yamada et al. 1984):
T~z=Dexp
- 3
[JexlD(EF)
when T > AI, A2,
(1)
when T < At, A2.
(2)
and TK = A---~Dexp
I&xlb(EF)
Here D, [Jex [ and D(Ev) are the band width, exchange energy and density of states, respectively. If we postulate TK ~ 5 K, for D = 104 K, zll = 100 K and A2 = 200 K, the value of T~ ~ 50K is obtained, which is compared to the S = ½-Kondo temperature of 10 3 K defined as T ° = D exp(-1/IJex I D(EF)). These large values of Kondo temperatures shown in eqs. (1) and (2) are due to the orbital degeneracy of the 4f levels. Therefore, even at low temperatures the Kondo temperature is not T ° but TK shown in eq. (2). On the other hand, the magnetic ordering temperature is about 5 K in the Ce (or Yb) compound, which can be simply estimated from the de Gennes relation under the consideration of the Curie temperature of about 300K in Gd. Therefore, T~ is much higher than the magnetic ordering temperature, but TK is close to it. Therefore, it depends on the compound whether or not magnetic ordering occurs at low temperatures (Brandt and Moshchalkov 1984). As shown in table 1, some compounds such as CeB6 or CeAI2 order antiferromagnetically below 5 K, while CeCu6 (TK = 4 K) does not order magnetically. The ground-state properties of dense Kondo systems are interesting in magnetism, which is highly different from the dilute Kondo effect. In the cerium intermetallic compounds such as CeCu6, cerium ions are periodically aligned whose ground state cannot be a scattering state but becomes a coherent Kondo-lattice state. The electric resistivity p decreases steeply with decreasing temperature, following p ~ A T 2 with a large value of the coefficient A. The v/A-value is proportional to the effective mass of the carrier and thus inversely proportional to the Kondo temperature (Kadowaki and Woods 1986). Correspondingly, the electronic specific heat coefficient y roughly follows the simple relation y ~ 104/TK (mJ/K2mol). It reaches 1600mJ/K2mol for CeCu6 because of a small Kondo temperature (Satoh et al. 1989). The Ce Kondolattice compound with magnetic ordering also possesses the large y value even if the RKKY interaction overcomes the Kondo effect at low temperatures. For example, the ~, value of CeB6 is 250 mJ/K 2 mol, which is roughly one hundred times larger than that of LAB6, 2.6 mJ/K 2 tool. The conduction electrons possess large effective masses and thus move slowly in the crystal. These heavy electrons become superconductive in CeCuaSi2
Y. ONUKI and A. HASEGAWA Table 1 Characteristic properties of Ce compounds~ Compound
Crystal structure
a (.&)
Tn (K)
(a) Non-Kondo lattice compounds with magnetic ordering CeGa2 hexa 4.32 11.4 CeRu2Ge2 tetra 4.27 8.5
Tc (K)
y (mJ/K2mol)
8.2
9
7.5
20
H c (kOe)
(b) Kondo lattice compounds with magnetic ordering CeSb cubic 4.54 16.2 Celn3 cubic 4.69 10.2 CeA12 cubic 3.49 3.8 CeCu2 ortho 3.57 3.4 CeB6 cubic 4.14 2.3 b CeCu2Si2 tetra 4.11 0.7 c
20 130 135 82 250 1000
38 >150 53 18 15 70
(c) Kondo lattice compounds without magnetic ordering CeCu6 ortho 4.83 CeRu2Si2 tetra 4.19 CeNi ortho 3.59 CeSn3 cubic 4.72
1600 350 65-85 53
20 80
" Symbols: a, distance between nearest Ce atoms; TN, N6el temperature; Tc, Curie temperature; TQ, quadrupolar ordering temperature; To, superconducting transition temperature; ~/, electronic specific heat coefficient; He, critical field for metamagnetic transition. b TQ=3.2K. e T0=0.7K '
(Steglich et al. 1980). Therefore, the Kondo-lattice system is called a heavy-electron or heavy-Fermion system. W h e n E f < V, the 4 f electrons may tend to be delocalized, manifesting the valencefluctuation regime. CeSn3 and CeNi were once called valence-fluctuation compounds or mixed-valent compounds. The magnetic susceptibility in these compounds follows the Curie-Weiss law at higher temperatures than room temperature, possessing the magnetic moment near Ce 3+, while it becomes approximately temperature-independent with decreasing temperature, showing a broad m a x i m u m around 150-200 K (Gschneidner et al. 1985). Thus the valence o f Ce atoms seems to change from Ce 3+ into Ce 4+ (nonmagnetic state) with decreasing temperature. The ionic radius o f the lanthanide atom decreases with increasing number o f 4 f electrons, which is well known as lanthanide contraction. A plot o f the lattice constant o f the lanthanide compound versus the atomic number o f the lanthanide element shows a nearly straight line, except for some Ce, Sm, Eu, Tm and Yb compounds, where the lanthanides can take integral valencies different from 3 as in Ce 4÷ and Sm 2+, Eu 2+, Tm 2+, Yb z+. The valence change in these compounds is brought about by changing the constitution x (such as in Sml-xLaxB6 Kasaya et al. 1980) or by
FERMI SURFACESOF INTERMETALLICCOMPOUNDS
7
introducing pressure (for SmS Jayaraman et al. 1970) or a magnetic field (YbB12 Sugiyama et al. 1988), as well as by changing the temperature as mentioned above for CeSn3 and CeNi. The first insulating valence fluctuations were studied by Jayaraman et al. (1970) for SINS. An insulating black phase of SmS at ambient pressure changes into a metallic golden phase at high pressures. In other words, divalence of Sm 2+ changes into the intermediate valence between 2+ and 3+. The application of hydrostatic pressure is associated with a smaller volume, which introduces the 4f valence transition and consequently delocalization of 4f electrons. Fermi surface studies are very important to know the ground-state properties of these various magnetic compounds (Norman and Koelling 1993, Onuki et al. 1991a). Even in the localized system, the presence of 4f electrons alters the Fermi surface through the 4f-electron contribution to the crystal potential and through the introduction of new Brillouin zone boundaries and magnetic energy gaps which occur when 4f electron moments order. The latter effect may be approximated by a band-folding procedure where the paramagnetic Fermi surface, which is roughly similar to the Fermi surface of the corresponding La compound, is folded into a smaller Brillouin zone based on the magnetic unit cell, which is larger than the chemical unit cell. If the magnetic energy gaps associated with the magnetic structure are small enough, conduction electrons undergoing cyclotron motion in the presence of a magnetic field can tunnel through these gaps and circulate the orbits on the paramagnetic Fermi surface. If this magnetic breakthrough (or breakdown) occurs, the paramagnetic Fermi surface may be observed in the de Haas-van Alphen (dHvA) effect even in the presence of magnetic order. For Kondo-lattice compounds with magnetic ordering, the Kondo effect is expected to have minor influence on the topology of the Fermi surface, representing that Fermi surfaces of the Ce compounds are roughly similar to those of the corresponding La compounds, but are altered by the magnetic Brillouin zone boundaries mentioned above. Nevertheless, the effective masses of the conduction carriers are extremely large compared to those of La compounds mentioned above. In this system a small amount of 4f electron most likely contributes to make a sharp density of states at the Fermi energy. Thus the energy band becomes flat around the Fermi energy, which brings about the large mass. There is a big difference in f-electron character between the Kondo regime and the valence-fluctuation regime. One may be tempted to think that the 4f electrons in a Kondo lattice compound with a large value of TK are itinerant. This seems to be true, as shown later in detail for CeSn3 and CeNi or CeRu2 Si2. In the following sections we present the dHvA results of the lanthanide compounds shown in table 2, which are compared to the results of energy band calculations. Comparisons of the dHvA experiments with band calculations are essentially important to determine the f character, namely whether the 4f electrons are itinerant or localized. These Fermi surface properties should shed light on the basic understanding of the strongly correlated 4f-electron system.
Y. (3NUKI and A. HASEGAWA Table 2 Rare earth compounds for which dHvA results and energy band calculations are presented in the text. Elements
La
Ce
Pr
Nd
B
LaB 6
CeB 6
PrB 6
NdB 6
Ag
LaAg Prln 3
Ndln 3
Zn
Y
Lain3
Celn 3
Sn
LaSh 3
CeSn 3
Bi
LaBi
CeBi
Sb
LaSb
CeSb
As
Smln 3
Gdln 3
PrSb
SmSb
GdSb
CeAs YA12
LaA1z
Yb
Ga
LaGa2
CeG%
LaRu2Siz
CeRu2Si2
Ru/Ge
LaRu2Ge2 CeRu2Ge z
Cu/Si
YbAs
CeAIz
Ru/Si
SmGa 2
CeCu2Si2
Ni Cu
Gd
YZn
In
A1
Sm
LaNi YCu z
CeNi
PrNi
CeCu 2 LaCu 6
CeCu 6
SmCu 2 PrCu 6
NdCu 6
SmCu 6
2. Theory of energy band structure 2.1. Relativistic effect in the lanthanide atoms The lanthanide atoms have fairly large atomic numbers and their compounds contain other heavy atoms as the constituent elements. Therefore, it is essential to take into account the relativistic effect in calculations of the energy band structures for the lanthanide compounds. In this section, we explain how the energy and the wave function of an electron in these compounds may be influenced by relativity. We treat the neutral cerium atom as an example, and explain the important effect of relativity on the electrons in its outer shells such as the 4f, 5d and 6s electrons. The electrons in the s states in both inner (the Xe core) and outer shells have finite probability amplitudes at the nucleus. As the nuclear potential is deep in the vicinity of the nucleus, electron velocity approaches light velocity and consequently the relativistic effect becomes appreciably large. Compared to the non-relativistic theory, the corresponding energy of all the s (l = 0) electrons decreases significantly, because the s electrons have relatively large probability amplitudes at the nucleus and their wave functions contract toward the nucleus. This direct relativistic effect on the s electrons induces an indirect effect on the other (l ~ 0) electrons. Namely, the s electrons tend to screen more effectively the nuclear potential which the 4f and 5d electrons feel, and therefore the latter would be bound more loosely. As a result, their energies increase and their wave functions tend to spread outward in contrast to the 6s electrons.
FERMI SURFACES OF INTERMETALLIC COMPOUNDS
9
.72_ 5d
V
'> 1, it is possible to know whether the compound under investigation is a compensated metal with an equal carrier number of electrons and holes, ne = nh, or an uncompensated metal, n e e nh, and whether or not open orbits exist. Here, coc = ell~roSe is the cyclotron frequency, r is the scattering lifetime, mS is the effective cyclotron mass and cocr/2~r means the number of the cyclotron motions performed by the carrier without being scattered. The characteristic features of the high-field magnetoresistance are summarized as follows: (1) when all cyclotron orbits are closed, (a) for the uncompensated metal the magnetoresistance saturates, A p / p ~ H °, and (b) for the compensated metal the magnetoresistance increases quadratically, A p / p ~ (wcz) 2. (2) When some of the cyclotron orbits are not closed but form open orbits, the magnetoresistance increases quadratically and depends on the current direction as
FERMI SURFACESOF INTERMETALLICCOMPOUNDS
27
A p / p ~ H2cos2c~, where a is the angle between the current direction and the open orbit direction in k-space. This is true regardless of the state of compensation. If we count the number of valence electrons in a primitive cell, most of the lanthanide compounds are even in number, meaning that they are compensated metals. In this case the transverse magnetoresistance increases as H n (1 < n ~2) become vanishingly small, and the fundamental one (r= 1) becomes dominant in the usual dHvA measurements. However, when the cyclotron mass is not large and the temperature becomes lower than 1 K, the higher harmonics become detectable. To distinguish the higher harmonics from the fundamental one, it is necessary to check carefully the magnitude, intensity and angular dependences of the dHvA frequencies and their cyclotron masses. The quantity ]OzS/Ok~i]-1/2 is the inverse square root of the curvature factor 02S/Ok~. The rapid change of the cross-sectional area around the extremal cross-sectional area along the field direction diminishes the dHvA amplitude for this extremal area. The term cos(~grmS/2mo) is called the spin factor. When g = 2 (free-electron value) and m* =0.5m0, this term becomes zero for the fundamental oscillation (r= 1) and the dHvA oscillation vanishes for all values of magnetic field. This is called the zero spinsplitting situation in which the up and down spin contributions to the oscillation cancel
FERMI SURFACES OF INTERMETALLIC COMPOUNDS
29
LaSh3
(a)
Magnetic Field Fig. 5. Schematic picture of the change in the extremal cross-sectional areas depending on the up and down spin states. AF~ and AF2 mean the different antiferromagnetic states, and H c is the critical field showing the metamagnetic transition. St, and S~ are the extremal areas for the up and down spin electrons, respectively, obtained from the dHvA measurements in the AF2 region (Harima 1988).
I
r
I
'Y,Ti
80
90kOe
H// (b)
0.SK ~7z-- Or
2,e
L, ojhlll,
7,+2z!
II
0 5 10 15x1070e Fig. 6. dHvA oscillation and its FFT spectrum for LaSn3 (Umehara et al. 1991a). The Greek letters in the FFT spectrum designate the various orbits.
out, and this can be useful for determining the g value. Note that in this situation the second harmonics for r = 2 should have a full amplitude. When the extremal area changes linearly with increasing external field, the dHvA frequencies of the up and down spin electrons coincide, giving the extremal crosssectional area for zero field mentioned above. Many lanthanide compounds show a magnetically ordered state at low temperatures. Conduction electrons in this system have different Zeeman and exchange energies, depending on the up and down spin electrons. For example, the antiferromagnetic AF~ state of these compounds often changes into a different antiferromagnetic AF2 state or into the field-induced ferromagnetic (paramagnetic) state. In this case, we usually get different Fermi surface areas for the up and down spin electrons, S T and St, when the field is increased above the critical field showing the metamagnetic transition He, as shown in fig. 5. The spin factor Sr becomes
y'grm e
=c°S 2mo
(62)
30
Y. (3NUKIand A. HASEGAWA
where Hex is defined by the exchange splitting energy Eex = ~BHex. In ferromagnetic compounds, it is possible to obtain different Fermi surface areas associated with the up and down spin electrons in zero field. Simply thinking, the dHvA oscillation is detected when the high-field condition is almost satisfied; ~oer/2zr > 1 and the spacing between the Landau levels is larger than the thermal broadening kBT; hcoc > kBT. I f the magnetic field H is 100kOe or 10T and the carrier possesses a cyclotron mass of 10m0, the following conditions for the temperature and the scattering lifetime are required: T < 1.3 K and 7: > 3.6× 10-11 s or TD < 0.03 K. A temperature of 0.4 K can be attained in the He3-cryostat (Windmiller and Ketterson 1968), and much lower temperatures are obtained in a dilution refrigerator (Reinders et al. 1987). Values of 77= 10-12-10 -11 s or TD=0.1-1 K are usual in samples. The exact dHvA oscillation contains many dHvA frequencies Fi (i = 1, 2, 3, ... ) or cross-sectional areas Si and becomes a sum of their contributions, which are analyzed by the fast Fourier transformation (FFT) method. The amplitude Ai corresponds to the amplitude in the FFT spectrum. Figure 6 shows the dHvA oscillation and its FFT spectrum for a field along the (111) direction of the cubic crystal LaSn3 at 0.5 K (Umehara et al. 1991a). From the FFT spectrum we can see many dHvA oscillations due to harmonics or sums and differences of the several dHvA frequencies.
4. Experimental results and comparisons with band calculations 4.1. Fermi surfaces in the simple cubic Brillouin zone 4.1.1. RB 6 The rare earth hexaborides RB 6 crystallize in the cubic (CaB 6 type) structure which possesses a CsCI type arrangement of R atoms and B6 octahedra. Figure 7 shows the crystal structure of RB6 and its simple cubic Brillouin zone. LaB6 is a reference non-f compound. CeB6 is a typical Kondo-lattice compound undergoing two magnetic ordering (a)
I
(b)
()
Fig. 7. (a) RBt-cubic crystal structure. Large spheres without pattern and small spheres with pattern show the R atoms and the B atoms, respectively.(b) Brillouin zone of the simple cubic crystal lattice.
FERMI SURFACES OF INTERMETALLIC COMPOUNDS
31
Table 4 Characteristic properties of the RB 6 compounds with a cubic crystal structure~ Compound
T N (K)
n
7 (m J/K2 tool) 2.6
LaB 6
Pauli para
ne
CeB6
2.3 TN = 3.2 K Kondo lattice
n~
PrB6
7.0
ne
Ndt36
7.8
n~ = nh
250
Fermi surface three ellipsoids connected by necks similar to LaBr, but spin-split
similar to LaBr, but spin-split strongly altered by MBZ
Symbols: n~, number of electron carders; nh, number of hole carders; when no=nh the carders are compensated. MBZ, magnetic Brillouin zone.
transitions at the quadrupolar ordering temperature TQ = 3.2 K and at the Nrel temperature TN=2.3 K (Effantin et al. 1985, Komatsubara et al. 1983). Existence of quadrupolar ordering is due to the quartet F8 ground state in the 4flevels. PrB6 (TN = 7.0 K) and NdB6 (TN = 7.8 K) are typical localized 4f systems with magnetic ordering. Their characteristic properties are summarized in table 4. The measurements of the dHvA effect in LaB6 (Suzuki et al. 1988, Ishizawa et al. 1977, 1980, Arko et al. 1976), shown in fig. 8, revealed that the Fermi surface consists of a set of three equivalent nearly spherical ellipsoids, denoted by ai (i = 1, 2 and 3), which i
f
~
i
i--~
LaB6 i lZ { 1 0 0 }
i
¢
I
i
3.
*
I
i
,
{110}
10 8
o~ {D
1
o}
~i0 7
I
6 >
10 5
80
0
30
60
Field Angle (Degrees)
90
Fig. 8. Angular dependence of the dHvA frequency in LaB 6 (Ishizawa et al. 1977, 1980, Suzuki et al. 1988). The solid and dashed lines connecting the data are guidelines. The Greek letters designate the various orbits.
32
Y. 0NUKI and A. HASEGAWA R
LaB6
(b) M
(a)
/
R
(e)
"q---------- ~" R Fig. 9. (a) Cross-sections of the multiply connected ellipsoidal Fermi surfaces (Ishizawa et al. 1977). Co) Main three multiply connected ellipsoidal Fermi surfaces (Hasegawa and Yanase 1977b). (c) Twelve pocket Fermi surfaces in LaB 6 (Harima et al. 1988). The pocket Fermi surface is enlarged for visual convenience. The Greek letters designate the various orbits.
are connected by necks. This topology of the Fermi surface was constructed from the magnitude of the dHvA frequencies and the angle range where the dHvA branches a i were detected. The energy band structure of LaB6 is characterized by the wide B 2s-2p bands which are split into the bonding and antibonding bands and by the La 5d bands which lie across the energy gap between the bonding and antibonding bands. This feature originates from a particular configuration of atoms in the CeB6 crystal structure. The six s states of the B atoms in an octahedron form d-like orbitals with F12 symmetry about the center of the octahedron, and the six p states of these B atoms also form d-like orbitals with both F12 and F25 symmetries about the same center (Longuet-Higgins and Roberts 1954). These d-like orbitals and the La 5d states have nearly equal energies, and therefore strong hybridization occurs between them. The strong hybridization causes a large wave-vector dependence of the d bands, and the Fermi surface is formed by one such d(eg) band (Hasegawa and Yanase 1977b). The Fermi surface of LaB6 is shown in figs. 9a,b. It consists of three equivalent electron sheets which are centered at the X point and are connected by small necks which intersect the E axes in the simple cubic Brillouin zone. The total number of carriers is almost equal to one electron per primitive cell. The electrons on the Fermi surface have dominantly La d character, and on the average the magnitude of their cyclotron effective masses is smaller than the free electron mass.
FERMI SURFACESOF INTERMETALLICCOMPOUNDS
33
The neck orbit was not detected, however, in the above mentioned dHvA measurements done by Ishizawa et al. (1977) and Arko et al. (1976). Later, branches Pi (i = 1. . . . . 6) shown in fig. 8 by open circles were detected by the torque method (Ishizawa et al. 1980) and were attributed to the necks because the angular dependence of branches Pi are consistent with the topologies of the necks. This Fermi surface of the neck is, however, thin and rather cylindrical, which is inconsistent with the short and thick neck constructed from the unobserved region of the ellipsoidal branches cti and also the results of band calculations. This puzzle was solved later by a combination of the improved ultrasonic dHvA measurements done by Suzuki et al. (1988) and the careful band calculations done by Harima et al. (1988). In fig. 9c twelve pocket Fermi surfaces calculated by Harima et al. are shown as an enlarged scale by a factor of ten. It was shown that branches p; are not due to the necks but due to the small and flat electron Fermi surfaces. The data shown as triangles in fig. 8 were obtained by the ultrasonic dHvA measurements (Suzuki et al. 1988). The complete observation of branches P3 and p5 is a clear evidence for existence of the small closed Fermi surfaces. New band calculations done by Harima et al. were made by shifting the unoccupied La 4f levels upwards by an amount of 0.10 Ry, which leads to a new band which crosses the Fermi energy very slightly. Langford et al. (1990) also confirmed existence of the pocket Fermi surface by the LMTO band calculations. The neck orbit is, however, not detected experimentally because of the rapid variation of the cross-sectional area around the extremal neck orbit, implying a large curvature factor 02S/Ok~. Similar Fermi surface topologies were obtained in CeB6 (0nuki et al. 1989a, Joss et al. 1987, 1989, Goto et al. 1988a, Suzuki et al. 1987, van Deursen et al. 1985) and PrB6 (Onuki et al. 1985b, 1989d, van Deursen et al. 1985), as shown in figs. I0 and 11, respectively. Judging from the values of branches ai for field along the (100) direction, the main Fermi surface is more spherical in CeB6 than in LaB6 and PrB6. The ratio of the maximum to minimum areas of the ellipsoidal Fermi surface is about 1.16 in CeB6, 1.24 in PrB6 and 1.27 in LAB6. We also show in fig. 12 the cross-sectional area of the small and flat Fermi surface deduced from branch pi for RB6. It is approximated as an ellipsoidal Fermi surface. The Fermi wave vectors kFi (i = x, y and z) along the three principal axes are kvx = 0.012 (2~v/a), kFy = 0.023 (2st/a) and kvz = 0.0044 (2Jr/a) in LAB6. In PrB6 two kinds of pockets Pi and pf as well as the ellipsoids a3 and a~ are found, as shown in fig. 11. The cross-sectional areas ofpi and pf are 118 and 28 times larger than in LAB6, respectively. The existence of two kinds of Fermi surfaces in PrB6 is explained by an exchange splitting of the up and down spin states of the conduction electrons as shown in fig. 5. This is due to a change of the antiferromagnetic spin structure at about 10kOe in PrB6 (Galera et al. 1992). The up and down spin states have different effective Fermi surface areas and cyclotron masses. For example, branches a3 and a~ in PrB6 have the values of 8.19x 1070e (1.95mo) and 7.25x 1070e (2.52m0) for field along the (100) direction, respectively. A similar spin splitting of the Fermi surfaces is expected in CeB6 because the antiferromagnetic state of the so-called phase III changes into that of phase II
34
¥. 0NUKI and A. HASEGAWA I
'
I
I
' --
I
CeB6
{lOO} 0~i
10 8
+4--
'
[
~
'
I
'
'
PrB8
{11o}
(i00}
! ~ ~ o {Ii0}
0~
108
L+-:~-o-~-o-+ ~
2 _~_~
~__a~j~-~-~F~-
_ .~
. . . . . .
%, O o) O
"
o
~=-~-+~-o.__~_o~ . . . . .
107
I
~
> ~'Lx -
P3~, P4
'
~P3 ~ D5
p,
106 -.e.-,a--',,~o~ ~ I
30
,
s ,
i
,
,
I
,
,
I
0 30 60 F i e l d Angle (Degrees)
~
,
/
90
Fig. 10. Angular dependence of the dHvA frequency in CeB 6, Data shown by circles, crosses, squares and triangles are cited from ()nuki et al. (1989a), van Deursen et al. (1985), Joss et al. (1987, 1989) and Suzuki et al. (1987) and Goto et al. (1988a) Goto (1992), respectively. The solid lines connecting the data are guidelines. The Greek letters designate the various orbits.
LaB6
CeB6
,
I
30
,
,
,
L
I
4
,
I
0 30 60 F i e l d Angle (Degrees)
,
,
]
90
Fig. 11. Angular dependence of the dHvA frequency in PrB~ (Onuki et al. 1985b, 1989d). The solid and dashed lines connecting the data are guidelines. The Greek letters designate the various orbits.
PrB 6
O!
p' ¢- 0.2 @rc/a~
Fig. 12. Cross-sections of the pocket-Fermi surfaces in LAB6, CeB~ and PrB 6. These electron pockets are fiat in character (()nuki et al. 1989a).
(quadrupolar ordering) at about 15 kOe. Goto (1992) confirmed that branches P6 and p~ shown in fig. 10 are due to two kinds of Fermi surfaces with different spin states. The Fermi surface of branch Pi in CeB6 accidentally possesses the same size as branch pf in PrB6.
FERMI SURFACES OF INTERMETALLIC COMPOUNDS
35
Table 5 dHvA frequencies F and cyclotron masses m~ in RB 6 compounds (Ishizawa et al. !977, 1980, Onuki et al. 1989a,d, Goto 1992) a RB 6
a3 F
a~ m~
F
y m~
F
LaB 6
7.89
0.64
3.22
CeB 6
8.67
14-21
2.19
PrB 6
8.19
1.95
7.25
a F NdB 6
9.90
2.52
2.00
F 3.44
2.43
F 1.27
p'
m~
F
0.85
0.49
0.0052
0.046
1.30 0.188
9.2 5.5
0.120
1.7-3.5
0.080
4.6
1.94
0.94 0.79
0.94 0.66
0.590
0.64
0.150
0.28
m~
F
g m~
p
F
15.5
3.27
c m~
e m~
m~
F
m~
hi
1.47
0.95
m* 1.08
F values in 107 Oe, m~ expressed in m 0.
Here, we note the occurrence of dHvA branches with frequencies of (1-2)x 107 0 e in CeB6 and (3-4)x 107 0 e in PrB6. These branches are not present in LAB6, and are probably produced by the small antiferromagnetic Brillouin zone boundaries in CeB6 and PrB6. The cyclotron masses in LaBr, CeB6 and PrB6 are summarized in table 5. All masses in CeB6 are heavily renormalized by the many-body Kondo effect compared to those of LaB 6 and PrB6. The cyclotron masses in PrB6 are also three times larger than those in LAB6, which should be attributed to the usual electron-magnon interaction. The cyclotron mass of branch a3 in CeB6 shows a striking variation as a function of magnetic field, as shown in fig. 13. Quite a different field dependence is observed in the electronic specific heat coefficient y (Mfiller et al. 1988), as shown also in fig. 13. It varies from 250mJ/K2mol in zero field to 50mJ/K2mol in 220kOe. Here, the masses shown by the solid line through the crosses in fig. 13 were estimated from the y value of CeB6 by using the relation ofmc(CeB6 ) = me(LaB6) [y(CeB6)/y(LaBr)], where mc(LaB6) = 0.6 lm0 for a3 and y (LaBr)= 2.6 mJ/K 2 tool. There exists a clear discrepancy between the results of two types of experiments. The reason for this is thought to be as follows. When one compares the Fermi surface of CeB6 to that of PrBr, one is led to believe that the observed a3-Fermi surface in CeB6 corresponds to branch a3 in PrB6. In PrB6, the mass of branch a~ is larger than that of branch a3. Therefore, it is natural to assume that branch a~ in CeB6 has also a larger mass and hence could not be observed experimentally. Therefore, the missing branch af is the main origin of the present discrepancy. We note that the field dependence of the cyclotron mass or the yvalue was discussed briefly in sect. 2. The theoretical treatment for CeB6 was done by Wasserman et al. (1989). The dHvA frequencies observed in NdB6 (Onuki et al. 1989d) are substantially different from those of LAB6, PrB6 and CeBr, as shown in fig. 14. One main reason for the discrepancy between the dHvA branches in NdB6 and in LaB 6 or PrB 6 seems to be the
36
Y. 0NUKI and A. HASEGAWA '
I
7--
I
'
I
{100} [ {110l /•
CeB6 H//
i00
10 8 • o o o o o O O O
NdB6
~OOOoo O O o o o
D .................... .; .................
a
I
o
+•+
c g phase
50
:
° ° ° g @'15° b
~
~i~6o-o-o ° d~
hs .........
•
i
I
f8 ............
::"
0
I
30 [101]
,
,
0 [001]
I
,
30
I
60 [111]
,__
9O
[110]
0
0 [001]
30
[i01]
Field Angle (Degrees)
30
60 [111]
90 [110]
Field Angle (Degrees)
Fig. 51. Angular dependence of the dHvA frequency Fig. 50. Angular dependence of the dHvA frequency in the F phase of CeSb (Aoki et al. 1991, 1985). in the S' phase of CeSb (Aoki et al. 1985). The solid The solid lines show the results of band calculations lines connecting the data are guidelines. The Greek (Kasuya et al. 1987, Sakai et al. 1985). The Greek letters designate the various orbits, letters designate the various orbits.
HI[O01 ]
[IO0]
[001].
[100]
[110]
Fig. 52. Ellipsoidal Fermi surfaces of CeSb for the magnetic moment in the [001] and [100] directions (Crabtree et al. 1987). According to the p - f mixing model, branch/34 is the most important band. In earlier experiments, however, branch/34 was not observed. This fact caused some investigators to doubt the strong p - f mixing model and to apply a weak p - f mixing model (Norman and Koelling 1986). Later, branch f14 was observed by acoustic and usual d H v A measurements (Aoki et al. 1991, Kasuya et al. 1987). Generally thinking, it may be difficult to detect branch/34 by the usual d H v A experiments because the small amplitude o f F F T spectrum
FERMI SURFACES OF INTERMETALLIC COMPOUNDS
65
Table 13 Cyclotron masses m~ for the field along (100) in the RX compounds (Settai et al. 1993, Aoki et al. 1985, Goto et al. 1993, Ozeki et al. 1991, Tanaka et al. 1993, Takeda 1992, Takeda et al. 1993) Compound LaSb CeSb
a3
0.14 0.23
PrSb
0.19
SmSb
0.21 0.28
GdSb CeAs YbAs
0.24 0.35 0.18
al, az
3
0.94 0.82
0.15 0.50 (/30 0.97 (./32)
0.82
0.26
0.60 0.52
0.27 0.23 0.47
[Y
0.49
0.89 (/33) (/34) 0.40 0.74 0.64
for branch/34 with its large mass is masked by the huge amplitudes of higher harmonics for the other branches with small masses. The difficulty in observing branch/34 is thus ascribed to its large mass. The mass enhancement in CeSb is quite large, more than twenty. However, the cyclotron masses in CeSb, except branch/34, are not large, as shown in table 13. They are in the range of 0.3m0 to 0.9m0 mass enhancement factor of two or three (Kitazawa et al. 1988, Aoki et al. 1985). Therefore the mass &branch/34 should be large, it is estimated to be about 10m0. Unfortunately, it has not yet been clearly determined by experiments. We mention dHvA measurements in other RX compounds, dHvA measurements on CeBi were made by Kasuya et al. (1987). The result is not perfect, but the observed branches ai, [31 and/32 agree very well with the results of band calculations. dHvA measurements were also done for PrSb, SmSb and GdSb (Goto et al. 1993, Ozeki et al. 1991, Tanaka et al. 1993). Figures 53-55 show the angular dependence of the dHvA frequency in PrSb, SmSb and GdSb, respectively. The Fermi surfaces obtained are similar to that of LaSb. For the antiferromagnetic compound SmSb, the dimensions of the Fermi surfaces are the same in both paramagnetic and antiferromagnetic states. The cyclotron masses in the paramagnetic (antiferromagnetic) states are 0.21m0 (0.28m0) for branches a3, 0.82m0 (0.60m0) for branch al and a2, 0.26m0 (0.27 m0) for branch/3, and 0.74m0 (0.64rn0) for branch y for field along the (100) direction, which are 1.5-2 times larger than those of LaSb. Shubnikov-de Haas oscillations were detected in CeAs (Kwon et al. 1991, Takeda et al. 1993). For a good stoichiometric sample of CeAs, the carrier number is one order of magnitude smaller than that of CeSb. Branches ai and 3 were observed, although branch/31 due to a hole Fermi surface in band 3 was not observed. The topology of the Fermi surface is similar to that of LaSb, although the volume is small compared to LaSb, as shown in fig. 56.
66
Y. 0NUKI and A. HASEGAWA 15 PrSb
I
{100}
i
{110}
o
10 o o)
r+,
I I
lO6
105
j6(~)
I 30
,
i
,
I
,
l
0 30 60 F i e l d Angle (Degrees)
i
9O
The measured cyclotron masses in CeAla are 1. lm0 for branch e and 16m0 for branch ~. The enhancement factor for the mc value of LaAlz is seen to vary and falls between 5 and 10. Here, the y value of CeA12 at low temperatures (Bredl et al. 1978) is 135 mJ/K 2 mol, while that of LaAI2 is 11 mJ/K 2 tool (Hungsberg and Gschneidner 1972). Therefore, the enhancements of mS and y in CeA12 over their values in LaAI: are of comparable magnitudes. 4.3. Fermi surfaces in the hexagonal Brillouin zone 4.3.1. RGa2 RGa2 compounds crystallize in the simple hexagonal A1B2-type structure. The primitive cell contains one molecule of RGa2. Figure 63 shows the crystal structure of RGa2 and its hexagonal Brillouin zone. Among them, CeGa2 is a highly anisotropie ferromagnet with the easy axis in the basal plane. The magnetic phase diagram is not simple, indicating the ferromagnetic state below 8.4 K and two or three complicated antiferromagnetic states in the temperature region between 8.4 K and 11.4 K (Jerjini et al. 1988, Takahashi et al. 1988). From resistivity data and other magnetic properties, it is concluded that CeGa2 is not a Kondo lattice compound but a usual f-localized one. SmGa2 is also an f-localized compound with a N6el temperature of 20K. We summarize in table 16 the characteristic properties of RGa2 (Umehara et al. 1992c, Tang and Gschneidner 1989, Tang 1989, Dijkrnan 1982). We show in figs. 64 and 65 the angular dependences of dHvA frequency in LaGa2 (Sakamoto et al. 1990) and CeGa2 (Umehara et al. 1991d, 1992c), respectively. The dHvA
FERMI SURFACES OF INTERMETALLIC COMPOUNDS
71
kz
(b)
Fig. 63. (a) The hexagonal A1B2 type crystal structure of the RGa2 compounds. Spheres with and without pattern show the Ga atoms and the R atoms, respectively; (b) Brillouin zone of the body-centered tetragonal crystal lattice for c/a > v'~. Table 16 Characteristic properties of the RGa2 compounds Compotmd
TN (K)
LaGa2
Pauli para
CeGa2 SmGa~
8.4 20
Tc (K)
11.4
n
7 (mJ/K2moO
nh
4.1-5.6
nh nh
8.9-9.1
Fermisurface two kinds of ellipsolidal hole Fermi surfaces (bands 3 and 4) and a multiply connected hole Fermi stu-face (band 5). similar to LaGa2, but spin-split similar to LaGa2, but affected by MBZ
branches in CeGa2 are similar to those o f LaGa2, although all branches in CeGa2 are split into the up and down spin states o f the electrons due to the ferromagnetic exchange interaction. The exchange energy is estimated to be about l 7 m e V from the spin factor. Branches a and/3 correspond to the ellipsoidal Fermi surfaces o f revolution along the c-axis ( F A direction). We note that the branch denoted b y / 3 actually consists o f two separated branches in LaGa2. Its topology has dumb bell characteristics. It is not easy to clarify the topologies o f branches 7, e and 6 from the present data. The magnetoresistance was measured for CeGa2 (Umehara et al. 1991d, 1992c). The magnetoresistance increases in a wide angle range, with a H 13-1'8 dependence. W h e n field is applied along the [1010] direction, the magnetoresistance saturates. It was concluded that CeGa2 possesses open orbits in a wide range o f angles, namely, in the basal plane and arotmd the [0001 ] direction. Owing to the simple hexagonal crystal structure with one molecule per primitive cell belonging to the symmorphie space group (P6/mmm), LaGa2 is a compound like LaSb for which the energy band structure can be calculated most easily i f the one-electron potential
72
Y. O N U K I a n d A. H A S E G A W A
108_ ' ' I ' ' I ' ' -
~
LaGa2
' ' ! ''
t/
"
"'--J
' I ' '
] 0 8 ~
' 1 ' ' 1 ' '
''
' ' 1 ~ ' 1
''
', 6 d
I
CeGa2
6
o "~
5
.....
-
i
"
-
107
FA FM FK FA 1061 , , I ~ , I , ~ I ~ , I ~ , I , , I , , I 90 60 30 0 0 30 60 90
[0001]
[10i0] [1150] Field
Angle
[0001]
(Degrees)
Fig. 64. A n g u l a r dependence o f the dHvA frequency in LaGa 2 (Sakamoto et al. 1990). The solid lines connecting the data are guidelines. The dashed lines show the results o f band calculations for band 5 ( H a r i m a and Yanase 1991b). The Greek letters designate the various orbits.
FA 90
[0001]
60
30
FM
F'K
0
0
FA 30
[10i0] [1150] Field Angle (Degrees)
60
90
[0001]
Fig. 65. Angular dependence o f the dHvA frequency in CeGa 2 (Umehara et al. 1991d). The solid lines connecting the data are guidelines. The Greek letters designate the various orbits.
is constructed appropriately. Nevertheless, its Fermi surface proved to possess a sheet with a fairly complicated topology. Harima and Yanase (1991b) performed LAPW band calculations for LaGa2. An ellipsoidal hole Fermi surfaces exist in bands 3 and 4, centered at the A point, which correspond to branches a and fi, respectively. A mukiply connected hole Fermi surface, which favors the open orbits, exists in band 5, as shown in fig. 66. The broken lines in fig. 64 are the results of band calculations for band 5. The band 5 Fermi surface consists of twelve multiply connected arms which stretch from A to K, possessing a hollow in the center F. Detected branches 7, 6 and e are ascribed to this Fermi surface. The cyclotron mass of LaGa2 is in the range of 0.15m0 to 1.83m0, which is similar to that of CeGa2, 0.32m0 to 1.44m0. The masses of branches a and fi in CeGa2 are twice as large as those of LaGa2. On the other hand, the masses of the other branches in CeGa2 are almost the same as those in LaGa2. The mass enhancement is anisotropic, depending on the band, as shown in table 17. Here we note the 7 value of CeGa2. The 7 value determined at temperatures lower than the magnetic ordering temperature is about 9 mJ/K 2 mol (Umehara et al. 1992c, Dijkman 1982), while Tang and Gschneidner (1989) estimated it as 32.6 mJ/K2 mol from the paramagnetic state. Gsehneidner (1993) suggests
FERMI SURFACES OF INTERMETALLIC COMPOUNDS
[0001]
,
i
t
i
i
,
i
I
'
i
73 !
i
i
,
4
1
,
,
i
s.~a~2 ~° 1
108
E
T
0 o
i07
H
[ioio]
[1120]
Fig. 66. Multiply connected hole Fermi surface in band 5 of LaG% (Harima and Yanase 1991b). The Greek letters designate the various orbits.
FA i061, , , 90
30
G0
[oooi]
FM
FK
0
0
FA 30
60
[10i0] [1120] Field AngLe (Degrees)
90
[0001]
Fig. 67. Angular dependence of the dHvA frequency in SmGa2 (Sakamoto et al. 1990, 1992). The solid lines connecting the data are guidelines. The Greek letters designate the various orbits.
Table 17 dHvA frequencies F and their cyclotron masses m~ a in the RGa 2 compounds for the field along [0001] except in branches 0, r/, V for the field along [100] (Sakarnoto et al. 1990, 1992, Umehara et al. 1991d) RG~
0 F
q m e*
F
6 m~
LaG%
71.7
CeGa 2 SmG~2 128.3
F
66.0 64.0 2.5
77.15
1.6
y m*e
F
1.83 37.6 1.42
e
3
mc*
F
me*
1.30
18.3
0.94 1.33 1.28
33.0
1.41
28.85
1.2
18.0 16.0
F
a me*
F
me*
4.98
0.27
2.21
0.15
4.50 4.00 3.75 4.96
0.25 0.41 0.44 0.25
1.88
0.32
2.28
0.11
a F values in 106 Oe, m~ expressed in m0.
t h a t b o t h v a l u e s a r e c o r r e c t . T h a t is, o n o r d e r i n g , t h e d e n s i t y o f s t a t e s at t h e F e r m i e n e r g y is r e d u c e d b y a f a c t o r o f a b o u t 3.5 i n C e G a 2 . S m G a 2 is a n a n t i f e r r o m a g n e t . T h e e - a x i s c o r r e s p o n d s to a n e a s y a x i s a n d m e t a m a g n e t i c t r a n s i t i o n s o c c u r at 13, 3 2 . 5 , 35, 36.5 k O e a n d m o s t likely at h i g h e r fields. F i g u r e 67
74
Y. ()NUKIand A. HASEGAWA
shows the angular dependence of the dHvA frequency (Sakamoto et al. 1990, 1992). Branches a and/3 are split into the up and down spin states of the electrons. The splitting energies are 10meV at fields of 17kOe to 27kOe and 26meV at fields of 45kOe to 60kOe. The cyclotron mass in SmGa2 is in the range of 0.1m0 to 2.5m0, the same magnitude as in CeGa2. The mass enhancements of CeGa2 and SmGa2 are due to the usual electron-magnon interaction. 4.4. Fermi surfaces in the tetragonal Brillouin zone 4.4.1. RRu2Si2 and RRu2Ge2 RRu2(Si, Ge)2 compounds possess the tetragonal ThCrzSi2-type crystal structure with one molecule per primitive cell. Figure 68 shows the crystal structure and its tetragonal Brillouin zone. LaRuzSi2 or LaRu2Ge2 is a non-4f reference compound. CeRu2Si2 is thought to be a non-magnetic Kondo-lattice compound. Reflecting a rather low value of Kondo temperature of about 20 K, the electronic specific heat coefficient y is large: 350mJ/K 2 mol (Besnus et al. 1985). CeRuzGe2 is not a Kondo lattice compound but an f-localized ferromagnetic compound with a Curie temperature of 8 K, similar to CeGa2, as shown in tables 1 and 18. Figures 69 and 70 show the angular dependence of the dHvA frequencies in LaRu2Si2 (Onuki et al. 1992) and LaRu2Ge2 (Fukuhara et al. 1993). The detected branches are simple in their angular dependences. Branch a is the main one. This Fermi surface is assumed to be an ellipsoid of revolution shrunk along the [001] direction. The volume of the Fermi surface becomes 1.3 x 1024 cm -3 for LaRu2Si2, which is about half of the volume of the Brillouin zone. Here, the volume of the Brillouin zone is (2Jr/a)2(4Jr/c) of 2.912x1024cm-3 if we use the lattice parameters a = 4 . 2 1 5 A and c = 9 . 9 3 0 A for
[001]
kz r~ ...................
l
ElOOlli '
I
(a)
kx
(b)
J
010 ]
,
~
2
~
Fig. 68. (a) Body-centeredtetragonal ThCr2Siz type crystal structure. Spheres without pattern, with simple cross pattern and with complexpattern show the Th, Cr and Si atoms, respectively;(b) Brillouin zone of the body-centered tetragonal crystal lattice for c/a > v/2. The rectangularparallelepipedwhich is equivalent to the Brillouin zone is indicated by the dashed lines.
75
FERMI SURFACES OF INTERMETALLIC COMPOUNDS Table 18 Characteristic properties of the RRu2Si 2 and RRuzGe 2 compounds Compound
T¢ (K)
n
LaRuzSi2 CeRuzSi z
Pauli para valence fluctuation
n~, n¢ = n h
LaRuzGe 2
Pauli para
nh
CeRuzGe2
8
nh
'
'
I
'
'
I
'
7 (m J/K2 tool) Fermi surface large hole Fermi surface (band 14) large hole Fermi surface (band 14); and a multiply connected electron Fermi surface (band 15) with open orbits similar to LaRuzSi2 similar to LaRu2Si 2
6.5 350
20
'
'-
I
Ru2Si2
i
'
r
LaRu2Ge~ O~
108
I
1o 8
o o)
g o 'eeoeoooo~ o
oosm~e
o
o
o~
o
_
j
~
_
I~
o
#i~
~
oeo
107
~
90 [001]
I
60
~
,
I
30
,
I
0
[100] F i e l d Angle (Degrees)
r
]
30
90
[110]
Fig. 69. Angular dependence of the dHvA frequency in LaRuzSi 2 (Onuki et al. 1992). The solid lines are the results of band calculations (Yamagami and Hasegawa 1992). The Greek letters designate the various orbits.
60
30
[001] Field Angle
0
[100l (Degrees)
30
[n0]
Fig. 70. Angular dependence of the dHvA frequency in LaRu2Ge 2 (Fukuhara et al. 1993). The solid lines connecting the data are guidelines. The Greek letters designate the various orbits.
LaRu2Si2 in calculation. The other branches fib /32 and [33 also originate from small ellipsoids, similar to rugby balls in topology. The cyclotron masses for these branches are in the range of 0.5mo-2.4mo, as shown in table 19. It was revealed by a relativistic APW calculation (Yamagami and Hasegawa 1992) that the main Fermi surface of LaRu2Si2 is a large closed hole sheet which is centered at the Z point in band 14. It is essentially a sphere but highly distorted. Although its volume is
76
Y. ()NUKI and A. HASEGAWA Table 19 Cyclotron masses for the field along [100]
Compound
a
fll
f12
f13
m~
mb
m~
mb
m~
mb
LaRu2Siz
1.44 2.37 b
1.20 2.59b
0.84 0.67b
0.85 0.40b
0.53 0.55b
0.58 0.30b
LaRu2Ge2 CeRuzGe2
1.95 5.6
0.76 1.5 0.97 b
5.7
0.43 0.87
~4 mb
0.62 b 0.81
mb
1.9 b 0.84
1.5 b
m~ 0.52 0.51 b 0.47 0.63 2.3
0.43 0.85
1.5 b 1.5
0.97 b
m~
1.5
0.62 b
1.1 b
m~ CeRu2Si2~
120
2.3 2.6 b
References: 0nuki (1993), Aoki et al. (1992), Onuki et al. (1992), Fukuhara et al. (1993), King and Lonzarich (1991), Lonzarich (1988).
1.8 1.0b
19.7
20
12.3
b Values for the field along [001]. c Field along [100] for ~;, along [110] otherwise.
nearly equal to h a l f o f the Brillouin zone, it has an extraordinarily large cross-sectional area in the (001) plane which exceeds the size o f the Brillouin zone itself. The Fermi surface is a flat ellipsoid with steep concave and convex curvatures as shown in fig. 71. The solid lines in fig. 69 are the results o f band calculations. Additionally, three rugby balls are present in bands 11, 12 and 13 centered at Z, which correspond to/33,/32 and/31, respectively. Branch/34 s e e m s to be an orbit circulating along the tube o f the doughnut in a band 15 electron Fermi surface. The calculated )'b value is 6.95 mJ/K 2 mol for LaRu2Si2, which is nearly the same as the experimental y value o f 6.5 mJ/K 2 mol. Therefore the band masses are the same as those o f the experimental cyclotron masses, as shown in table 19. The field dependence o f magnetoresistance for LaRu2Si2 shows a saturated behavior for the whole angle region, indicating that LaRu2Si2 (LaRu2Ge2) is an uncompensated metal and possesses no open orbits ((3nuki et al. 1992). This is simply expected because the primitive cell contains one molecule o f LaRu2Si2 and the La ion is trivalent, La 3÷, which is consistent with the results o f band calculations. The d H v A data for the ferromagnetic compound CeRu2Ge2 in fig. 72 (King and Lonzarich 1991) are similar to those o f LaRu2Ge2 or LaRu2Si2, although every branch is split into the up and down spin states. The cyclotron masses for branch a is 5 . 6 5.7m0 which is roughly three to four times larger than 1.95m0 o f LaRu2Ge2 or 1.44m0 o f LaRu2Si2, as shown in table 19. We note that branch a is not detected around [001] in LaRu2Ge2 and CeRu2Ge2. This is mainly due to a resolution problem because the
FERMI SURFACES OF INTERMETALL1C COMPOUNDS
77
LaRu2Si 2 band 11 band 12 band 13
~ ~ ~h01e /~3
band hole
14 centered
at Z
/~
~, centered at Z
b a n d 15 electron c e n t e r e d
at F
Fig. 71. Fermi surfaces of LaRu2Si2 (Yamagami and Hasegawa 1992). The Greek letters designate the various orbits.
dHvA signal for field along [001] is strongly reduced by both the curvature factor and the cyclotron mass compared to the signal around [100] in LaRu2Si2. Figure 73 shows the angular dependence of the dHvA frequency in CeRu2Si2 (0nuki 1993, Aoki et al. 1992, Onuki et al. 1992, Lonzarich 1988). Two kinds of rugby balls denoted by 7 and/3 are present, which are similar to branches/31 and/32 of LaRu2Si2, respectively. On the other hand, branches to, e and a are not present in LaRu2Si2. The cyclotron masses are of the order of the free-electron mass for branches )' and/3, while the other branches possess extremely large values, 120m0 for branch tp, 20too for branch to, 19.7m0 for branch e and 12.3m0 for branch a, as shown in table 19. Under the assumption that the 4f electrons are itinerant, Zwicknagl et al. (1990) carried out band structure calculations for CeRuzSi2 by a relativistic LMTO method both with the LDA and the RB theory, and showed that the Fermi surface consists of four closed hole sheets centered at the Z point and one complicated multiply-connected electron sheet. Under the same assumption, Yamagami and Hasegawa (1993) also calculated an energy band structure for CeRuzSi2 by a relativistic APW method with LDA. In fig. 73, the calculated results for the dHvA frequencies by Yamagami and Hasegawa (1993) are shown by solid lines which are compared to the experimental results. The theoretical
78
Y. 0NUKI and A. HASEGAWA I
[
60
30
'
CeRuiGe~ 108
io 8
i c)
•~
107
107
90
60
[001]
Field
30
0 [100] Angle (Degrees)
30
[110]
Fig. 72. Angular dependence of the dHvA frequency in CeRuzGe2 (King and Lonzarich 1991). The solid
90 [001]
0
[100]
30
[110]
Field Angle (Degrees) Fig. 73. Angular dependence of the dHvA frequency in CeRu2Si2 (Onuki 1993, Aoki et al. 1992, Onuki
et al. 1992, Lonzarieh 1988). The solid lines are the lines connecting the data are guidelines. The Greek results of band calculations(Yamagamiand Hasegawa letters designate the various orbits. 1993). The letters designatethe various orbits.
Fermi surface sheets which were used to calculate the dHvA frequencies in fig. 73 are shown in fig. 74. The Fermi surfaces proposed by Zwicknagl et al. (1990) and Yamagami and Hasegawa (1993) actually look similar to each other. In calculations of the former, adjustable parameters were used to fit the theoretical dHvA frequencies to the observed ones, while no such phenomenological procedure was employed in calculations of the latter. Therefore, we discuss the origins of dHvA branches on the basis of the Fermi surfaces calculated by Yamagami and Hasegawa. The hole Fermi surfaces in CeRu2Si2, centered at Z, are similar to those of LaRu2Si2. The large hole Fermi surface denoted by a in figs. 73 and 74 corresponds to branch t/t, although it is observed in a limited angle region. The cyclotron mass of ~ is extremely large. The band mass is theoretically calculated as 1.93m0 for field along the [100] direction and as 4.12m0 for [001] (Yamagami and Hasegawa 1993). The experimental mass of 120m0 is about 60 times larger than the band mass. The cyclotron mass is thus estimated as 260m0 for [001]. This extraordinarily large mass is consistent with the large 7 value and also the prediction of the renormalized band structure calculations (Zwicknagl et al. 1990), which gives a mass exceeding 200m0 for [001]. Branches/3, y, to, e and a most likely correspond to hole bands 12 (denoted by c) and 13 (b), band 15 electron orbits j, h and k, respectively.
FERMI SURFACES OF INTERMETALLIC COMPOLrNDS CeRu~Si~ (a) hole (centered at Z) bandll bandl2 bandlS
79
(b) electron (band15)
centered at Z
bandl4
centered at X
Fig. 74. Fermi surfaces of CeRu2Si 2 (Yamagami and Hasegawa 1992). The letters designate the various orbits.
The magnetoresistance of CeRu2Si2 is also useful to determine the nature of the 4f electrons as in CeSn3. In figs. 75 and 76a we show the angular dependence of the magnetoresistanee zlp/p = [p(H)- p(0)]/19(0) under constant fields and in fig. 76b the field dependence of the magnetoresistanee for currents along [110] and [001], respectively. The magnetoresistance shows a sharp peak at the critical field Hc of 75 kOe for field along the [001] (c-axis) direction. This corresponds to the metamagnetic transition. We will now discuss the magnetoresistances at lower fields than the critical field. In the configuration of J [I [110] and/-/[1 [001], the magnetoresistance Ap/p follows a Hl'7-dependence below 65kOe, while in the configuration of J II [110], H II [1t0] it saturates with increasing fields, reflecting a Shubnikov-de Haas oscillation with the dHvA frequency of 2.8x105Oe. The angular dependence of magnetoresistance under field of 65kOe shows a maximum and a minimum at H II [001] and H II [110], respectively. Moreover, when the direction of field is rotated from the [100] direction to [110] direction for current along the [001] direction, the magnetoresistance increases over the whole field direction, typically showing a Hl8-dependence in the J [I [001] and //It [110] configuration as shown in fig. 76b. These results indicate that CeRu2Si2 in the ground state is a compensated metal with an equal carrier number of electrons and holes and that open orbits exist along the J x H direction, namely [001 ] (c-axis) direction. The open orbits originate from the multiply connected electron Fermi surface mentioned above.
Y. ONUKI and A. HASEGAWA
80 '
(a)
I
J
(b)
]
J//[ilO] 0.5K
A
/150kOe ~
q~
\
l
Q
Hc (Rossat-Mignod et al. 1988). Correspondingly the lowtemperature specific heat coefficient of 350mJ/K2mol is reduced t o 80mJ/K2mol at 200kOe (van der Meulen et al. 1991). There remains a possibility that the main Fermi surfaces with a dominant 4f component disappear in topology when field crosses the critical field. This is open to future studies.
4.4.2. CeCu2Si2 dHvA oscillations have been observed in the typical Kondo lattice compound CeCu2Si2 (Hunt et al. 1990, Springford 1991), having the same crystal structure as CeRu2Si2. Superconductivity and very weak antiferromagnetic order coexist in this material below 0.7 K. The characteristic properties of CeCu2Si2 are shown in table 1. Figure 77 shows the angular dependence of the dHvA frequency. Although only part of the Fermi surfaces is observed, the detected carriers possess relatively large masses of 5m0 for field along the a-axis. Judging from the large value of the electronic specific heat coefficient, 1000 mJ/K2 mol, carriers with much larger masses should exist in this material. Band calculations were made for CeCu2Si2 by Sticht et al. (1986), using a Kondo-lattice ansatz for the cerium 4f state and LDA potential parameters. Harima and Yanase (1991 a, 1992a) also calculated the energy band structure for LaCu2Si2 and CeCu2Si2. As regards the observed part of Fermi surface, the calculated Fermi surface of LaCu2Si2 seems to fit the experimental results of CeCu2Si2 better than the itinerant f-electron Fermi surface for CeCu2Si2. Figure 78 shows the multiply connected Fermi surface in band 19 for LaRu2Si2 which corresponds to the observed dHvA branches. The 4f electrons in CeCu2Si2 are thus most likely localized and do not affect the Fermi surface significantly. Precise experiments are necessary to clarify the real situation.
82
Y. ONUKI and A. HASEGAWA I
o/
f
T-- I
CeCu2Si2
LaCu2Si 2
]
o o
o
0
30
60
Fig. 78. Multiply connected Fermi surfaces in band 19 of LaCu2Si2 (Harima and Yanase 1991a, 1992a).
90
c-axis a FieldAngle(Degrees)
Fig. 77. Angular dependence of the dHvA frequency of CeCuzSi z (Hunt et al. 1990). The solid lines connecting the data are guidelines.
4.5. Fermi surface in the orthorhombic Brillouin zone 4.5.1. RNi RNi crystallizes in an orthorhombic structure. Figure 79 shows the CrB crystal structure and its Brillouin zone. The primitive cell contains two molecules of RNi. CeNi can be characterized as a valence-fluctuating compound, similar to CeSn3. Its Kondo temperature kz
(a)
I
""-,
D~ "',r'>j
"x
i
I
-]
°
i
,1,.
! I
I
_LJ
Fig. 79. (a) c-base centered orthorhombic CrB type-crystal structure. Spheres with and without pattern show the B atoms and the Cr atoms, respectively. (b) Brillouin zone of the e-base centered orthorhombic crystal lattice for a < b. The rectangular parallelepiped which is equivalent to the Brillouin zone is shown by the dashed lines.
83
FERMI SURFACES OF INTERMETALLIC COMPOUNDS Table 20 Characteristic properties of the RNi compounds T~ (K)
Compound LaNi CeNi PrNi
n
g Fermi surface (mJ/K2 tool)
Pauli para n¢= nh valence fluctuation n¢= nh 20 n~= nh
multiply connected Fermi surfaces with open orbits multiply connected Fermi surfaces with open orbits similar to LaNi but should be spin-split
5.0 65-85
,
(a) LaNi J//e-axis 10
l
l
l
l
l
t
This difference can be clearly distinguished by the magnetoresistance. The experimental results are as follows. The magnetoresistance in LaSn3 and LaRu2 Si2 saturates over a wide angle region, representing uncompensated metals. The magnetoresistance in CeSn3 and CeRu2Si2 increases over a wide angle region. This result shows that CeSn3 and CeRuzSi2 are compensated metals. Therefore, it is concluded that the 4f electron is itinerant in CeSn3 and CeRu2Si2 in the ground state. For the compounds belonging to the Kondo regime, the dHvA data can be explained by putting one 4f state below the Fermi energy and the other unoccupied 4f bands above the Fermi energy. Therefore the Fermi surface is essentially similar to that of the La compound, as well as to those of the well localized 4f systems. The mass enhancement factor for the conduction electrons in the Kondo regime is quite large, of the order of 10 to 100 which becomes anisotropic in the some compounds such as in CeSb.
FERMI SURFACESOF INTERMETALLICCOMPOUNDS
97
The large cyclotron mass of 80m0 is detected in the non-magnetic Kondo-lattice compound CeCu6. It is, however, not clear whether the 4f-electron character of CeCu6 is itinerant or localized. (3) The 4f electron character of Yb compounds is supposed to be similar to that of Ce compounds. The dHvA measurements for Yb compounds are small in number. The Fermi surface of YbAs with magnetic ordering is similar to that of LaSb. (4) Fermi surfaces of Pr compounds with the singlet ground state such as PrIn3, PrSb and PrCu6 are almost the same as those of the corresponding the La compounds, although their cyclotron masses are twice as large as those of La compounds. Even in the antiferromagnetically ordered Pr compounds such as PrB6, most of the dHvA branches are roughly similar to those of La compounds, while some dHvA branches are not present in the La compounds. They are probably produced by the antiferromagnetic Brillouin zone boundaries. The cyclotron mass of PrB6 is roughly three times larger than that of LAB6. The Fermi surface in the ferromagnetic compound PrNi is similar to that of LaNi, although the directions of open orbits are a little different between them. (5) The magnetic energy gaps associated with the magnetic ordering are small enough and thus the electrons undergoing cyclotron motions can break through these energy gaps and circulate on orbits of the paramagnetic Fermi surface as in Pr compounds, even if the magnetic field is not strong. The occurrence of this effect becomes more difficult as the number of f electrons increases. The electrons follow the orbits on the antiferromagnetic Fermi surfaces in Nd, Sm and Gd compounds. Typical examples are shown in NdIn3 and NdB 6. For example, the paramagnetic (or field-induced ferromagnetic) Fermi surface of NdIn3 is almost the same as that of Lain3. A nearly spherical Fermi surface in the paramagnetic state, which corresponds to the band 7 electron Fermi surface of Lain3, is changed in the antiferromagnetic state into a multiply connected one with necks. On the other hand, if a Fermi surface is small and is located at the center of the Brillouin zone, it remains in the antiferromagnetic state because it is contained in the magnetic Brillouin zone. Branch d in Lain3 is most likely observed in the magnetic RIn3 compounds. The small Fermi surfaces of the monopnictides, RX, also are not changed by the magnetic Brillouin zone. Mass enhancement due to the electron-magnon interaction in magnetically ordered compounds is large compared to the one due to the electron-phonon interaction. The mass enhancement factor is in the range of 1-2. (6) Sm compounds have interesting magnetic behaviors, dHvA measurements have been performed on some compounds such as SmIn3, SmSb, SmGa2, and SmCu6. They are, however, not valence-fluctuation compounds but f-localized ones. Therefore, the situation is similar to the Nd system. Fermi surface studies for valence-fluctuating Sm compounds are open to future studies. (7) We found that the band theory worked fairly well for studies of the electronic structures in various lanthanide compounds. The energy band structures and the Fermi surfaces were clarified for many La compounds, and the theoretical results were used as a good starting point for understanding of the electronic structures of the Ce and other light lanthanide compounds, in which the 4f electrons are believed to be localized. Moreover,
98
Y. ONUKI and A. HASEGAWA
the band theory could provide clear evidence that the 4f electrons in some Ce compounds, especially CeSn3, belonging to the valence-fluctuation regime, are itinerant in the ground state, and contribute directly to the formation of the Fermi surface. The agreement between theory and experiment is as good as that attained for the 3d electron system in the iron series transition metals, as far as the topology of the Fermi surface is concerned. (8) Some drawbacks of the band theory are apparent. The disagreement between theory and experiment becomes larger when it is applied to the complicated crystal structures, like in LaNi, CeNi, YCu2 and LaCu6. Even in the La compounds with cubic crystal structures, some of the dHvA frequency branches cannot be explained well quantitatively, especially in the low-frequency region. The theory can certainly be improved by taking into account non-muffin-tin shape corrections via a full-potential scheme, and some disagreements may be removed for these La and Ce compounds. It seems to us, however, that a treatment of the exchange-correlation interactions is more serious, and it is essential to improve the theory so as to go beyond LDA. Such an improvement should be carried out in a new framework of band theory in which the exchange interaction is taken into account explicitly with the screening effect. (9) As for an appropriate band theory for the localized 4f-electron system, an attractive approach based on the p - f mixing model was proposed, and was applied to CeSb. A future problem is to refine the approach so as to carry out quantitative calculations in a self-consistent way. The anomalously large enhancement factors for the cyclotron effective masses and the y values observed in the Ce compounds cannot be explained by band structure alone. Quantitative analysis of the mass enhancement factor is a problem challenging to many-body theory. There is still much room for improvement for a complete understanding of the electronic structures of lanthanide compounds.
Acknowledgement We are very grateful to T. Kasuya, O. Sakai, K. Ueda, A. Yanase, H. Harima, H. Yamagami, Y. Kubo, T. Komatsubara, T. Suzuki, T. Goto, K. Satoh, H. Aoki, H. Sato, I. Umehara, I. Sakamoto, K. Maezawa, M. Springford and G. Crabtree for helpful discussions, and to T. Yamazald for typing the manuscript.
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Seitz, E., and B. Legeler, 1979, J. Phys. Colloq. C 5, suppl. 5, 40, 76. Sellmyer, D.J., ER. Szofran and J.W. Weymouth, 1975, J. Low Temp. Phys. 18, 85. Settai, R., H. Natsui, Y. Ohe, T. Goto, T. Fujimura, Y. ()nuki, E Iga and M. Kasaya, 1990, J. Magn. & Magn. Mater. 90&91,446. Settai, R., T. Goto and Y. 0nuki, 1992, J. Phys. Soc. Jpn. 61,609. Settai, R., T. Goto, S. Sakatsume, Y.S. Kwon, T. Suzuki and T. Kasuya, 1993, Physica B 186--188, 176. Settai, R., T. Goto and Y. ()nuki, 1995, unpublished. Shoenberg, D., 1984, Magnetic Oscillations in Metals (Cambridge University Press, Cambridge). Slater, J.C., 1937, Phys. Rev. 51,846. Springford, M., 1991, Physica B 171, 151. Springford, M., and P.H.P. Reinders, 1988, J. Magn. & Magn. Mater. 76&77, 11. Steglich, E, J. Aarts, C.D. Bredl, W Lieke, D. Meschede, W. Franz and H. Schafer, 1980, J. Magn. & Magn. Mater. 15-18, 889. Sticht, J., N. d'Ambrumenil and J. Kfibler, 1986, Z. Phys. B 65, 149. Strange, D., and D.M. Newns, 1986, J. Phys. F 16, 335. Sugiyama, K., F. Iga, M. Kasaya, T. Kasuya and M. Date, 1988, J. Phys. Soc. Jpn. 57, 3946. Sumiyama, A., Y. Oda, H. Nagano, Y. 0nuki, K. Shibutani and T. Komatsubara, 1986, J. Phys. Soc. Jpn. 55, 1294. Suzuki, T., 1993, Physica B 186-188, 347. Suzuki, T., T. Goto, A. Tamaki, T. Fujimura, Y. (3nuki and T. Komatsubara, 1985, J. Phys. Soc. Jpn. 54, 2367. Suzuki, T., T. Goto, S. Sakatsume, A. Tamaki, S. Kunii and T. Kasuya, 1987, Jap. J. Appl. Phys. 26, 511. Suzuki, T., T. Goto, Y. Ohe, T. Fujimura and S. Kunii, 1988, J. Phys. C 8, 799. Taillefer, L., G.G. Lonzarich and P. Strange, 1986, J. Magn. & Magn. Mater. 54-57, 957. Takada, S., 1966, Prog. Theor. Phys. Suppl. 36, 224. Takahashi, H., and T. Kasuya, 1985, J. Phys. C 18, 2697, 2709, 2721, 2731, 2745, 2755. Takahashi, M., H. Tanaka, T. Satoh, M. Kohgi, Y. Ishikawa, T. Miura and H. Takei, 1988, J. Phys. Soc. Jpn. 57, 1377. Takayanagi, S., N. Wada, T. Watanabe, Y. 0nuki and T. Komatsubara, 1988, J. Phys. Soc. Jpn. 57, 3552. Takayanagi, S., N. Wada, Y. Onuki and T. Komatsubara, 1991, J. Phys. Soc. Jpn. 60, 975. Takeda, N., 1992, Thesis (Tohoku University).
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Handbook on the Physics and Chemistry of Rare Earths Vol. 20 edited by K.A. Gschneidner, Jr. and L. Eyring © 1995 Elsevier Science B.V.. All rights reserved
Chapter 136 THE INTRICATE WORLD OF RARE EARTH THIN FILMS: Metals, Alloys, Intermetallics, Chemical compounds, ... M. G A S G N I E R
Centre National de la Recherche Scientifique, Laboratoire de Chimie Mdtallurgique et Spectroscopic des Terms Rares, UPR 209 CNRS Bellevue, 1, place A. Briand, 92195 Meudon Cedex, France
Co~e~s Symbols, abbreviations and units 1. Introduction 2. Rare earth metals 2.1. Introductory remarks 2.2. Valence changes in rare earths: from vapor to solid state 2.2.1. Introduction 2.2.2. R atomic vapor 2.2.3. R clusters and surface characterizations 2.2.4. R sub-, mono-, and multi-layers on oriented crystals 2.2.4.1. Samarium 2.2.4.2. Ytterbium 2.2.4.2.1. The Yb/Ni system 2.2.4.2.2. The Yb/A1 system 2.2.4.2.3. The Yb/Mo system 2.3. Crystallographic properties 2.3.1. Introduction 2.3.2. Epitaxial crystal growth 2.3.2.1. R/W systems 2.3.2.2. R/Re systems 2.3.2.3. R/V systems 2.4. Electrical properties 2.4.1. Crystalline films 2.4.2. Amorphous samples 2.5. Magnetic properties 2.5.1. Crystalline state 2.5.1.1. Thin oriented and polycrystalline R films on oriented substrates 2.5.1.1.1. W (110) substrates 2.5.1.1.2. Fe (100) substrates
108 108 111 111 111 111 112 114 t 15 115 116 116 116 117 118 118 118 118 119 119 120 120 121 122 122
122 122 124 105
2.5.1.t.3. Cu (100) and Ni (111) substrates 2.5.1.2. Polycrystalline films 2.5.1.2.1. Ferromagnetic order at R surface 2.5.1.2.2. Ferromagnetic films 2.5.1.2.3. Multilayer (Er, Tm/Lu),-type films 2.5.1.2.4. Theoretical models 2.5.2. Amorphous films 2.5.3. Magnetic domain structures 2.6. Optical properties 2.6.1. Very low energy range (below 7eV) 2.6.1.1. Scandium films and single crystals 2.6.1.2. Yttrium 2.6.1.3. Europium, gadolinium, terbium, dysprosium, holmium, erbium, thulium and ytterbium 2.6.2. Low energy range (7-70eV) 2.6.2.1. Scandium films and single crystals 2.6.2.2. Yttrium 2.6.2.3. Lanthanum and cerium 2.6.2.4. Gadolinium, dysprosium, thulium, and lutetium 2.6.2.5. Samarium 2.6.2.6. Europium and ytterbium 2.6.3. Medium energy range (70600 eV)
124 124 124 125
125 125 125 126 126 126 126 127
127 128 128 128 129 129 130 130 130
106
M. GASGNIER 2.6.3.1. 2.6.3.2. 2.6.3.3. 2.6.3.4.
Scandium and yttrium Lanthanum Cerium Gadolinium, thulium and lutetium 2.6.3.5. Ytterbium 2.6.4. High energy range (beyond 800 eV) 2.7. Applications relative to metallic films and foils 2.7.1. The piezoresistance response of Yb foils 2.7.2. Diffusion barriers: Sm and Yb metal interfaces 2.7.3. Tunnel junctions: Yb/oxide/pInAs 2.7.4. Magnetic devices 2.8. Metallic or contaminated films or fine particles? Remarks about the fcc phase 2.9. Formation and properties of the rare earth hydrides 2.9.1. Formation of the hydrides 2.9.1.1. Contamination of thin R films 2.9.1.2. Residual hydrogen 2.9.1.3. Reaction of R elements with water vapor 2.9.2. Physical characteristics 2.9.2.1. Electric resistance and resistivity 2.9.2.2. Work function 2.9.2.3. Surface magnetization 2.10. Rare earth deuteride and tritide 2.10.1. Bulk materials 2.10.1.1. Introduction 2.10.1.2. Gettering 2.10.2. Thin films 2.10.2.1. Scandium and yttrium 2.10.2.2. Erbium 2.11. Formation of the rare earth nitrides 2.12. Reactivity with CO, C Q and CnH. gases 2.12.1. Rare earth/CO and C,H n interactions 2.12.2. Lanthanide/CQ reactions 3. Metallic R-alloys 3.1. Permanent magnets 3.1.1. Introduction 3.1.2. [R(Pr, Nd),R'(Dy)]xFeyBz alloys 3.1.2.1. Magnetic properties 3.1.2.1.1. Thick and thin films
130 130 131 131 131 131 132 132 132 133 133 133 135 135 135 135 137 137 137 140 140 140 140 140 140 141 141 141 142 143 143 144 144 144 144 145 145 145
3.1.2.1.2. Multilayers and modulated films 3.1.2.1.3. Magnetic domains 3.1.2.2. Hydrogen treatments 3.1.2.3. Microstructural properties 3.1.2.4. Other compounds: RFe(N or C) 3.1.2.5. NdH Fe4B4 3.1.2.6. AI, Cr, Mn, Ga, Nb, Zr, Cu and W addition effects 3.1.2.6.1. AI addition 3.1.2.6.2. Cr and Mn additions 3.1.2.6.3. Ga addition 3.1.2.6.4. Nb addition 3.1.2.6.5. Zr addition 3.1.2.6.6. Si addition 3.1.2.6.7. W addition 3.1.2.7. Applications 3.1.3. RTiFe(Co) alloys (R=Sm, Nd, Dy) 3.1.3.1. (Sm, Nd)TiFe magnets 3.1.3.2. (Sin, Dy)TiCo magnets 3.1.4. Smx(Co,M)y substituted alloys (M=Fe, Cu and Zr) 3.1.5. RCo(B) amorphous films 3.1.5.1. Sm~Col0o_xalloys 3.1.5.2. Amorphous NdCoB magnetic thin films 3.1.5.3. Applications 3.2. (TM/R)n modulated and multilayered films. (R = Y, La, Ce, Nd, Gd, Tb, Dy; TM=Fe, Co, Ni) 3.2.1. fie/R), films 3.2.1.1. (Fe/Y),, 3.2.1.2. (Fe/La), layers 3.2.1.3. (Fe/Nd), and (Fe/Dy), films 3.2.1.4. (Fe/Gd), films 3.2.1.5. (Fe/Tb), films 3.2.1.6. (Fe/Nd, Er, Tm), films 3.2.2. (Co/R), films 3.2.2.1. (Co/(Pr, Nd)), films 3.2.2.2. (Co/Gd), films 3.2.2.3. (Co/Tb), films 3.2.2.4. (Co/Dy), films 3.2.3. (Ni/R), films 3.2.3.1. (Ni/Ce), layers 3.2.3.2. (Ni/Dy), layers 3.2.4. Other multilayer systems
146 147 148 150 151 152
152 152 153 153 153 153 153 155 155 155 155 155 156 156 156 157 157
157 157 157 158 158 159 160 161 162 162 162 164 164 165 165 165 165
THE INTRICATE WORLD OF RARE EARTH TH1N FILMS 3.2.4.1. YCo/(Nd, Gd, Er)Co/YCo sandwiches 3.2.4.2. (TbFe/Ni-Fe-Mo) bilayer films 3.2.4.3. (PtMnSb/TbFe) bilayer films 3.2.4.4. (Fe/TbFe) bilayers 3.2.4.5. (Zr-Fe/TbFe)~ amorphous multilayers 3.2.4.6. (ZnS/GdFe) multilayers 3.2.4.7. (TbFe/SiO), muttilayers 3.2.4.8. Insulating/magnetooptic/insulating systems 3.2.4.8.1. Si3N4 3.2.4.8.2. SiO2/GdTbFe 3.2.4.8.3. Dielectric/Nd-DyFe~2o-Ti/Si3 N 4A1N on plastic 3.2.4.9. Amorphous
165 165 165 166 I66 166 166 166 166 166
166
(TbxFel_x/A1203)n
3.3.
3.4.
3.5.
3.6.
multilayers 3.2.5. Formation of sandwiched layers: R(Dy, Tb) ions implanted in Fe and Ni films. Structure and magnetic properties R-Fe,Co/hydrogen and other gaseous contaminants: changes in magnetic properties RNi 5 and RC% as hydrogen storage films 3.4.1. LaNi 5 alloy 3.4.1.1. Hydrogen absorption Crystalline states 3.4.1.2. Electric resistivity 3.4.1.3. Hydrogen separation and permeation 3.4.2. Other RNi 5 alloys 3.4.3. RC% alloy (R = La, Sm) 3.4.4. Remark Polytypic structures 3.5.1. Ferromagnetic samarium-nickel alloys 3.5.2. Samarium-cobalt alloys 3.5.3. Rare earth trialuminides R-noble metal alloys 3.6.1. The R-Cu system 3.6.1.1. Amorphous R-Cu films (R = Y, Tb, Dy) 3.6.1.1.1. CUxYI_~ 3.6.1.1.2. Dy-Cu and Tb-Cu 3.6.1.1.3. Cu addition to TbFe-Co
166
167
167 169 169 169 170 171 172 172 172 172 173 174 177 177 177 177 177 178 178
3.6.1.2. Crystalline R-Cu films (R =Y, Ce, Dy, Ho, Er and Yb) 3.6.1.2.1. (Cu/Y), 3.6.1.2.2. Ce/Cu interface 3.6.1.2.3. Cu-Dy, Cu-Ho, CuEr 3.6.1.2.4. Yb/Cu 3.6.1.3. R-Cu samples as precursors for synthesis catalysts 3.6.1.4. Ion-beam mixing 3.6.2. The R-Au system 3.6.2.1. Amorphous GdAu and GdFeAu films 3.6.2.2. Crystalline films 3.7. R-Pd alloys (R=Ce, Eu, Er, Yb) 3.7.1. Valence change in R-Pd alloys 3.7.1.1. Ce-Pd amorphous crystalline samples. Comparison to other materials 3.7.1.2. Eu and Yb-Pd amorphous specimens 3.7.2. Rx-Pdy crystallographic properties 3.8. Superconducting materials 3.9. Miscellaneous R-M alloy films and thin crystals 3.9.1. Y, La-Pb multilayer samples 3.9.2. Transport properties in U-R films (R = ad, Yb) 3.9.3. Quasicrystal Co-Er alloys 4. Metalloid R-compounds 4.1. Rare-earth chalcogenide and bismuth systems 4.1.1. RAs films (R=Tb, Dy, Er, Yb and Lu) 4.1.1.1. ErAs, ErxScl_xAs and ErP, As~_x specimens 4.1.1.2. YbAs films 4.1.1.3. Yb-As2S3 films 4.1.2. RSb films (R=Sm, Tm, Yb) 4.1.3. RBi films (R=Gd) 4.2. Pb(Eu, Yb)(Te, Se, S) thin films 4.2.1. Lead--europium films 4.2.2. Lead-ytterbium films 5. Conclusion References
107
178 178 178 179 179
179 180 180 180 180 18I 181
18 I 182 182 184 185 185 185 185 186 186 186 186 187 187 188 188 188 188 190 190 190
108
M. GASGNIER
Symbols, abbreviations and traits AES bee dhcp Eg e-beam e-gun EDP EDX EELS ESR fcc Hc hcp HREM kAm-1 Ku L LEED
Auger electron spectttm body centered cubic double hexagonal close packed energy gap electronbeam electrongun electrondiffraction pattern energy dispersive X-rays electronenergy loss spectrum electronspin resonance face centered cubic coercive force or coercivity hexagonalclose packed high resolution electron microscopy 12.5 Oe (1 kOe=80kAm-1) uniaxial magnetic anisotropy (uniaxial perpendicular energy) Langmuir (deposit at 10-6 Torr s = 1.33x 10-4 Pa s) low-energyelectron diffraction
MBE Ms Pa R RBS rf RHEED SQUID STEM T Tc TCR TEM TM UPS XAS XPS XRD
molecular beam epitaxy saturation magnetization 133.33 Torr rare earth elements Rutherford backscattering radio frequency (sputtering) reflection high-energyelectron diffraction superconducting quantum interference device scanning transmission electron microscope Tesla (10 kGauss) superconducting transition temperature temperature coefficientof resistance transmission electron microscope transition metal ultraviolet photoemission spectroscopy X-ray absorption spectroscopy X-ray photoemission spectroscopy X-ray diffraction pattern
1. Introduction During the last decade numerous papers have reviewed and commented the main physical and chemical properties o f the rare earth elements. Eyring (1979), Gasgnier (1980, 1989) and Boulesteix (1982, 1984) have reported the main characteristics o f the sesquioxides (R2 03) and o f the intermediate oxides (ROx, with R = Ce, Pr and Tb, and 1.5 ~<x ~ 2). Netzer and Bertel (1982) and Netzer and Matthew (1987) have provided much informations relative to the surface reaction (adsorption), valence and electronic states and catalysis properties o f rare earth metal alloy, hydride and oxide as thin samples. The characteristics o f rare earth compounds (sulfides, silicides, borides,... ) have been reviewed by Gasgnier (1989). Eschenfelder (1980a, 1980b), Gasgnier (1982), Buschow et al. (1982) and Busehow (1984) have presented a large number o f results on the rare earth-3d transition metal alloys as amorphous or crystallized thin and bulk materials. The properties of permanent magnets, superconductors (other than those o f the new high-To ceramics) and magnetic multilayers have been reviewed by Burzo and Kirchmayr (1989), Coey (1991) and Gasgnier (1991). Before investigating the results given in the literature, one must emphasize three main problems which seem to be always in competition. Indeed, and in spite of the numerous reliable experimental results and theoretical studies published by several research groups,
THE INTRICATEWORLDOF RARE EARTHTHIN FILMS
!09
"strange" and "extraordinary" new properties are always being reported now and again in different articles. The first problem is relative to the oxidation state, and we should like to exclaim: "poor rare earth valency!". So, recently, Savrin et al. (1988) have reported an tmexpected series of oxides as Pr2Os, Nd205 and Nd6Oll. However, a careful survey of the published Xray diffraction patterns shows that these "compounds" correspond to Pr(OH)3, Nd(OH)3 and C-Nd203 respectively. The misappreciation of the oxidation states of the R elements is hardly understandable. Indeeed, the authors claim that the Pr and Nd oxidation states correspond to the electronic 4f3(6s 2) and 4f4(6s 2) structures, respectively, and therefore they conclude that these elements have a +5 valence, includingf electrons in the valence band. Such electronic configurations are known to be related to the neutral atoms, but in the elemental metallic state the basic configuration becomes 4fn(5d16s 2) except for Eu and Yb which retain the 4fn(6s 2) configurations (n = 7 or 14). To explain the valences of the R elements, one must recall the works of D.A. Johnson (1969, 1977) who has studied the stability of the RC12 compounds with respect to the disproportionation reaction: 3RC12(s) + R(s) --+ 2RC13(s). The dichlorides are stable if the change in free energy is positive. The following order for the relative reducibility of the lanthanides has been deduced: Eu, Yb, Sin, Tm, Dy, Nd, Ho, Er, Pr, Tb, Ce, Gd and La. In this way, one can remember the useful classification of the R elements: pure +2 (EuO) Eu Yb, Sm, Tm
+2 with S, Se, Te (very unstable with 02)
La to Lu (incl. Sc + Y)
+3 (R203)
Ce, Pr, Tb
+4 (Ro2)
+3 --+ +4 (ROx) Ce, Pr, Tb Under standard conditions of temperature and pressure it is not possible to obtain other oxides. The second problem concerns the reactivity of the lanthanides. Numerous research groups have demonstrated that they are excellent getters for hydrogen and that they can absorb (OH)- radicals. But such properties often remain misappreciated, and numerous physical and chemical results and interpretations are then hidden or altered. Indeed, the hydrides or the hydroxides can be formed as chemical compounds either at the surface of a sample or at grain boundaries. This getter effect is strongly enhanced in the case of thin films which are characterized by a large surface/volume ratio. Besides, in the case of multilayer sequences, the interface between two different materials must be carefully studied. Two phenomena can occur concurrently: one is relative to the cation and/or anion diffusion and the other to the possible formation of chemical compounds and alloys. So, in the case ofW/C/W/C.., as a stacking sequence, the formation of a WxCyOz compound (0.5-1 nm thick) has been observed at ambient temperature (Gasgnier et al. 1983). In the same way, the formation of passivation thin films, even if their thickness does not exceed
110
M. GASGNIER
some 10nm, becomes a "poison" for some physical measurements. A rapid calculation, in the case of a film with a thickness of about 100nm, demontrates that about 10% of the total thickness is far from the "ideal" metallic material. Therefore, many times it is difficult to neglect the formation of thin contamination films at the interfaces. The last problem is relative to the crystallographic phases. They are often deduced from electron diffraction patterns (EDP's). Various phenomena which occurred in the course of the study of thin samples are sometimes badly known, or else the patterns can be misinterpreted and the indexation becomes wholly wrong. Recently Z. Li et al. (1988) have claimed to the formation of new polymorphic erbium oxide phases. These were in fact the well-known ErH2, C- and B-Er203 compounds (Gasgnier 1980, 1990). Other misinterpretations result from decided opinions on chemical reactivity, phase transitions, compound formation (as Lu(OH)4 for example) (Gasgnier 1991) ... and/or on disorder between two crystallographic phases. The rare earth series display basic chemical and physical properties which are now well established. Moreover, the new micro- (and even nano-) analysis apparatus should be used in a systematic way to insure accurate determination of the specific properties of the materials. Another remark must be made: it is appropriate that authors should report all the pertinent references in their articles, but many times this is not the case. So, it is often observed that compounds like SmO (this one is something of a "myth" for numerous authors) and Sm20 (Eick et al. 1956, Ellinger and Zachariasen 1953) are always taken into account. However a later paper of Felmlee and Eyring (1968), which demonstrated that these compounds are actually SmNl_xOx and SmH2, respectively, is never listed. As an example, one can mention the results of Tkach et al. (1980) who claim to the formation of SmO (with a fcc parameter as a = 0.502 nm) instead of the SmNl_xOx compound. In the same way one can add that these authors have "deduced a new Sm-hcp metallic phase", which is in fact the dhcp phase (Gasgnier 1980) which seems fully unknown to them. A second example is also noteworthy: Curzon and Chlebeck (1972, 1973) had, at first, claimed that rare metal films crystallized as a new fcc phase. However, later on (see Gasgnier 1980 for accurate comments) they agreed to have been confused and concluded that this phase was in fact the rare earth dihydride. These authors have published a large number of papers which refer to the dihydride films, but others only reference the first articles. So the following questions can be put: "Why is the gettering action of R elements for hydrogen neglected and/or ignored by some research groups? Is it to fit some theoretical results?" In conclusion one can notice that the second example overlaps the three problems discussed in this Introduction. These remarks allow us to understand why some properties of rare earth elements have always been the subject of hard polemics and debates. Therefore, our purpose is to demonstrate that the physical and chemical properties of rare earth metallic and rare earth alloy thin films or single-crystals must be cautiously analyzed. Particularly, the lack of crystallographic spectra (X-ray or electron diffraction), of chemical analyses (absorbed or adsorbed gases, surface contamination, impurities,... ), of structural investigations (grain size, defects. . . . ) for example, is truly detrimental to precise characterization of the materials. In this way one can claim that numerous
THE INTRICATEWORLD OF RARE EARTHTHIN FILMS
111
polemics become unfruitful because the arguments of the different authors are often strictly not convincing.
2. R a r e earth metals
2.1. Introductory remarks For about twenty years the problem of the purity of rare earth metals either as thin films, or thin particles, or thinned materials is a matter of fact. These metals are quite sensitive to various gaseous contaminants. So, processes like vacuum deposition, annealing, aging, and thinning treatments either under vacuum or at ambient atmosphere, must be carried out very cautiously. Consequently the possible formation of chemical compounds and/or surface or volume contamination might be proven. So, one can point out that the experiments of Onsgaard et al. (1979), Onsgaard and Ignatiev (1982) and Tougaard and Ignatiev (1981) have shown that the (10.0) and (00.1) single crystal surfaces of scandium exhibit segregation of impurities like S, C1, C and O. After heating (between 813 and 1213 K) and/or krypton ion bombardment a clean Sc surface has been obtained, as demonstrated by the Auger spectra. Another example is from SIMS measurements by Reichl and Gaukler (1986). At the surface of a Y evaporated film the following species have been observed: YH +, YHO +, YO-, YO] and Y203. It is unlikely that the presence of such poisons, and also that of composite materials (e.g. metal + hydride and/or oxide) are always verified, and thereby the physical and chemical properties are changed compared to the ones of the pure bulk metal. 2.2. Valence changes in rare earths: from vapor to solid state
2.2.1. Introduction The problem of mixed-valence behavior which is sensitive to particle size has been studied for Sm, Tm and Yb metals. A review paper by Connerade and Karnatak (1990) points out, for vapors and clusters, the main calculations and interpretations which have been done to explain this property. The authors report numerous XAS results which demonstrate experimentally the valence change with cluster size. Netzer and Bertel (1982) have given numerous results relative to the mechanism of surface oxidation. A theoretical approach of valence fluctuations has been done by B. Johansson (1979) and Rosengren and Johansson (1982 and refs. therein). The latter is a review paper which allows to have a good understanding of the main results and hypotheses published up to this date. Before discussing the results, one must add the following remarks. The first was made by B. Johansson (1979): "This means that experimental results, obtained from a surface-sensitive technique, must be carefully analyzed before a specific structure of the spectrum can be said to originate from the bulk or the surface, respectively". The second one is that the divalent state of Tm has not been convincingly demonstrated up to this date.
112
M. GASGNIER
2.2.2. R atomic vapor The problem of the electronic (or ionic) configurations for the three different states of the R elements: vapor, metal and oxide, has been described in detail by Gsehneidner (1971), Gschneidner and Daane (1988), Gschneidner et al. (1990), and Beaudry and Gsehneidner (1978). In the gaseous state two types of configuration are encountered: (1) 4fn(5d16s 2) for La, Ce, Gd and Lu [Sc with 3da4s 2, and Y with 4d15s 2 must be added]. This is the normal configuration whieh leads to a difficult reducibility of the elements (see D.A. Johnson 1969, 1977). (2) 4fn+d(6s2) which is the most common configuration for Pr--+ Eu and Tb ~ Yb. In the metallic state the configuration change leads to the following electronic states: (1) 4fn(5d16s2), i.e., the normal trivalent state for Sc, Y, La --+ Sm, Gd ~ Tm and Lu. (2) 4fn(6s 2) for Eu and Yb, i.e., the divalent state and the more reducible metals of the R series (see D.A. Johnson 1969, 1977). The first experimental absorption spectra have been reported by Materlik et al. (1983b). The LIII (2p --+ 5d transition) absorption edges of Ce, Sm, Gd and Er as vapors and metals are compared. From previous works (Materlik et al. 1983a), it is asserted that Sm and Gd to Lu metals exhibit similar white lines well described by the ground-state potential and that no major redistribution of the valence electrons occurs. (The authors demonstrated that the white line and the near-edge structure can be well described by a single-particle band-structure calculation.) In the case of metallic vapor of Ce and Gd the Lni edges almost coincide with those of the metal. In contrast, for Sm, and Er, the peak of the white line is shifted towards higher energies by about 8 eV. In the same way the LI spectra give identical results (shift of about 5 eV). The authors conclude that a configuration change occurs for Sm and Er (4f6--* 4f 5 and 4f~2--~ 4f 11, respectively) upon solidification. Blancard et al. (1989, 1990a,b), Sarpal et al. (1991) and Connerade and Karnatak (1990) have carried out accurate experiments to establish the valence of Sm and Tm vapors. The Mw-v (3d--+ 4f transitions) edges recorded by XAS show that Sm and Tm atoms have characteristics of the +2 valence state. This is well demonstrated by a remarkable evolution in the spectra as one changes from the atomic vapor to matrix-
......
ib
......
ib~ . . . . . 1i
~
ib 3 ...... i
u
Fig. 1. The evolution of valence (by adding 2 to IAnl) with clusterconcentrationfor Sm (solid squares) and Tm (opensquares). (Thetermclustersizerelatesto the average number of atoms in the first coordinationcell, as revealed by EXAFS.) (By courtesy of Drs. R.C. Karnatak and J.M. Esteva, Univ. Paris-Sud, LURE, Orsay,France).
THE INTRICATE WORLD OF RARE EARTH THIN FILMS Samarium
Tm CLUSTERS NIv
,.~ :%.:
....
__1
113
;.
M v
".
M IV
SOLID
....--."v.......__
/"x.,"
~(~/Tm) = 8o:1
'-
____.j.....". ,;" X._,."
/". :' "" ""
"
Vff)
-
-
~..e . . . .
"
__
Bulk
50
bJ
I00
2 0
3 0
4.00
500
THICKNESS,
600
700
800
900
.~
Fig. 13. Thickness dependence of resistivity of HoH z films (7-90nm). (By courtesy of Dr. M.S. Rahman Khan).
109
108
107.
10~-
a-_ 10~'.
I0~ 1
d7 ~ / xz/ V..~,
1o7]
100
Fig. 14. Change of resistance with atomic ratio r = H/Yb. Solid and dashed curves are for films that were hydrided slowly and quickly, respectively. (After Surplice and Kandasamy 1982.)
resistivity in RH2 indicates that most of the modifications of the conduction band occur in the mixed phase; this could be due to the R-RH2 structural transformation between the metal and the metal + dihydride phases. In the case of H-Yb system, in which the hydride is a poor conductor, the solubility limit (the position of the first phase boundary) has been estimated. Changes of resistance with atomic ratio are reported in fig. 14.
140
M. GASGNIER
2.9.2.2. Workfunction. The changes in work function in the course of hydrogenation have been determined for Sc and Er thin films by Miiller and Surplice (1977) and Kandasamy and Surplice (1985). As for the electric resistance they correlate the variations with changes of phase in the R/H system. In a general manner, first, small doses of H2 reduce the work function to about 0.!0 eV below the value for the clean metal; second, larger doses increase it to about 0.20 eV above this value; and third, further doses quickly raise the work function to a maximum of about 0.55 eV above the one of the clean metal. The results relative to the metallic phase can be interpreted as changes of surface potential; but for the other phases they depend on changes of the Fermi level of the H/R system as well as on the surface potential. Moreover these results are compared to those obtained for other metal hydrides (La, Ta, Ti, U, Pd, Nb and Zr). Similar observations have been reported by Eley and Needham (1984) for Gd films. 2.9.2.3. Surface magnetization. Cerri et al. (1983) have studied the spin-polarized emission of clean and hydrided (submonolayer coverages) polycrystalline Gd thin films. At 20 K, hydrogen coverage (chemisorption) drastically reduces the spin polarization from 70% (clean surface) to 45% (N0.5L H2) and 30% (~I.0L H2). With increasing temperature the polarization decreases linearly, up to 130K, then rises to a maximum near 200K, and finally decreases again. Extrapolation of the linear part of the curves shows that chemisorbed hydrogen strongly reduces the ordering temperature and induces a canted or disordered spin structure at the Gd surface. This experiment is a sensitive monitor of hydrogen contamination. 2.10. Rare earth deuteride and tritide 2.10.1. Bulk materials 2.10.1.1. Introduction. As a short introduction, one must emphasize the latest results of Adachi et a1.(1992) who report the possibility of "cold fusion" using the system D2LaNis. This has been deduced from analysis of H2 in gases resulting from D2 absorption with an LaNi5 ingot at 100-300 K under a pressure of ~5x 105 Pa. Such an assertion calls for new experiments and will certainly be the subject of new polemics. 2.10.1.2. Gettering. Maienschein (1978) has reported that cerium is one of the best chemical getters which can be used to scavenge tritium from inert gases. Indeed, this metal, as well as Sc, Y and Er, has low dissociation pressures for temperatures between 298 and 523 K. Maienschein assumes that dissociation of the tritium molecule to two tritium atoms and diffusion of tritium atoms through the solid tritide (due to the flaking and spalling effects of the material during tritiding) are both rapid. As cerium hydrides are stable and exhibit plateau regions, it is also assumed that the gas-phase mass transfer is the controlling step in the gettering process. Hubberstey et al. (1976) have used yttrium sponge as a getter for hydrogen isotope removal from liquid lithium. The rate of gettering is remarkably rapid at 673K. Hydrogen isotope concentration in Li can be reduced from 1.00 to less than 0.05 tool%
THE INTRICATE WORLD OF RARE EARTH THIN FILMS
141
x (x = H or D). Such a result should be extrapolated to lithium-tritide solutions. In the same way Buxbaum (1982) have used yttrium for the separation of tritium from the liquid lithium breeder-blanket of a fusion reactor. 2.10.2. Thinfilms 2.10.2.1. Scandium and yttrium. Malinowski (1981)has shown, from AES spectra, that the so-called LMV peak of Sc might be a useful indicator of film deuterium content. Indeed, he reports a linear dependence of the Sc LMV peak height on the deuterium content of the film (100nm thick). This is observed as a function of the fractional decomposition of the film such as S c D 2 ----r ScD0.5 --+ Scmetal
(at 673
K).
One must notice that films were contaminated by C and O (from evaporator), and S (from Mo substrates). Cowgill (1979) has studied dynamic deuteron implant effects (at 40keV) using Sc targets (previous experiments gave results at 200keV, see Cowgill (1977)). The experimental system is useful for studying D2 retention and mobility in materials under deuteron bombardment. Isotopic hydrogen exchange has been observed dynamically at 413 K. It is also shown that oxygen implants deplete the target of D2 within the implant range due to the formation of ScaO3. Cowgill (1981) has used the same technique for measuring D2 diffusion in films. He notices that no significantly different behavior is observed for films of different thicknesses (0.5-5.5 ~tm), the diffusion being identical to the one observed in bulk samples. Singleton and Yannopoulos (1975) have used Sc and Y films (500-1200 nm thick) for fabrication of radioactive electron emitters (tritriated electron sources). The stability of the sources in flow gas streams increases from Ti to Y to Sc. Once again, it is shown that the surface contamination has a profound influence on both the loading and loss of tritium in the films. Bacon et al. (1984) have manufactured SoD2 and ScDT thin film targets (10-50gm) for neutron protection inside an intense neutron source for use in cancer therapy. The films must not be heated at temperatures over 723 K to maintain their chemical stability. 2.10.2.2. Erbium. Thin ErD2 or ErT2 films are used for neutron generator targets (or tubes), for high-intensity rotating target neutron sources, for radiotherapy, and for highintensity neutron sources for cancer research. Provo (1979) has studied the hydriding process for the following system: Er (400600nm thiek)/Cr (100-500nm thick)/Cu (substrate). He determines that to achieve an E r D 2 / T 2 occhider film gas-to-metal atomic ratio of 1.7, a minimum of 150nm of Cr underlay is required for an in situ hydriding process, whereas such a minimum is 300 nm for an air-exposed hydriding process. The formation of oxides at each interface and the interfacial metal loss (diffusion) at the Er/Cr edge can limit the optimum hydriding process. Another characteristic of ErT2 films has been studied by Mitchell and Patrick
142
M. GASGNIER
(1981) and Mitchell and Provo (1985). They report the temperature dependence and irregularities of helium release rates from EfT2 films. Some fragmented results had been reported previously by Beavis (1980), Beavis and Kass (1977) and Kass (1977). Mitchell and Patrick (1981) give details on He release fraction as a function of aging and of temperature. The samples are aged over very long periods (70-2587 days), either maintained at different temperatures (from 77 to 500K) or sometimes annealed in the course of aging. The main results indicate first that large changes in He release rates follow immediately upon temperature changes and second that the accelerated release process is reversible. Then, Mitchell and Provo (1985) observe that nonuniformity of the release is greatest for samples undergoing the transition into accelerated release, which occurs when the oecluders (EFT2 films, 0.5-2 ~tm thick) approach the maximum quantities of helium that they can retain. It is concluded that the variability in He release rates might be due to a bursting activity: 3He is released in bursts of at least 109 atoms; this release is also stimulated by vibrating or flexing the film substrates. Holloway et al. (1978) and Antepenko and Holloway (1980) have studied the degradation of ErD2 and ErT3 films, ranging in areal density from 0.012 to 0.534 mg/cm2, and deposited by e-beam onto Mo substrates. It is shown that the total unavailable metal for the nonannealed films, if converted to total oxide, would be 11.5 nm. For in situ hydrided films this thickness does not excess 5 nm. It has been also determined that 0.01 mg/cm2 of Er is not hydrided for films that were e-beam deposited and in situ hydrided. Lastly samples subjected to vacuum annealing at 773 K (1 h) exhibit a total nonhydrided metal quantity of ~0.02 mg/cm2, therefore a total surface oxide level of 16.5 nm. 2.11. Formation o f the rare earth nitrides
The formation of pure rare earth nitrides is often difficult to carried out, because the presence of oxygen can lead to the formation of oxynitrides. However under certain experimental conditions it is possible to form pure nitrides. One of these procedures consists of carrying out the interaction of nitrogen with continuously renewed films of rare earth metals as reported by Varkanova and Nazarov (1977), Varkanova and Morozova (1981), Varkanova (1982) and Varkanova et al. (1982). These studies have been done for Sc, Y, Sm, Gd, Er and Yb metals. The absorption of nitrogen has been investigated as a function either of the rate of condensation of the metals, or of the temperature (between 298 and 473 K), and/or of the nitrogen pressure (between 10-6 and 5x 10-4pa). The most important study is relative to the sticking coefficient of nitrogen against the various parameters above-mentioned. In a general manner, the functions obey linear, increasing or decreasing, laws. Two kinds of composition have been observed. For scandium in the gas-excess regions it forms a singlephase nitride system (ScN0.9, fec with a = 0.453 rim). In the metal-excess region there is a mixture of two phases: one relative to the metal and the other to the nitride. Varkanova (1982) has also established, as a first approximation, that the changes in the sticking coefficient are due to the heat of sublimation of the metal: higher heat of sublimation
THE INTRICATE WORLD OF RARE EARTH THIN FILMS
143
leads to higher sticking. The nitrogen absorption of rare earths is always compared to that of titanium which seems to be similar. Another technique has been carried out by Ma et al. (1987): thin films (150nm thick) are deposited onto Si or NaC1 substrates, and then irradiated at high dose with nitrogen ions (2-5×1017N+cm-2). In the case of gadolinium there is, at lower doses (2 × 1017N+cm-2), formation of a compound of which the crystallographic parameters do not exactly correspond to the lattice standard value of GdN due, probably, to a deficiency in nitrogen content. In the same way, XRD indicates that the gadolinium lattice is also not correct. This is possibly due to a metastable structure of gadolinium supersaturated with nitrogen. At higher doses the GdN compound becomes predominant and the interplanar spacings are close to the standard values. However, one must remark that the correct XRD interplanar spacings show clearly that the "so-called" Gd (110) line (with a low intensity) with a spacing value of 0.187 um is in fact the (220) line of GdH2. In this way the formation of a new metastable compound seems less probable. The presence of hydrogen throughout the starting material is once again not surprising (the authors do not give their vacuum evaporation parameters). 2.12. Reaetioity with CO, C02 and CnHn gases 2.12.1. Rare earth~CO and CnHn interactions In an earlier chapter of this Handbook series, Netzer and Bertel (1982) have reviewed work carried out in order to study the reaction of rare earth metal surface with carbon monoxide. Affrossman (1981) has studied the reactions of CO with clean scandium film. He reports, from XPS experiments, that this metal dissociates CO to form a carbide and sorbed oxygen. The behavior of scandium shows strong similarities with that of tungsten. In the same way methanol and ethanol dissociate to leave oxygen preferentially at the Sc surface at low exposures and to form carbides at higher doses. In this case, there is formation o f a "~-CO" type layer. Cern~ and Pientka (1987) and Cern~, and Smutek (1990) for thin Dy films (150 nm) report, from calorimetric experiments (heat measurements), that CO dissociates on the metal surface (see also Surplice and Brearley 1978). This is followed by rapid penetration of the oxygen atoms (formation of the oxide), while the carbon atoms remain on the surface and cause a gradual blocking. They do not observe the formation of carbides. Moreover, it is determined that the rate of heat production is fairly high, but lower than with hydrogen at the same H/Dy ratios (Boeva et al. 1986). From mass spectrometry studies Curzon (1984) reports that the reduction of CO, inside the vacuum chamber, leads to the formation of CH4 (and consequently of CH3, CH2 and CH). The results indicate that the CH4 (and also H2) arises from the reduction of the CO (and also H20, which reacts with CO). That is another way to explain the formation of hydrides with rare earth thin films. The adsorption of C3H6, C2H2 and CH4 on clean polyerystalline Dy films at 295K has been studied by Cern~ and Smutek (1990). The experiments suggest that at low doses, the gases are completely dissociated into C and H atoms. The bonding of these atoms to Dy is assumed to be equivalent to that which
144
M. GASGNIER
occurs in chemisorption of CO. That leads to a surface-blocking effect of the formed species, and Dy films possess a higher chemisorption capacity for C2H2 than for C3H6. 2.12.2. Lanthanide/C02 reactions Little research has been carried out to study lanthanide/CO2 reactions (see Netzer and Bertel 1982). Mehrhoff (1980) has studied the gettering of CO2 by erbium thin films deposited onto Mo substrate discs heated at about 700 K. The reaction begins near 570 K in an abrupt manner (no reaction is detected with Mo). Mehrhoff (1980) also reports isothermal measurements, ratios of CO2 pumped by the films at various temperatures (from 890 to 1185 K), sticking coefficients versus exposure to CO2, and monolayers of CO2 absorbed as a function of the temperature. It is also shown that there is formation of CO near 770 K, that could be due to the interaction of CO2 and erbium metal. Arakawa et al. (1988) have reported the dissociation of CO2 on some rare earth (Pr, Nd, Sm, Dy and Er) films (1 ~tm thick). The oxidation of the metal is investigated by measurement of the resistivity of the films. Under CO2 atmosphere the resistivity increases strongly: for Dy, at 603 K, it is 14 times that at 298 K. Above 823 K the films have insulating properties due to the metal --+ sesquioxide transformation. For praseodymium the resistivity behaviour is fully different, which is possibly due to the formation of a non-stoichiometric oxide.
3. Metallic R-alloys Metallic R-alloys are now being studied increasingly in order to obtain numerous manufactured products. However, as for pure metallic thin films, the cross-shaped problem is the contamination by atmospheric gases. This is a dramatic feature, not always pointed out by numerous research groups, and it can be on the contrary a benefit in the case of hydrogen storage materials like RNi5 or RCos. 3.1. Permanent magnets 3.1.1. Introduction Numerous papers have been published on these permanent magnet materials; we cannot list all of them in this chapter (see Burzo and Kirchmayr 1989 and Gasgnier 1991 for example). A publication of the Gorham Advanced Materials Institute (May 10, 1991) showed that the global permanent magnet market was clearly influenced by the increasing NdFeB sales ($2.7 billion or 12.652 metric tons, therefore 17% of the market), and by the continued penetration of RCo alloys (11% of the market). One of the most important problems relative to the synthesis of these materials remains the formation of new phases and structural inhomogeneities inside the matrices. From XRD after heat treatment at 740K of NdFeB melt-spun ribbons, Strzeszewski et al. (1990) have pointed out four phases: Nd, Nd203, and two (Nd, Fe)O iron-rich phases (with tetragonal and hexagonal structures, 70 at.% and 85 at.% Fe, respectively). TEM imaging showed that such phases were present as spherical groins. As different kinds of
THE INTRICATEWORLDOF RAREEARTHTHINFILMS
145
phases can be formed, it follows that the magnetic properties can be different from one sample to the other. The aim of this section is to report the new experiments and results obtained since about 1987. 3.1.2. [R(Pr, Nd),R' (Dy)]xFeyBz alloys In a previous paper (Gasgnier 1991) we have shown that, since 1984, the research and development on these materials was growing more and more. Thus, there are a lot of recent papers which give details on new experimental methods and unusual synthesis treatments.
3.1.2.1. Magnetic properties. 3.1.2.1.1. Thick and thin films. Sputtering deposition methods of R-TM permanent magnet films (SmCos, Sm2(Co, Fe, Zr)17, Sm-Yi-Fe and Nd2Fel4B) which exhibit high intrinsic coercive forces, large remanent moment values, and special anisotropies have been studied by Cadieu (1988). In the case of thick crystallized Nd2FeI4B films (thickness 0.8-3.2 ~xm), Cadieu claims that, as a function of the sputtering rates, it is possible to synthetize in-plane or perpendicular easy direction of magnetization. So, at deposition rates 1256kAm-1). The sputtered and annealed (up to 823K) films are magnetically soft with a low coercivity (l.5nm/s exhibit a columnar structure with voids between the columns. The latter possess an effective vertical anisotropy. It is concluded that grain size and orientation are the most important factors determining the coercivity. Other parameters are the degree of isolation between grains and the density of faults which increases with the sputtering rate. For the thinnest amorphous films (100nm) deposited by triode sputtering onto substrates maintained at 293 and 77K, and then annealed upto 773 K, Alameda et al. (1990) show that the in-plane magnetic (induced) anisotropy, measured at the glass-film interface, increases at low temperature and falls to low values after annealing. The same
146
M. GASGNIER
result is valid for Ku. The authors give a clear correlation between the behaviors of these macroscopic and microscopic anisotropies (i.e. the product of the magnitude of local anisotropy and the volume where the principal axes of these anisotropies are correlated). 3.1.2.1.2. Multilayers and modulated films. Aylesworth et al. (1988, 1989) report the properties of Nd17(Fe0.9Co0.1)76B7/Fe or Ag sputtered multilayer specimens deposited onto mica or tantalum substrates at different temperatures (between 293 and 993 K). The individual layer thicknesses are 10-50urn for the alloy and 0.5-20 nm for the Fe or Ag, the total thickness being 1 ~tm. After annealing at 873 K, XRD reveals first the formation of the Nd2Fe17 and AgNd alloys, and second the presence of a contaminant labelled as "NdO" with a fcc structrue (a0 ~ 0.510 nm). One must point out that this compound does not exist. Moreover, although the measured interplanar spacings (0.288 and 0.250urn for the two first diffraction lines) are consistent with a fee lattice (dm/d2oo = 1.15), they have been indexed as a bcc structure, i.e., according to the (110) and (200) planes (dllo/d2oo = 1.415). In fact, the value of the fcc lattice parameter corresponds to that of NdNxOy which is formed after moderate annealing of R thin films (Gasgnier et al. 1976). This compound cannot be confused with NdH2, NdN, or C- and A-Nd203. The authors observe that the "NdO" contaminant diminishes in amount when the mica substrate is covered by an Fe layer (50nm) and disappears completely if a Ta substrate is used. However, in the case of (ProrNd)2Fe14B/Ta cosputtered multilayers this contaminant coexists with the Nd2Fe14B and Fe2Ta alloys (Aylesworth et al. 1991). But, in the case of Pr2Fe14B/Pr or Ta multilayers this contaminant is not observed (Aylesworth et al. 1990, 1991). Multilayers which are contaminated have larger coercivity, lower magnetization and are more randomly aligned than clean films prepared under similar conditions. The grain orientations and the anisotropies strongly depend on the substrate material and the insitu applied magnetic field. So, non-multilayer samples deposited onto mica tend to have larger Ku than similar films deposited onto Ta. Moreover a magnetic field (104 kA m -1) applied parallel to the film plane during Nd2(FeCo)14B formation, produced films with in-plane anisotropy. For these samples, after annealing between 723 and 873 K, He can reach values as 800kAm -I at 293 K. Variations of Hc versus maximum applied field (NdFeB/Fe samples), temperature (PrFeB/Pr samples) and nominal Ta thickness ((Pr or Nd)FeB/Ta samples) are shown in figs. 15, 16 and 17, respectively. Martinez et al. (1988a,b) have investigated Nda6Fe68B6 or Nd12FesoB6/Fe92B8 compositionally modulated films with a modulation length varying between 0.34 to 5.47 um for the Nd-rich alloy, and a thicker Fe-rich layer (200 urn). At helium temperature and as a function of the applied magnetic fields (perpendicular or parallel to the substrate), the magnetization increases as these fields increase. From hysteresis loops it is shown that the spin-wave modes (collective excitations) depend on both the thickness and the modulation of the multilayers (geometry of the samples). The perpendicular magnetization values decrease as the modulation lengths increase. This phenomenon may be attributed to the increase of the number of paramagnetic Fe atoms, as deduced from Mtssbauer spectra which show an increase of the paramagnetic doublet contribution with increasing modulation length. From these spectra it is shown that both the hyperfine fields and the easy magnetization magnitude are not correlated.
THE INTRICATE WORLD OF RARE EARTH THIN FILMS I
1
i
147
I
perpendicular
T=2OOK X
~fl~
I ~ 1 1 1 ~
8 °
C3 c£ Fig. 15. Coercivity versus maximarn applied field at T=200K for a NdFeB (20nm)/Fe(0.5nm) sample. The result indicates that magnetization reversal in the easy direction is controlled by a domain-wall pinning mechanism. (By courtesy of Dr. D. Sellmyer,Behlen Lab. of Physics, Univ. Nebraska, Lincoln, NB, USA).
:£o
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,,IJ~,,I,~,,l,~l,,,~l,~,,lJ,,,
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Fig, 17. Coercivity versus nominal Ta thickness with the field applied perpendicular to the film for "aligned" PrFeB (20nm)/Fe (xnm) and "aligned" and "randomized" NdFeB (20nm)/Ta (xnm) films (By courtesy of Dr. D. Sellmyer).
Fig. 16. Summary of coercivity versus temperature data with the field applied perpendicular to PrFeB film plane. (By courtesy of Dr. D. Sellmyer).
3.1.2.1.3. Magnetic domains. In a general manner magnetic domains are observed either by means o f Lorentz electron microscopy investigations (thin specimens) or by decorative methods (thick samples). In the first case, Bras et al. (1988a,b, 1990) have improved the suitable conditions to investigate magnetic domain nucleation, domain wall motion, domain size and wall energy in highly uniaxial magnetocrystalline anisotropy materials. This technique is available by using the magnetic field o f the standard objective lens
148
M. GASGNIER
which induces magnetic structure variations and by optimizing the grain orientation (i.e., a small angle between the anisotropy axis and the normal to the foil). The "optimal orientation" is obtained by means of a rotating specimen holder. This allows separate study of small grains and their interactions. In the case of a thinned Nd2Fe14B ribbon the authors have determined from the unusual Foucault mode images the wall width, the diameter of bubbles near stripe domains (70-100nm) and their stability, the global grain magnetization which permits one to deduce that the reversal domain nucleation arises under the influence of a demagnetizing field, and the neighbouring grain influence (abrupt change in the grain magnetization). Examples of strip domains obtained by 200 kV Foucault images are shown in figure 18. In another set of experiments Griitter et al. (1988, 1990a,b) have used magnetic force microscopy (Heinzelmann et al. 1987) to study Nda4FeglB5 materials having optimum magnetic properties. This allows them to observe magnetic domains in air, and to achieve a high lateral magnetic resolution ( 5) and were found markedly pulverized and peeled off from the glass substrate, whereas the amorphous specimens with a lower solubility (H2/LaNi5 < 0.5) show neither pulverization nor the peeling effect. By using aluminium and copper foil substrates, Sakaguchi et al. (1986a) show that amorphous flash-evaporated films do not disintegrate after 75 cyles. S.K. Singh et al. (1985) have observed by TEM that hydrogenation leads to enhancement of amorphosity. For sputtered films Sakaguehi et al. (1988) report larger thermal conductivities than for bulk samples. The mechanical properties show that the film-substrate adhesion occurs in the following order for the substrate used: Ni foil > Ni > AI foil > Cu foil > Cu > A1 > glass. Such an order appears to be due to the difference of the thermal expansivity at the film-substrate interface. 3.4.1.2. Electric resistivity. The effect of H2 absorption on the electric resistivity of LaNi5 films has been studied by Adachi et al. (1981, 1982, 1985a,b) and Sakaguchi et al. (1985b,e). The films (0.3-1.8 ~tm thick) prepared by evaporation of the powder placed on a tungsten filament and deposited onto quartz plate, are amorphous. As a function of temperature, thickness, and H2 pressure, the variation of the resistivity with the time of H2 absorption-desorption cycles presents an initial increase and a sharp decrease during H2 absorption. Figures 22a--c show the variations of the electric resistance as a function of the time of application of 1-12pressure. The resistivity decreases as the number of cycles is increased; increases as the temperature is raised to 363 K; and saturates at a H2 pressure of 1.2× 106 Pa. However, Adaehi et al. (1985a) noticed that the low 1-12 uptake for the
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Fig. 22. Variation of the resistivity versus time during activation (first and second cycles at 313 K, others at 363 K; hydrogen pressure 2.5×106 Pa): (a) thick LaNi 5 film (0.63 btm); (b) thin LaNi 5 film (0.20 p.m); (e) very thin LaNi 5 film (0.038 btm). (By courtesy of Prof. G.Y. Adachi, Dept. Applied Chemistry, Fac. Engineering, Osaka Univ., Osaka, Japan).
THE INTRICATEWORLDOF RAREEARTHTHIN FILMS
17i
films in comparison with that for the bulk, is due to the amorphous character and to the presence of a surface oxide such as Ni-free La203 which is a passivation layer for H2 absorption. For thinner films (50-150 nm) Ramakrisna and Srivastava (1987) claim that the dependence of resistivity on hydrogenation time is originates solely from the surface characteristics of the films. The resistivity, for aged layers, drops rapidly after exposure to air. Such a phenomenon is explained to be due to the formation ofa La203-free Ni surface layer. S.K. Singh et al. (1985) observe a curious variation of the electric resistivity which decreases to nearly zero during the early exposure on hydrogenation and then increases and reaches a saturation value. Larsen et al. (1981) report measurements of resistance as a function of H2 pressure. 3.4.1.3. Hydrogen separation and permeation. Adachi et al. (1984) have investigated the property of flash-evaporated LaNi5 films for the separation of hydrogen. This material is less expensive than thin palladium films. The LaNi5 film (10 gm thick) is deposited onto a stainless steel disc which is inserted into a special apparatus, where Hz-Ar and H2-N2 gas mixtures are blown. It is observed that above 333 K hydrogen does not permeate the films. For Hz-C3Hs, Hz-CH4, Hz-N2 and Hz-Ar gas mixtures, Sakaguchi et al. (1986b) have studied hydrogen separation in the case of stainless steel discs/Ni or A1 films/LaNi5 flash-evaporated films. The results are discussed first in terms of microcracks formed during H2 absorption, second as a function of the film thickness, and third according to the nature of the intermediate metallic layer. In particular it is observed that A1 allows the highest value of H2 concentration. Sakaguchi and Adachi (1990) have studied the influence of CO on the hydrogenation of amorphous LaNi5 films and on hydrogen separation. The H2-CO gas separation is performed by using films deposited onto Nicoated polyimide membranes. In the case of multilayer Ni (1.4 gm)/LaNi5 (0.1 gin) films the H2 permeability (penetration rate) is greater than that for Ni films up to 373 K. Moreover, LaNi5 films are found to have excellent resistance to harmful CO in comparison with the crystalline bulk material (H2 is concentrated to more than 98 tool% in the permeated gas). Another interesting experiment has been reported for Hz-D2 gas mixtures by Sakaguehi et al. (1989b). The rf magnetron sputtered LaNi5 films are deposited onto teflon and polyimide membranes. Isotope separation is mainly influenced by the difference in solubility of H2 and Dz atoms in metals, the difference in diffusivity in metals, and the polymer's own isotope effects. LaNi5 films have a permeability coefficient about twice as large as that of Ni films, and less than one-thousandth that of Pd films. Previously, Adaehi et al. (1986, 1987), in the ease of amorphous WO3/Metal/LaNi5 sandwich-type films, have studied the hydrogen permeability for various metals. The amorphous WO3 films, which have electrochromic properties, become blue only under the area covered by the LaNi5 layer when H2 is introduced into the system. The authors conclude on the following order for hydrogen permeability: LaNis, Pt, Pd > Fe > Ni, Co, Ti > Mn > Cu > Mg, Cr > A1 > Au, Ag, Zn.
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M. GASGNIER
In the same way, Shirai et al. (1990) have studied the H2 penetration into amorphous V205 films. For a LaNis/VzOs/WO3 multilayer system, the diffusivity at the VzOs/WO3 interface seems to be much smaller than that at the Cu/WO3 interface. 3.4.2. Other RNis alloys Other studies report that MmNi4.sMn0.5 films (Mm--mischmetal, generally as a (La, Pr, Ce, Nd) mixture) have resistivities almost identical to that of LaNi5 films. However, the former are more easily oxidized (Adachi et al. 1982). S.K. Singh et al. (1985) prepared RNi5 films (R = Sm, Gd, Ho, Mm and Mm cerium free) by thermal vapor deposition; these are initially amorphous, and then crystallize on annealing. S.K. Singh et al. (1985) conclude that the amorphous state absorbs the hydrogen more easily. 3.4.3. RCos alloy (R = La, Sin) Sakaguchi et al. (1985a, 1987) have studied the effects of hydrogen absorption on the electric resistivity of LaCo5 films deposited as LaNi5 layers (Adachi et al. 1985a). The resistivity behavior of LaCo5 specimens during H2 absorption-desorption cycles resembles that for the LaNi5 films. However, LaCo5 films absorb less 1-12.But the amount of absorbed H2 increases with increasing film thickness. The pressure-composition isotherms indicate a monotonous increase with increasing pressure, while a plateau pressure is absent. For SmCo5 films Sakaguehi et al. (1985a,b) report that, as a function of thickness, the resistivity varies differently depending on the 1-12absorption-desorption cycles. Hydrogen molecules are absorbed on the surface and then dissociate into atoms. The dissolved H2 anions diffuse into the films and then react with Sin, giving a highly conductive hydride which lowers resistivity. It is asserted that the H2 concentration in SmCo5 is of an order of magnitude 5 times smaller than that of LaNi5 films (in the bulk the ratio is close to 3/7). 3.4.4. Remark R(Ni, Co)5 thin and thick films are available as materials for hydrogen storage. The different authors referred to throughout sect. 3.4 report the possibility of a lot of applications. However, to our knowledge, no patent has been taken out during the last decade. This should be explained from the fact that these materials do not present the perfect characteristics of stability during aging, annealing, H2 absorption-desorption cycling, etc. The formation of compounds such as RH2, R203, ... seem to attest this explanation. 3.5. Polytypic structures Verma and Krishna (1966) have reported the main properties of polytypic materials. Different notations have been used to describe the stacking sequence of successive packed layers in the hexagonal unit cell. This has been chosen as the basic lattice because it
THE INTRICATEWORLD OF RARE EARTH THIN FILMS
173
includes at one and at the same time the cubic (C), rhombohedral (R) and hexagonal (H) structures. The different structures are characterized by the following law relative to the lattice parameters: a = constant, c = n x h (n = number of block layers, h = spacing between two layers).
3.5.1. Ferromagnetic samarium-nickel alloys Polytypic and intergrowth properties of SmxNiy alloys have been studied by S. Takeda et al. (1982, 1983), S. Takeda (1983), Horikoshi et al. (1985) and Komura (1989). This system appears somewhat complex. So, the following intermetallic compounds have been observed: 3C; SmNi2: SmNi3:
3R;
Sm2NiT:
2H, 3R, 4H, 5T (trigonal) 9R and 12R"
2H, 3R, 4H, 5T, 6T, 7T, 9R, 12R, 15R and 18R. SmsNi19: A model of stacking sequences is shown in fig. 23. HREM studies show, first, that such structures can coexist inside thin crystals electrolytically polished, and second, that anomalous intergrowths can occur. For instance, in the first case small "blocks" of Sm2Ni7 can grow in the matrix of SmsNi19, and in the second case small "blocks" of Sm7Ni29 and SmNi4 can grow in the same matrix. Such intergrowths can be caused by a small amount of concentration fluctuation in one part of the specimen. Moreover, such crystals are characterized by various complicated defect structures: non-periodic stacking sequences and stacking faults of the block layers. The oT
OSrn
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oo c
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)°°0 Y
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)~°~v
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b
x
x
x
c
d
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174
M. GASGNIER
presence of intergrowth phases and of defects could affect the physical properties of these materials, but apparently the above-mentioned authors have not resolved this problem up to now. So, the problem of layer sequences, intergrowths, syntaxies, . . . , becomes very complex because a great number of compounds can be formed but also each of them can be characterized by a wide range of crystalline structures (ten at least, in the case of SmsNi19). 3.5.2. Samarium-cobalt alloys The approach of using crystallographic polytypic structures was been reported first by Cromer and Larson (1959) and later on by Parth6 and Moreau (1977) who have discussed the problem in terms of stacking-blocks of various rare earth alloys. C.W. Allen et al. (1974a,b, 1977); Melton and Perkins (1976), Melton and Nagel (1977) and Fidler and Skalicky (1978, 1981) have investigated by electron microscopy the polytypic stacking faults and defect structures in R2Co17 and SmCo5 materials. C.W. Allen et al. (1974a) have reported the first atomic arrangements for six structural modifications (2H, 1R, 4H, 5H, 6H1 and 61-12) of R2Coa7. They correlate such structures, by the way of R sites, to magnetic properties. For example they conclude that an intrinsic fault in the 1R structure could provide a source for domain-wall nucleation. The authors illustrate the various stacking sequences for different stacking faults in 2H and 1R R2Col7 alloys. More detailed results have been given by Komura et al. (1981), S. Takeda (1983), and Sahashi et al. (1983). The studies were carried out on thinned materials by electron microscopy (TEM, EDP and HREM). This has allowed them to observe the classical structures as: SmCo3-3R, Sm2CoT-2H and 3R and SmsCo19-2H and 3R; and to find new long-period structures such as Sm2Co7-4H and 15R and SmsCo19-18R types. The lattice parameters for the 15R and 18R structures are respectively: 15R: Sm2Co7: a=0.50nm and c= 19.50nm, i.e., 15×l.3nm 18R: S m 5 C o 1 9 : a=0.50nm and c=31.00nm, i.e., ~18× 1.72nm (1.30 and 1.72nm being, respectively, the values of the c parameters of the 2H basic structure for each alloy). HREM imaging permits one to observe stacking faults inside the stacking sequences. This also allows one to build these sequences, recognize the different polytypic structures, and determine the possible stacking sequences. Thus, the 18R polytype relative to the Sm5Co19 alloy can be depicted according to three different sequences. An interesting conclusion comes from the experiments by S. Takeda (1983). He notices that, for electrolytically polished specimens, the axial ratios co/ao obtained from EDP are about 6-8% greater than those obtained by the X-ray method. Such a discrepancy was not observed in the case of crushed specimens. The author concludes that possibly a chemical reaction of inclusions occurred in the course of polishing. Other studies have dealt with the eutectic decomposition of these alloys. Linetski and Salo (1989) report, from X-ray investigations, that thick (20-200~tm) sputtered amorphous layers, as SmxCoy (18-34% Sm), can form a great number of alloys: Sm2C017, Sm2C024, Sm2C026, SmC05, SmC07, SmCo8, SmCo8.5, SmCo9, SmCo9.5, SmC012, SmC013 and other unidentified phases. The results are discussed on the basis of
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the equilibrium diagram. It is concluded that the formation of a wide range of continuous metastable solid solutions on crystallization from the amorphous state is probably due to the similarity of the free energies and related crystal structures of the SmC05 and Sm2Co17 phases. Such observations seem to be a general phenomenon as reported by Gasgnier (1982) for other binary amorphous R-TM alloys. The amorphous system can be also taken as thermodynamically far from equilibrium and the amorphous ~ crystalline transition and the reerystallization which follow as the temperature increases, are often very complex. Moreover one cannot exclude the important role of impurities (overall oxygen) which can act as catalysts. Pan et al. (1989) have studied polished and ion-beam thinned SmCo5 platelets between 673 and 1023 K. They observed first, the formation of Sm2Co17 precipitates (as homogeneous centers formed at 693 K) and second, the eutectic decomposition below 1023 K (formation of Sm2Co7 and Sm2Co17 phases). It is noticed that at 1023 K the coercivity degraded abruptly, but it can be restored after annealing at 1123-1273 K. Such a phenomenon has been attributed to the various microstructure changes as a function of the temperature. Shen and Laughlin (1990) have prepared near stoichiometric (Sm0.75Pr0.25)sCo19 materials. TEM studies were carried out after ion-milling of the specimens. Thermomagnetic analysis indicates that this alloy consists mainly of the 5:19 phase (>85%), 2:7 phase and 1:5 phase (10nm)
THE INTRICATEWORLDOF RAREEARTHTHINFILMS
179
which contains about 80 at.% Ce ions. These Ce ions are in their trivalent state. After exposure to oxygen Ce 4+ ions are formed and the copper film is not oxidized. 3.6.1.2.3. Cu-Dy, Cu-Ho, Cu-Er. The crystallization behavior in amorphous vacuumdeposited Cu-Dy, Cu-Ho and Cu-Er films has been investigated by Shikhmanter et al. (1982, 1983a) and Venkert et al. (1987). Either Dy(or Er)0.a0Cu0.60 films or (Cu/Ho)n (45 at.% Ho) multilayers have been studied. The nucleation and crystallization processes are determined by TEM and EDP. As expected from the R-Cu phase diagram (Franceschi 1982), the DyCu and ErCu alloys (CsCl-type structure) are formed at about 430K. Kinetics of crystallization and nucleation sites are discussed and analyzed with simple models. The presence of the R203 compound has been observed in all cases. For (Cu/Ho)n samples it is reported that the initially crystallized films (160 nm thick) become nearly amorphous after heating at 373 K, and become crystalline again at 533 K due to the formation of HoCu2 and Ho203. The mixing process and the depth profiling have been analyzed by XPS, UPS and AES measurements. It is observed that, first, the topmost layer formed is Ho203, which is induced by surface segregation of Ho, and second, the interfaces are not sharp due to interdiffusion between the two metals. 3.6.1.2.4. Yb/Cu. Y.S. Huang and Murgai (1989) report that Yb/Cu films annealed up to 873 K form the YbCu2 alloy. In the course of this reaction the ytterbium valence changes from 3 to 2.2. It is asserted that the YbCu2 alloy is characterized by a homogeneous mixed valence state. The results are discussed in terms of the number of f holes and 4ff contributions to the photoemission spectra.
3.6.1.3. R-Cu samples as precursors for synthesis catalysts. Nix and coworkers (Nix and Lambert 1987, Nix et al. 1988a, 1989a) and Jaffey et al. (1989) have shown that at 3001100K pure Nd and Sm overlayers on Cu (100) and Cu (11 l) substrates transform to Nd(Sm)Cu and Nd(Sm)Cu5 intermetallie phases. The interaction of Nd with Cu has been widely studied by AES, XPS, UPS and LEED. It is shown that at 300 K pure Nd films grow on the Cu substrate by a layer-by-layer mechanism. At higher temperatures (800 K) rearrangement occurs with the formation of alloy phases. Nix et al. (1988a) compared the results obtained for Cu (111) and Cu (100) substrates, and those reported by Jaffey et al. (1989) for the Sm/Cu (111) system. Such studies have been carried out in order to broadly investigate the properties of the Nd(or Ce)-Cu intermetallic catalyst precursors as reported by Nix and Lambert (1989a,b), Nix et al. (1987, 1988b, 1989b), Owen et al. (1987), Bryan et al. (1988), Hay et al. (1988) and Jennings et al. (1989). The oxidation of Nd (or Ce) overlayers; oxidation by dissociative chemisorption of CO; sorption, chemisorption and desorption of H2; treatments with CO2, CO/Hz, N2 and N20/H2; and, overall the activation and performance of methanol synthesis catalysts have been studied. The whole of these results, obtained by different experimental procedures, shows that the mechanism by which low-temperature methanol synthesis occurs on these catalysts is quite different from that which operates on commercial Cu/ZnO/A1203 catalysts (Nix et al. 1989b). Jennings et al. (1989) have shown that for R/Cu precursors, C Q causes strong irreversible deactiviation, whereas inclusion of Ti, or A1, or Zr enhances poison resistance.
180
M. GASGNIER
3.6.1.4. Ion-beam mixing. In order to prepare the new high-Te superconductors as thin films, a large number of methods have been used. One of them, ion-beam mixing, has been investigated by Borgensen and Lilienfeld (1989) and Mathevet et al. (1990). The former have irradiated their Cu/Y/Cu samples ~vith 600 keV Xe ions. The results are analyzed by RBS spectra. The formation of YCu2, YCu4, YCu5 and YCu7 alloys has been determined. It is concluded that, as a function of temperature, the mixing phenomenon varies strongly. At 100K it is dominated by thermal spike effects, whereas at 323 K the rapid growth of the hexagonal YCu7 phase becomes predominant. In another investigation, Mathevet et al. (1990) have irradiated La(OH)3/Cu bilayers with 3.65 MeV Au ions, at 300 K and 700 K. The results are analyzed by RBS spectra and XRD. It is concluded that a homogeneous depth distribution is not reached, and that ion irradiation simultaneously breaks down the La-O-H bonds and pushes in the Cu atoms. This induces the formation of unknown alloys and/or compounds. These results seem to indicate that the above methods of ionbeam mixing do not form a preferential route for fabricating the ternary RBa2Cu307 and La2_xSrxCuO4 ceramics. 3.6.2. The R-Au system 3.6.2.1. Amorphous GdAu and GdFeAufilms. The magnetic properties, Hall conductivity, Curie temperature and resistivity of GdxAUl-x films (x = 0.26-0.72) have been studied by Gambino et al. (1981). It is suggested that conduction-electron spin polarization determines the magnitude of the spontaneous Hall effect. Gambino and McGuire (I 984) have determined that the addition of a non-S-state heavy lanthanide (Tb, Ho, Er or Tin) to ferromagnetic Gd-Au does not increase the spontaneous Hall effect to a greater extent than would be caused by a similar increase in Gd. In contrast, the addition of Nd leads to a significant increase in this transport parameter, von Molnar et al. (1982b) have shown that Dy-Au amorphous alloys are highly anisotropic magnets. They develop a spontaneous moment at any temperature, and never reach infinite susceptibility. One must also point out the work of Hartmann and McGuire (1983) and Hansen and Hartmann (1986) relative to the magnetic and magneto-optics properties of GdFe-Au films. We also note the investigations of De Luca et al. (1981) relative to the bias-field dependence of domain drag propagation velocities in GdCoAu bubble films. 3.6.2.2. Crystallinefilms. Schwarz and Johnson (1983) have studied (La/Au)n multilayers at temperatures of 323-353K. The unannealed samples are characterized by the coexistence of the well-crystallized Au and ~-La (fcc) and/or (~-La or LaH2 phases (the interplanar spacings being equal). The most interesting result is the formation, after heating at 353 K for 4 h, of a single amorphous phase. This is essentially due to the fast diffusion behavior of Au in La, and the existence of a negative heat of mixing in the amorphous alloys. The latter provides the necessary chemical driving force for the reaction. Raaen (1990) has investigated the Ce/Au system by means of XPS. Ce films of various thicknesses are deposited onto Au films (>20nm thick). XPS core-level intensities for
THE INTRICATEWORLDOF RAREEARTHTHINFILMS
181
Au 4f and Ce 3d emissions indicate the formation of a mixed amorphous interface (5 nm thick) with an average volume content of Ce estimated at -35%. The Au 4f level shifts by 0.8 eV to higher binding energies which may be explained by changes in final-state screening caused by alloying of Ce and Au. Shikhmanter et al. (1983b) have carried out TEM experiments in order to study the crystallization behavior of some R-Au (R = Gd, Tb, Dy and Er) vapor-deposited amorphous films (120nm thick). Crystallization takes places in the temperature range of 463-513K, and further heating by an additional 50K leads to the formation of the RAu alloys (CsC1 structure type). Further annealing at 533 K induces an allotropie transformation such as CsC1 type (cubic structure) ~ CrB type (orthorhombic structure). The former is metastable, while the latter is, as in the bulk, more stable at low temperatures. The presence of R203 crystallites can act as catalyst for the transformation. It is concluded that conditions amenable to heterogeneous nucleation will appear on the R-Au films at higher temperatures than in the R-Cu films (413-423 K) or R A g films (388-398 K). L.I. Johansson et al. (1982a,b) have studied the chemically shifted surface core-level binding energies and surface segregation in Eu-Au and Yb-Au alloys. Photoemission spectra show that Au atoms deposited on the top of an Eu film dissolve into the film more readily at 293 K than for an Yb film. The authors studied mainly the intensity ratio [surf/Ibulk of Au, Eu and Yb 4f lines, and the chemical shifts upon alloying for different Au, Eu and Yb thicknesses and annealing temperatures. The most important feature is the persistence of the rare-earth surface 4f signal with increasing Au content. 3.7. R-Pd alloys (R=Ce, Eu, Er, Yb)
3.7.1. Valence change in R-Pd alloys 3.7.1.1. Ce-Pd amorphous crystalline samples. Comparison to other materials. The Ce valence-state disparity between crystalline and amorphous Ce-TM alloy films has been studied by Lu et al. (1985, 1986) and Croft et al. (1984, 1985). For CePd3 and CePdt.5 films (700 nm thick) Lm absorption spectra show that crystalline samples possess a lower valence state (3.17) than amorphous films (3.30). Moreover, Ag substitution for Pd in crystalline CePd3 acts to stabilize nearly pure Ce 3+ behavior. In the case of Cel-xMxPd3 materials (M=Y, La), the Ce valence decreases from 3.17 at x = 0 to 3.09 at x=0.75 (M = La), and increases to 3.23 (M = La) and 3.29 (M = Y) for x = 0.40. (In the case of Th 4+ and U 4+ substitutions the valence decreases to 3.10 at x = 0.40.) The results are discussed in terms of lattice-parameter changes, electronegativity arguments and band filling. These valence changes have also been determined for other metals, such as Cu, Ni, Co, Fe, Mn, Mo, Ru, Rh and A1 (or AlSo). Parks et al. (1983) have established a linear relation between the Lm-based valence estimates (from 3.00 to 3.21) and the bulk-property based valence estimates (from 3.00 to 4.00) in the Ce(Ag or Rh, Pd)3 systems. Then, Parks et al. (1984) in the case of fracturing clean RPd3 samples (R = La, Ce, Pr, Nd) have observed a 4f-derived resonant photoemission. The authors speculate that a mixed-valence state can occur in Ce systems
182
M. GASGNIER
only if the 4f holes are locally screened. The contraction of a valence electron may explain the anomalously large lattice contraction observed in these systems. 3.7.1.2. Eu and Yb-Pd amorphous specimens. For amorphous films of EuxPd~_x (0.16 ~<x ~~500°C are most appropriate for charging. Finally, it is important to know that the characteristics listed in table 1 are
212
P. V A J D A
Table 1 C r i t i c a l t e m p e r a t u r e s a n d e o n c e n t r a t i o n s in t h e c - p h a s e a
R
Vat (cm3/mol)
T m (°C)
T«~~ b (°C)
T ....
(°C)
T ....
(oc)
c~x (at.H/R)
C~oo*c (at.H/R)
Sc
15.039
1541
-
n.m. c
Y
19.893
1522
-
n.m.
n.m.
0.35
n.m.
400
0.20
/>0.32
La
22.602
918
350
-
-
-
0.04
Ce
20.696
798
380
-
-
-
0.06
Pr
20.803
931
380
-
-
-
0.06
Nd
20.583
1021
280
-
-
-
0.08
Sm
20.000
1074
200
-
-
-
0.15
Gd
19.903
1313
180
-
-
-
0.24
Tb
19.310
1356
140
-
-
Dy
19.004
1412
(80)
?
?
Ho
18.752
1474
-
90
Er
18.449
1529
-
120
340
0.06
0.32
Tm
18.124
1545
-
140
380
0.11
0.34
Lu
17.779
1663
-
160
420
0.20
0.36
a F r o m D a o u a n d V i a l l a r d (1972).
n.m.
-
0.26
0o
/0
¢..)
930
kù
(œY)
730
• "%,
xlt~
~3
o
*,x
xla eß
530
E E--,
e~aa
o
Oe &
o
\
/&
\
330
.a ,IP'*
13o
t
...............................................,,y2.............. , ~' •
-70
~,
u
t
Il
t ! ! !
-270
.........
0
, . . . . . . . . . . . . .ù~ ... 20
I0
r
30
. . . . . . . . .
~
40
. . . . . . . . .
~
. . . . . . . . .
50
f
60
. . . . . . . . .
i . . . . . . . . .
70
80
Atomic P e r c e n t Hydrogen Fig. 2. Phase diagram in the Y-H system assessed from thermodynamic and structural data. Note the abscissa scale with x = H/(Y + H) in at.% and the designations (x', 6 and ê for the et*, [3 and ¥ used in this review. The various symbols refer to different investigations, details are found in Khatamian and Manchester (1988).
sect. 3, where we shall also present partial phase diagrams as proposed from various physical measurements. In figs. 2 and 3, we are exhibiting the phase diagrams for the systems Y-H and La-H, respectively, which resulted from a critical assessment by Khatamian and Manchester (1988, 1990) of the available data. Note in particular the tetragonally distorted lowtemperature phase in the La-H system near the trihydride discovered by Klavins et al. (1984) and the ordered «*-phase in a-YHx. The latter has been seen in several c~-RHx systems (cf. also the Lu-H system in fig. 4) and has been determined by neutron scattering (Blaschko et al. 1985) to be due to H - H pairs ordered in chains along the c-axis. Figure 5 gives the Pr-H phase diagram, which resembles the La-H diagram at high temperature. For all other systems, reliable data are still lacking, in particular in the region of the y-phase existence (i.e. in the heavy R-H systems from Nd-H on), though there is some progress noted in the RH2+x systems at low temperatures (cf. sect. 3).
216
E VAJDA Weight Percent Hydrogen 0.5
1.5
2
25
1200
L
1100
1000
0
0 0
81111 700
~7
..~ 600
~7 400 310 3OO
283'C
200 100 0 -t00 0
I0
20
La
30 40 50 Atom/e Percent Hydrogen
60
70
BO
Fig. 3. Phase diagram in the La-H system assessed from thermodynamic and structural data. Note the abseissa seale with x=H/(La+ H) in at.% and the designation 6 for the 13used in this review. The various symbols refer to different investigations, details are found in Khatamian and Manchester (1990).
3. Structural properties 3.1. a-Phase solid solutions
The site occupation by hydrogen in solid solution in the rare earth metals has been determined in the early eighties, after some controversy, through unambiguous ionchanneling experiments on single crystals of c-LuDx (Danielou et al. 1981) as well as by neutron diffraction on c-YDx (Khatamian et al. 1981), on c-TmDx (Daou et al. 1983), and on a-ScDx (Saw et al. 1983). It has been established that the hydrogen atoms were localized on the T sites of the hcp lattice over the entire measured temperature range between 4 K and 300 K. Later quasi-elastic neutron-scattering experiments (e.g. Anderson et al. 1989) and NMR studies (Barnes et al. 1989) at high temperatures extended the validity of the T-site occupation to the whole domain of c-phase existence where a site can still be specified (several hundred °C). In table 3, we present the lattice parameters in the hcp a-phase for various hydrogen (or deuterium) concentrations and at various temperatures, together with their expansivities,
HYDROGEN IN RARE-EARTH METALS, 1NCLUDING RH2+~ PHASES 0
1
2
i
I
1000
217
Lu- H
800
600
6" o 1-
40O
200
F / -200 ~0 0.2
i
I
i
I
I
1 1.2 at.H/Lu
0.6
r
I
1.6
o•
I
1100
li:t 2 2.2
I
Fig. 4. Phase diagram in the Lu-H system constructed from resistivity and thermodynamic data. Open circles, Daou (1965) and unpubl, data; solid cireles, Beaudry and Spedding (1975); open squares, Subramanian and Smith (1982); solid squares, Jones et al. (1964); crosses, Daou et al. (1988b).
i
1
!
I
i
Pr(i )
p1000 q
(s) + PrH x(s ) 900
// -Pr (s,bcc)
j__
__.
8001 "w~~-~---~d-pr ' ~ Y 700 600
(s,fcc)/ /
Pr(s) + PrHx(s)
I
I
I
10
20
30
I
I
I
I
40 50 60 70 Atomic Percent Hydrogen
Fig. 5. Phase diagram in the Pr-H system constructed from thermodynamic data. Note the abscissa scale with x = H/(Pr+ H) in at.%. The various symbols refer to different investigations, details are found in Bischof et al. (1985).
both static (caused by H insertion) and dynamic (thermal), determined in most cases by Xray crystallography. We note that the c/a-ratio of the high-temperature c-phase decreases
R VAJDA
218
Table 3 Crystallographic parameters of the tl.c.p, a-phase, RH(D)x
Sc
Y
Gd Tb
Dy
Ho
Er Tm
Lu
Aa a~x (10-4/at%)
Ac
Aa
Ac
cAx
aAT
c&T
(10-4/at%)
(10-6/K)
(10~/K)
x (H/R ratio)
T(K)
0.33D
300
3.338
5.299
2.68
1.77
0.15 0.15
80 300
3.318 3.3215
5.2775 5.286
3.47 2.71
2.85 1.96
5.0 5.0
2.0 8.5
2 2
0.30
80
3.3295
5.2845
2.91
1.87
3.6
6.7
2
0.30
300
3.3340
5.2945
2.63
1.52
6.6
7.75
0.19
300
3.6636
5.7900
2.22
5.33
a (Ä)
c (A)
Ref.
1
2 3
0.176D
300
3.662
5.778
2.15
4.57
0.12
300
3.6542
5.7654
1.37
4.59
5.3
20.2
4
0.12
775
3.670
5.8175
2.28
3.81
11.9
22.9
5
0.22
300
3.6637
5.7940
1.93
4.76
2.9
16.4
5
0.22
775
3.678
5.838
2.23
3.68
12.2
14.9
5
0.2 0.2
775 775
c/a = 1.5890
3.6515
5.7735
5.52
3.57
7.1
16.3
0.2 0.2D
1000 800
3.6573 3.6511
5.7947 5.7752
5.33 5.36
3.22
7.1
16.3
6,7
3.57
7.8
16.7
6,7
0.2D
6,7
5
6 6,7
1000
3.6568
5.7945
5.23
3.21
7.8
16.7
0.2
675
3.6269
5.7255
4.15
3.21
6.5
18.7
6,7
0.2
950
3.6334
5.7550
4.11
2.97
6.5
18.7
6,7
0.2D
700
3.6304
5.7318
4.57
3.49
7.5
18.3
6,7
0.2D
950
3.6372
5.7580
4.64
3.23
7.5
18.3
6,7
0.2
645
3.6087
5.6985
3.38
3.47
9.9
16.2
6,7
0.2
900
3.6178
5.7220
3.94
3.16
9.9
16.2
6,7
0.2D
635
3.6103
5.7021
3.58
3.78
10.8
15.8
6,7
0.2D
875
3.6197
5.7237
4.19
10.8
15.8
0.035 0.27 0.08
300 775 300
3.5636 3.6035 3.5462
5.5960 5.700 5.5795
3.43 3.63 3.20
3.31 5.47
6,7 3
3.87
13.8
16.7
0.09D
300
3.5466
5.5868
2.73
5.95
8 3
0.11
300
3.5478
5.5890
2.90
4.36 5.09
6.2
25.0
9 9
0.175
775
3.572
5.656
3.53
4.06
0.205
300
3.5267
5.6071
2.98
5.05
8.7
14.8
9
0.20
300
3.5250
5.6082
2.76
5.18
9.2
13.2
0.20
775
3.5412
5.6385
2.73
2.78
10.9
10.9
10
0.19D
300
3.5222
5.6040
2.68
0.19D
775
3.5400
5.6386
2.78
5.18 2.88
9.9 12.3
14.9 12.2
10 10
3 10
continued on next p a g e
HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2+« PHASES
219
Table 3, notes
References (1) Saw et al. (1983) (2) Daou and Vajda, unpublished. (3) Beaudry and Spedding (1975) (4) Khatarnian et al. (1981)
(5) Juckum(1980) (6) Daou et al. (1981a) (7) Chiheb (1980)
(8) Bormet (1975) (9) Boanet and Daou (1979) (10) Daou and Bonnet (1974)
with increasing x for Gd, Tb, Dy and Ho, while it increases slightly for Er, Tm and Lu (Daou et al. 1981a), reflecting the evolution of the anisotropy and of the anharmonicity of the interatomic potential upon H insertion. Another interesting point is the exceptional behaviour of the static expansivity in the low-temperature a*-ScH(D)x: it is larger in the basal plane than along the c-axis leading to a decreasing c/a-ratio with increasing x, in contrast to all other «*-phase systems, probably a consequence of the unusually large elastie anisotropy ratio C *= C12/C13 in Sc (cf. Vajda et al. 1990b, 1991e). As already mentioned several times before, the hydrogen atoms in certain «RHx systems have a tendency to organize themselves in short-range-ordered (SRO) or long-range order (LRO) structures when cooled below temperatures corresponding to their mobility limit. The earliest manifestation of such low-temperature ordering was the appearanee of a resistivity anomaly near 170K in ct*-LuHx (Daou et al. 1976), which had been ascribed to a condensation into H-H pairs after interpreting the results of low-temperature electron irradiation experiments (Daou et al. 1977) and internalfriction measurements (Vajda et al. 1983a). The same anomaly was detected in all a*-RH(D)x systems, with R = Sc, Y, Ho, Er, Tm and Lu (for a review see Daou and Vajda 1988). Strong anisotropy manifestations in the magnetic system ~t*-ErH(D)x gave a further early indication as to a c-axis alignment of these H-H pairs (Daou et al. 1980a). The ordered configuration was finally identified through diffuse-neutron scattering experiments on single crystals of «*-LuDx (Blaschko et al. 1985, 1989a) as secondneighbor D-D pairs on T sites along the c-axis surrounding a Lu-atom (fig. 6). Several of these pairs then condense into zig-zagging quasi-linear chains parallel to the c-axis and shift along the b~axis in the basal plane, while the chains, on the other hand, interact repulsively to form a three-dimensional superstructure in the metal lattice (fig. 7). The above configuration was afferwards confirmed on the systems «*-ScDx (Blaschko et al. 1989c) and ct*-YDx (Fairclough et al. 1993). The number of pairs in a chain (i.e. the chain length) differs from one system to another and seems to correlate with the elastic anisotropy of the metal; the chain density varies as a function of H concentration. In table 4 we have collected various characteristics of the ordered structures in the a*-phase, such as the anomaly temperatures (Tan) in electric resistivity or the binding energies as determined from a kinetic analysis of the resistivity data in the vicinity of the anomaly via an Arrhenius plot (cf. Daou et al. 1988a). An immediately visible result (fig. 8) is the correlation between Tan and the c/a-ratio, indicating a lower ordering temperature (i.e. a higher mobility of H) for a c/a-ratio closer to the ideal (8/3) 1/2 = 1.63 (i.e. in systems with less distortion). Note also the isotope effect, with a 4-5 K higher Tan
220
P. VAJDA 0
o
1:3 0
0
~
o
:o o
o~
°!
0 D
O
I1
O
o
I°
o
o 0
~o
3~
o o
~ l° 0
C
0
a¢3q a/¢~
_
o
Q
o
o
o
D o
°°
O
0
o O
O
L
Fig. 7. Various two-chain arrangements made of D-D pairs Fig. 6. HCP unit cell of LuD x in the «*-phase on adjacent c-axes along the b-direction in a*-LttI)x. Open showing two adjacent D-D pairs (dashed lines) circles, metal atoms; open squares, empty T-sites; solid shifted along the b-axis. To, T l and T 2 are first squares, occupied T-sites (Blaschko et al. 1989a). and second neighbour tetrahedral sites along the c-axis (Vajda et al. 1986).
Table 4 Characteristics of the ordered H-configurations in ct*-RH(D, T)x
R
c/a 1.592 1.571 1.570 1.569 1.571 1.583
Sc
Y Ho Er Tm Lu Lu a (lla) Lu a
(llc)
Lu ~ (T for D)'
T~ù (K)
E b (meV)
Xmax
Rel.
H
D
H
D
152.5(5) 168.0(5) 174(1) 173(2) 169(1) 166(1)
160.5(5) 173.0(5) 179(1) 177(2) 174.5(10) 172(1) 174.0(5) 174.0(5) 180(1)
50(2) 61(2)
57(2) 70(2) 72(2)
0.35(2) 0.20(1) 0.03 0.065
1 2 3 4
-
0.11(1)
5
73(3) 65(3) 74(3)
0.20(1)
6 7 7 8
64(2) 63(2)
a Single crystal.
References (1) Daun et al. (1986b) (2) Vajda et al. (1987c) (3) Daou et al. (1987)
(4) Daou et al. (1981d) (5) Daou et al. (1981e) (6) Daou et al. (1986e)
(7) Vajda et al. (1986) (8) Jung and Lässer (1988)
HYDR.OGEN IN RARE-EARTH METALS, INCLUDING RH2÷x PHASES 190
~
,
221
,
180
D
v "~"~ 1 7 0 I.-160
150 1.57
1.58
c/a
1.59
Fig. 8. The anomaly temperature as a function of c/aratio of the metal R in c¢-RH(D)x systems (Daou and Vajda 1988).
in the case of deuterium and another 5-6 K for tritium (in the case of ct*-LuTx, Jung and Lässer 1988), again stressing the H mobility as an essential parameter for ordering; the same is true for the binding energy Eb. 3.2. il-Phase dihydrides As already discussed in sect. 2, it has been a problem for some time to separate the excess hydrogen atoms, x on O sites, from the "pure" dihydride H atoms on T sites in the non-stoichiometric dihydrides RH2+x. Thus, the assumption was that, for therrnodynamic reasons, the O sites began to be occupied before a complete filling of the T sites: that, for example, RHzl0 contained 1.95 H atoms on T sites and 0.15 H atoms on O sites. As has been shown above, the substoichiometry of the "pure" dihydride depended more on the metallurgical state of the specimen than on thermodynamics. It is, in faet, possible to obtain practically ideal T-site occupation in the dihydride, to +0.01 H/R, when using high-quality samples and working at high temperatures. In the following tables, we shall, therefore, either specify the "pure" dihydride concentration (when possible) or at least separate the x-coneentration, avoiding the sum composition, e.g. giving RH1.97+0 ' 13 instead of RH2.10. In table 5 the lattice parameters, a, of the cubic [3-RH2+x phases are presented as a funetion of x at several temperatures. The static and therrnal lattice expansions have been added when available. We note the well-known general contraetion (negative Aa/Axvalues) of the dihydride lattice with increasing x, which is an expression of the strong ionic character ofits interaction with the excess H atoms on O sites; an example is given in fig. 9 for the oase of YH2+x, where the break in the a(x)-curve at x = 0.10 H/Y indicates the limit of the pure [3-phase. Another phenomenon which can be observed through the lattice parameter is the lowtemperature ordering within the x-sublattice. It can either lead to a tetragonal distortion of the originally cubie unit cell given as a and e in table 5, such as in the cases of LaH2+x (fig. 10, for x = 0.80, Klavins et al. 1984), CeH2+x (fig. 11, for x = 0.16, Boroch and Kaldis 1989) and SmH2+x (for x=0.3, Greis et al. 1981, Zogal and UHéritier 1991) or just give rise to anomalies in the thermal behavior of the lattice parameter a such as e.g. in the case of GdH2+x for x ~>0.2 (fig. 12, Chiheb et al. 1993). Such ordering was first established in
222
P. VAJDA Table 5 Crystallographic parameters of the [3-phase, RH(D)2+x x (H(D)/R ratio)
Sc Y
0 0
Aa/Ax 104a (at.% H, D) -l
Aa/AT a
Ref.
(104/K)
4.784 5.2095
873
5.248
298
5.1996
873
5.242
0
298
5.2082
-0.50
5.0
0.05
298
5.2070
-0.50
5.5
3
0.10
298
5.2056
-0.50
6.2
3
1
2.3 18 2.2 20
2 2 2 2 3
0
90
5.2032
-0.45
4.2
3
0.05
90
5.2019
-0.45
2.6
3
0.10
90
5.2002
- 1.15
2.0
3
0
298 773
5.6698 5.7005
6.0
4
16.5
4
0
298
5.6656
-1.3
5
0.27
298
5.6498
-1.3
5
0.53
298
5.6270
-1.3
5
0.60
298
5.6239
5
30 a
5.604 (a) 5.619 (c)
5
298 30 a
5.6218 5.598 (a) 5.654 (e)
0.80
0.92
298
5.6186
-0.5
0.28D 0.41D
298 298
5.6295 5.6164
-1.8 -1.8
0.70D
298 30 a
5.6176 5.600 (a) 5.616 (c)
0.78D
298
5.6111
30 a
Ce
a (Ä)
298 298
0D
La
T (K)
5.587 (a) 5.649 (c)
0.91D 1.00D
298 298
5.6100 5.6064
0 0.16
298 298
5.581 5.650
200 a
5.5500 (a) 5.5727 (c)
340
5.5612
200 a
5.5455 (a) 5.5715 (c)
0.24 b
5 5 6
-1.8
5.0
7 7
continued on next p a g e
HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2+x PHASES
223
Table 5, continued R
x (H(D)/R ratio)
Ce (cont'd)
T(K)
Aa/Ax 104a (at.% H, D) -~
a (Ä)
Aa~AT a
0.63 b
285
5.5375
10
0.90
300
5.5364
13.5
0.18D
295
5.565
4.2 a 0.29D
370 4.2 ~
ReL
( 10-6/K)
5.547 (a) 11.13 (e) 5.564
5.544 (a) 11.125 (c)
er
Nd
Sm
0.9D
295
5.546
0.96D
295
5.536
0
298
5.518
-1.35
10
0.25
298
5.498
-1.35
10
0.47
298
5.483
-1.35
10
0D
298
5.505
-1.25
10
9 9
0.29D
298
5.484
-1.25
10
0.48D
298
5.472
-1.25
I0
0
298
5.4689
8.1
4
773
19.5
4
-1.4
10
-1.4
10
298
5.5005 5.465
0.27
298
5.444
0.47 0D
298
5.430
-1.4
10
298
5.455
-1.5
10
0.09D
298
5.447
-1.5
10
0.29D
298
5.431
-1.5
10
0
295
5.3773
4.3
85
5.3738
2.1
11
0.15
295
5.3693
-1.0
5.6
11
85 295
5.3648
-1.1
3.4
0.26
4.5
11 11
85 295
3.2
11
0.45
5.3637 5.3556
11
-1.0 -1.35
11 11
0D
85 295
5.3521 5.3430 5.365
-1.2
12
0.20D
295
5.3518
-1.2
12
0.40D
295
5.3400
-1.2
12
0.33
295 a
0.33D
295"
3.7780 5.3647 3.7716 5.3503
(a) (e) (a) (c)
12 12
continued on next page
E VAJDA
224 Table 5, continued R
x(H(D)/Rrafio)
2" (~)
a (Ä)
Aa/Ax 104a (at.% H, D) -~
Aa/AT a
Rel.
(lO-~/K) 13 13
Sm (cont~)
0.3
295 98 a
5.365 5.344 (a) 5.362 (c)
Gd
0
298
5.3022
773
5.3305
295
5.3025
4.4
14
95
5.2978
4.4
14
295
5.2990
5.0
14
95
5.2935
5.0
14
295
5.2960
-0.65
5.3
14
95
5.2905
-0.7
5.3
295
5.2926
95
5.2845
3.8
14
295
5.2485
90
5.2430
0.09
295 90
5.2433 5.2375
7.6 3.4 7.15
14 14 14
7.15
14
0.24
295 90
5.2380 5.2308
0.10 0.19 0.25 Tb
Dy
0
0
14
-0.7 -0.85
4 4
14 14
8.0
14
3.8
14
8.0
4
298
5.2060
773
5.2365
295
5.2056
5.6
14
90
5.1996
0.10
295
5.2020
5.6 6.6
14 14
90
5.1950
6.6
14
0.19
295 90
5.2000 5.1931
7.7
14
295 90
5.1988 5A911
5.8 14
14 14
0.27 Ho Er
8.3 16
0 0
17
-0.5 -0.7
4.9
4
14 15
295 298
5.165 5.1290
7.8
773
5.158
15.5
4
7.8
4
4
Tm
0
298 773
5.0925 5.122
Yb
0.55
295
5.192
4 16
0,27 0,44
500 517
5.253 5.192
16 17
0.70
295
5.178
23.5
-1.8
1
continued on next page
HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2+x PHASES
225
Table 5, continued R
x (H(D)/R ratio)
Yb (cont'd)
0.5 0.6
0
473-573 295 295 473-573 298 773 298 773
0D
a
a (Ä)
295 295
0 <x < 0.5 0.5D 0.6D 0 <x < 0.5D Lu
T (K)
Aa/Ax
Aa/AT
(at.% H, D) -I
( 10-6/K)
104a
a
Rel.
5.192 5.180
18 18
5.253 5.182 5.168 5.236
18 18 18 18 6.5 14.5 7.6 18
5.0338 5.062 5.022 5.054
cubic --~ tetragonal transformation below ~200-350 K.
4 4 4 4
b Corrected data.
References (7) Boroeh and Kaldis (1989) (8) Boroch and Kaldis (1987) (9) Schefer et al. (1984) (10) Müller et al. (1979) (11) Daou et al. (1989b) (12) Greis et al. (t981)
(1) Bashldn et al. (1978)
(2) Juekum (1980) (3) Daou and Vajda (1992) (4) Bonnet and Daou (1977) (5) Klavins et al. (1984) (6) Kaldis et al. (1987)
YH 2+x
(13) Zogal and UHéritier (1991)
(14) Chiheb et al. (1993) (15) Pebler and Wallaee (1962) (16) Drulis et al. (1988a) (17) Iwasieczko et al. (1992) (18) Knappe and Müller (1986)
v m
5.203
"X~ ,~~~a
-
5.208
-
5.207
-
5.206
295K
5.202
5.201
5.205
5.200
I 0.1
J x ( a t . H / Y )
0.2
Fig. 9. Lattice parameter of YH2+x as a function of x at room tempera~re and at 90 K (Daou and Vajda
1992).
t h e s y s t e m CeD2+x ( a n d l a t e r c o n f i r m e d f o r R D 2 + x w i t h R = L a a n d P r ) w h e r e s u p e r l a t t i c e r e f l e c t i o n s h a v e b e e n f o u n d b y n e u t r o n s c a t t e r i n g ( T i t c o m b et al. 1972, K n o r r et al. 1978 a n d F e d o t o v et al. 1982), i n d i c a t i n g d i f f e r e n t o r d e r e d s t r u c t u r e s a s a f u n c t i o n o f x.
226
E VAJDA I
I
I
I
l
La H2.8o
5.67
5.65 Z o3 Z
o 5,65 W I--
~5.61 QT,,~..~r. ~
5.59
x
I
o
x
x x I
I I I I00 150 200 TEMPERATURE (K)
50
Cell parameters
I 250
Fig. 10. Temperature dependence of the lattice parameters for LaHz80, showing the cubic---*tetragonal transformation below 248 K (Klavins et al. 1984).
I 500
vs. temperature
CEH2.16
CUB., a
--~ 5.5750
TETR., a
1-~
TETR., c
5.5700
- 5.5650
-15.6600
5.5550
5.5500 I 110
I
I
130 150
I
I
I
I
170
190
210
230
I
I
250 270
I
I
290
310
I 330
I
I
350 370
J Temperature
K
Fig. 11. Temperamre dependence of the lattice parameters for CeHz~6, showing the cubic--*tetragonal transformation below 290 K (Boroch and Kaldis 1989).
HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2+x PHASES a(Ä)
227
j'>
300
10
0.61
>300
10
0.65
253
3,10
0.76
250
10
0.06 0,1
185 200
11 11
0.19
265
11
0.32 0.44
>300 >300
11 11
0.56
165 295
11
Sm
Gd
Tb-3N
Tb-4N
Dy
Ho
Er
0.14
160 230 240
0.045
150
19
0.05D
19
0.088
150 175 180
0.09D
230
19
0.091
225
19
18
19
continued on next p a g e
HYDROGEN 1N RARE-EARTH METALS, INCLUDING RH2+x PHASES
229
Table 6, notes a Corrected data.
References (8) Abeln (1987) (9) Libowitz (1972) (10) Burger et al. (1988) (I1) Daou et al. (1992) (12) Vajda et aI. (1989b) (13) Vajda et al. (1991a) (14) Vajda and Daou (1993)
(1) Daou and Vajda (1992) (2) Klavins et al. (1984) (3) Bieganski and Drulis (1977) (4) Chowdhury et al. (1989) (5) Ito et al. (1982) (6) Ito et al. (1983) (7) Burger et al. (1991)
300
I
I
I
(15) Daou et al. (1986a) (16) Vajda et al. (1987a) (17) Vajda and Daou (1992a) (18) Daou and Vajda (1994) (19) Vajda and Daou (1994)
\ o
280 cub.
/
260
l*
Iv
f
I
~_
/
240
/
/
220
/o
180
0.5
I ~o
I
cu b! 200
ffI
1
t
I
I
I
I
I
0.6
0.7
0.8
0.9
X (D. H/La)
1.0
Fig. 14. Partia! phase diagram of LaH(D)2+x, for 0.5 ~2) bonds located below the d-band of the host. A direct consequence is the decrease of the carrier density upon hydrogenation, and a modification of the Fermi surface, where the Fermi level Er is pushed downwards. This results, for example, in an apparent diminution of the Fermi-surface anisotropy as observed in resistivity studies on single crystals of c~-LuDx (Vajda et al. 1986) and in changes of its nesting features in the case of non-stoichiometrie [~-phase hydrides as suggested from magnetic manifestations in ~-GdH2+x (Vajda et al. 1991a). This will be treated in detail in the next section. The decrease of the conduction-electron density is responsible for a general decrease of all related processes such as s-d scattering, electron-phonon coupling and, in particular, the magnetic interactions mediated through the Ruderman-Kittel-Kasuya-Yosida (RKKY) electron polarization.
244
P. VAJDA
The eleetrie resistivity p, which is the principal subject ofthis seetion, evolves in several stages. First, p inereases when dissolving H in the a-phase, «-RHx, where the hydrogen atoms aet as impurity scattering eenters for the eonduetion eleetrons; it deereases in the dihydride, ~-RH2, reaehing lower values than in the pure metal, mainly due to reduced eleetron-phonon eoupling; then the resistivity increases again upon adding of excess (x) H atoms in solution on octahedral sites, [3-RH2+x;fmally, the hydrides end up as insulators, going through a metal-semieonduetor (M-S) transition somewhere between RH2 and RH3 (in the B-phase for La to Pr, in the y-phase for all heavier lanthanides and Y): R ~ a-RHx + [3-RH2(_o) --~ ~-RH2+x --- RH3(_~). In the following we shall present detailed diseussions of the various specifie cand B-phase systems, treating - in addition to the resistivity data - heat-eapaeity measurements and, when available, results from optieal and photoeleetron speetroscopy. Specific phenomenä such as superconductivity and the Kondo effects will be treated, while a speeial subseetion shall be devoted to the field of the M-S transitions where reeently a new impetus has been given. 5•1• Solid solutions The effeet of dissolving hydrogen atoms as scattering centers for the conduction electrons can be measured either in the metastable low-T a*-phase or in the high-T solid-solution a-phase. Thus, the specifie resistivity of an added H atom is measured near 0 K as a residual-resistivity increase Aprréesin the former ease, and at some higher temperature in the latter. The condensation of hydrogen in the ordered H-H ehain eonfiguration of the a*-phase at 150-180K (cf. seet. 3) does not seem to influenee Ap~ s signifieantly (it is praetically the same at 4.2 K and at room temperature, cf. figs. 24, 25, 28), though a slight decrease of the eleetronie charge density was observed in NMR-measurements in a-ScHx and a-YHx upon H ordering (Liehty et al. 1989). In table 18 we present the values for Ap~ s in the six existing a*-phase systems, both at zero eoneentrations (i.e. determined from the initial slope of the experimental p(x)-eurves) and at maximum eoneentrations, the latter being usually smaller due to a saturation effect. The few investigations of a possible isotope effeet on Ap~ s were not eonclusive in the case ofa*-YH(D)x (Vajda et al. 1987e) but showed a deerease with inereasing isotope mass in the ease of a*-LuH(D, T)x, possibly implying a deereasing vibration amplitude of the interstitial hydrogen isotope (Daou et al. 1986e, Jung and Lässer 1988)• In figs. 24-28 we show several isothermals, p(x), of different RH(D)x-systems, which are useful for the determination of the solubility llmlt Xmax (ef. table 1), sinee the lower resistivity of the ~-phase (see next subseetion) leads to a decrease ofAp~ s when exeeeding the a-phase limit into the two-phase (a+ [3)-region; we also list these Xma x « values in table 18. The eleetronic speeific-heat coeffieient Yel is extraeted from an extrapolation to zero of the low-temperature linear part in the ep/T=f(T) plot. It usually inereases with
245
HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2+~ PHASES Table 18 Residual resistivity increase per at.%H, Ap~s,nfor a-RH(D, T)~ R
Sc
Tm
0.30 0.35 0.19 0.20 0.03 0.03 0.06 0.11
Lu
0.205
Y Ho Er
~pH~(0) a (~tff2crrdat.%H)
Xmax
Ap,o~(Xm=)H b (p~ff2cm/at.%H)
3.6
2.3 2.6
4.2 3.8 3.6
3.4; 3.1; 3.2(D) 2.4 3.3
Rel. 1 2 3 4,5 6 3,7
3.51Ic
3.111c; 3.0Hb
8
4.2
3.25
3,9
9.011c; 3.911b
6.0llc; 3.911b
10
3.75 3.3; 3.1(D)
3.15 3.05; 2.95(D)
3,11,12 13,14
2.30") 2.15(D)11c; 3.75(D)llb
15 16
0.1839 a Determined from the initial slope of the ,o(x)-dependence. b Determined at the maximum concentration in the c-phase.
References (1) Jensen and Zalesky (1980) (2) Daou et al. (1986b) (3) Beaudry and Spedding 1975) (4) Vajda et al. (1987c) (5) Juckum (1980) (6) Daou et al. (1987)
(7) Daou et al. (1981d) (8) Vajda et al. (1987b) (9) Daou et al. (1981c) (10) Vajda et al. (1989c) (11) Daou and Bonnet (1974)
(12) Daou et al. (1976) (13) Daou et al. (1986c) (14) Daou et al. (1981e) (15) Jung and Lässer (1988) (16) Vajda et al. (1986)
15(:
0
lOO E 0
c ¢Z
50 42K
o
I
0
0.1
I
0.2
1
0.3
I
0.4
I
_
0.5
x=at,H(D)/at.Sc
Fig. 24. Resistivity isothermals for ScHx (open symbols) and ScDx (solid symbols) at 4.2 K and 0°C as a function of H(D)-concentration x, indicating maximum solubility for Xm~=0.35(2)atM(D)/Sc (Daou et al. 1986b).
246
E VAJDA
+ 120 80
50
~
1oo
ù
~
~
~o ~
4 40
'~
«
6O
'0 Q
I 0.05
0
I 0.10
I 0.15
I 0.20
I 0.25 x.at.H(D)/at.Y
Fig. 25. Resistivity isothermals for YHx (open symbols) and YDx (solid symbols) at 4.2 K and 0°C as a function of x, indicating maximum solubility at Xmax= 0.20(1)at.H(D)/Y (Vajda et al. 1987c). 15
15 140
.~," ~ ~ ~ - ~' ù ~
'~
-~"~
.=
10 E o
c- t
lO c~
5 t¢ ¢1
0
o
o:os x(at.H/at.
I/
120/ 0
~-~*~+
I .01
1 .02
I .03
~
I .04
I .05
öse" E r)
Fig. 27. Residual resistivity of ErH~ crystals ]Ic as a function of x, indicating maximum solubility for Xmx= 0.065(5) at.H/Er (Vajda et al. 1987b).
x/at.H(D)/at.Ho
Fig. 26. Néel temperature TN, and residual resistivity of HoH~ (open symbols) and HoDx (solid symbols) as a function of x, indicating maximum solubility at Xm~x= 0.03 at.H(D)/Ho (Daou et al. 1987).
increasing x, sometimes passing through a maximum, such as in the case of ct*-LuHx, where it rises sharply from 7el=8.35mJ/gatK 2 at x = 0 to 11.34 for x=0.015 and then decreases continuously to 6.96 at the c-phase limit (fig. 29); Thome et al. (1978) and Stierman and Gschneidner (1984) attribute the sharp peak to hydrogen tunneling.
HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2+x PHASES
P42K et PSOK mu. Qcm
9C
P296K~ in u.Qcm J120
8C
~
7(
f
~o
247
~
~
t 1]0 J
~
" ~ "296K
~
-~.~~
4100
~o
30
60
20
50
10
1,0
I
I 0.1
I
I 0.2
I ot.H/otLu
Fig. 28. Resistivity isothermals tor LuH x at 4.2 K, 90 K and 296 K as a fimction of x, indicatJng maximum so]ubi]ity for x=a* = 0.20(])at.H/Lu (Daou et a]. ] 976).
12
~
T~
r
il I0
0
9
2 Qt%H
I.[xiO-6
« Q9
8 g-
7 \
i
e
\
i
\ è
4
\
\
3
\
\
\
\
2
\
\
\
I
0
~ 0
10
20
30
40
1 50
I 60
% t 70
ATOMIC PERCENTHYDROGEN
80
Fig. 29. Variation of the electronic specific-heat coefficient in the Lu-H system as a function of the Hconcentration. The inset shows the variation of the room temperature magnetic susceptibility. Note the abscissa scale, with c n = H / ( L u + H ) (Thome et al. 1978).
248
E VAJDA
The determination of Yel in magnetically ordering systems is more delicate because of the superposition of a magnetic term in Cp, which has to be subtracted. The only two existing experiments on tx-ErHx and ct-TmHx gave, for the former: )'el= 10.413.0mJ/gatK 2 for 0 ~<x ~ 0.65 attributed to a Mott mechanism. Schlapbach et al. (1986) reported peaks near the Fermi surface in photo-eleetron spectra below 70K for x=0.7, the latter interpreted as due to low-temperature removal of H atoms from the surface to the bulk and consequently pushing back of d-states towards EF to form a metallic band: a typical surface phenomenon. The complicated magnetic phase diagram due to the interplay between antiferromagnetic (AF) and ferromagnetic (FM) interactions will be treated in sect. 6, but here we have to mention the observation of an incoherent Kondo effect for 0 ~<x ~ 0.6. The resistivity isothermals of NdH2÷x exhibited in fig. 40 show an ordering plateau between x ~ 0 . 1 and 0.5 (just as PrH2+x) and a strong increase, up to 6000~tf2 cm, for x = 0.65 (close to the ~/(~ + y) phase boundary) as the concentration approaches the M S transition (Daou et al. 1992). In SmH2+x, where the phase boundary is at X~ax ~ 0 . 4 5 (Daou et al. 1989b), the resistivity curves (fig. 41) show that SRO already begins below x = 0.1, and that a clear LRO-stage exists for x = 0 . 2 6 (Vajda et al. 1989b). The heat capacity of the semiconducting orthorhombic europium hydride was measured by Drulis and Stalinski (1989) for EuHl.•5 and by Drulis (1993) for EuD2, who observed a k-type anomaly for the magnetic transition at Tc = 15.8K for the former and at Tc = 16.3 K for the latter (see sect. 6). The T-dependence of Cp above ~ 5 0 K exhibits a marked isotope effect which was analysed by Drulis (1993) on the basis of hydrogen optical modes as determined from infrared absorption spectra.
HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2+x PHASES
Bi
,oo
259
120 110
/j_T,~o
6050-
}
~4o
~~o!___~~_~_~~~ 20 4 30 2O
~
50
0
~
~
~
40 -
90 80 70
y
.
~o
o_:i~~~~ ~
a
o
~
20 10
0
I
50
t
100
I
150
I
200
I
250
I
300 T(K)
Fig. 37. Thermal variation of the resistivity for three CeH2+x specimens in the relaxed (open symbols) and quenehed (solid symbols) stare; Apq is the quenched-in resistivity inerease reeovering near 170 K (Burger et al. 1991).
The resistivity isothermals at zero K, Pres, and at room temperature/0295 K, of GdH2+x (fig. 42) are an indication of the LRO starting in the x-sublattice near x = 0.15 at low temperatures (Pres-maximum) and the continuous dissolution ofx-hydrogen atoms withõut ordering at 295 K (Vajda et al. 1991a). Fig. 43 shows the effect of quenching upon the x-sublattice and the magnetic transitions (see sect. 6) for x=0.16D and 0.21 as well as the M-S transition at 260 K for x = 0.305, at the [3-phase limit (Vajda and Daou 1993). Figure 44 indicates, as in GdH2+x, the presence of LRO in the x-sublattice of TbH2+x for x ~>0.15, an increasing ordering amplitude Apa~, and ordering temperature Ta~, with increasing x, while a small SRO-anomaly is visible for x=0.07 near 180K (Vajda and Daou 1993, Vajda et al. 1993). No M-S transition was observed in the sample with x =0.245 up to room temperature despite the proximity of the [3-phase boundary and
260
E VAJDA 900
I
I
I
I
I
801-
,o+ +
800
20
700 0
0,20
0•40
0"60
0•80
o
x(at.H/at.Pr)
o+ +• +o
600 oO
+ o +, Bx=O'76
500
g
o
C
+
o
o.
400
• • • .. •
.°
o~
o OoO ,
o+ +° +
o °
200
°
I
.'"
o
. -o°-
.o
°
~" ,
, •..
%
""
x=0"61
;~
o-
" ."" o° oo
°°
IO0"Z
o,~,
o
o"
oO°
°
oO
o
o
oo
o o
,o
. •~oO
• •
300
o
.
,¢¢
o°
,a' .o "° "°
.°"
o ~°°°
ù:il/o~2 .... ::o.:...o.o.O.o x=o.~~ I
I
J
I
[
50
100
150
200
250
300
T(K) Fig. 38, Thermal variation of the resistivity for three PrHz+x specimens in the relaxed (open symbols) and quenched (solid symbols) stare; Apq is the quenched-in p inerease measured at 80 K and plotted as a function of x in the inset. Note the hysteresis between 200 and 250 K for x = 0.76 (Burger et al. 1988).
the large Apan; a transition is expected above ~320K. The evolution of the magnetic ordering will be treated in sect. 6. The situation is similar in DyH2+x as for the other heavy lanthanide dihydrides (fig. 45). LRO occurs above x ~ 0.1, with the maximum effect apparently being attained before x=0.27 (Vajda and Daou 1992a). The latter alloy must already contain some y-phase precipitates, since its resistivity and the ordering amplitude are smaller than those for x=0.22 (el. also sect. 3). Ferreira et al. (1987) performed the first perturbed angular
HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2÷x PHASES
800~
261
Pr H 2,x
700
OOK 600
E
500
.i
«
400
300
200
100~-
Or O
/
~
I .20
M
I .40
///*~4.2K
I .60
I .80 x(at.H/at.tat
Fig. 39. Resistivity isothermals of PrH2+, at various temperatures as a function of x (Burger et al. t 988).
correlation (PAC) measurements on a rare-earth hydride with DyH1.83 and DyH2.95, in the pure [~- and y-phase, respectively. Along with the other data obtained, the authors estimated that the electronic contribution to the electric field gradient in the hcp y-phase is about three times that of the lattice contribution. HoH2÷x (together with ErH2+x) is another superstoiehiometrie dihydride system exhibiting clear M-S transitions as observed in YH2+x (cf. fig. 32). They were measured for coneentrations 0.106 ~<x ~ Hcrlla, for x > 0. Hcr generally decreased with increasing x in the case of polycrystals, while the paramagnetic Op dropped simultaneously from 40 to 31.5 K, and/tePfr remained roughly constant, 9.5 ~tB (Vajda et al. 1983b). Thulium orders in an AF CAM structure below TN = 57.5 K and mrns "ferrimagnefic" (three spins up and four spins down) below a Tc=39.5 K. Contrary to Er, the addition of H diminishes both transition temperatures: TN and Tc decrease by ~1K/at.%H (Daou et al. 1980b, 1981b, 1983, 1988e, Ito et al. 1984, Vajda et al. 1989c), while magnetisation measurements parallel to the c-axis of monocrystalline specimens gave a 2K/at.%H decrease in Tc (Daou et al. 1990), stressing the anisotropy of the magnetic structure. This indicates that the process at Tc is governed by an electronic rather than a magnetoelastic mechanism, the variation of the electronic structure probably overwhelming the magnetoelastic interaction. At the same time, the critical field for the ferri-to-ferromagnetic transition parallel to c, Her[ic, decreases strongly upon hydrogenation (fig. 52). Furthermore, the anisotropy between c-axis and basal plane favours the basal-plane magnetisation and, possibly, even the appearance of basal-plane AF ordering (Daou et al. 1990). 6)0 decreases from 19.1 K to 12.2 K and #Pfr from 7.61 ptB to 6.80~tB when going from pure Tm to «-TmH0.x0 (Daou et al. 1981b). Bennington et al. (1991) have noted, in inelastic neutron-seattering experiments, changes in the CF induced by hydrogen ordering, in particular a dispersionless peak near 15 meV, as welt as a coupling of magnetic excitations to H-vibration stares (cf. table 12 in sect. 4). A surprising phenomenon was observed in resistivity experiments on single erystals of ct-TmHx (Vajda et al. 1989c). While the introduetion of hydrogen essentially resulted in
270
E VAJDA
(~ TmH x//b
100
~o o
~°
Ê 70
!...
O
•
60 O. 50
"o»t~..~~
... °°
.,"~. • "
~
° o o ° °
;.f.~. ~
i........~-o
•
-
40
."
30
' ""
•
"
."
"
/
• "• ." " t " " "
~o iii;.. il"
42.6
."
~~ " " ~ " " . . . - "
,~ ~ ~ ~ ,
•
1.3J
/ 50
701
~
I 2 100
" " ~ ~ "• - 30.6
..... I
4
;
I"
6I 150
"~
• -31.0
.......
_t. .,.,. ,.....,. • .o. , ' . ~ 1.5~ .~...«..... ». o...- ...
10 0 .... " 0
•
i
I
I
8
T(K)
o.
,oo 10.4
I
lOK 200
TmHx / / C
(b)
P
0.10
::k O.
0
x=O 0
I 50
I 100
I 150
T(K)
I 200
Fig. 53. (a) Thermal dependence of the resistivity of ct-TmHx crystals [Ib; the arrows indicate TN and the structural anomaly near 170K. The inset shows the low-temperature part demonstrating the growing contribution of the magnetic excitations with x. (b) Same as (a) for a-TmHx crystals ]1c; the low-temperature part demonstrates the suppression of the ferrimagnetic ordering manifestation with x (Vajda et al. 1989c).
an increase o f the residual resistivity in the b-axis crystals (fig. 53a), the picture changed qualitatively for the c-axis crystals (fig. 53b). The low-temperature decrease in p due to ferrimagnetic ordering is strongly suppressed and vanishes completely for x > 0.05. The latter is attributed to a modification (by ~30% for x = 0 . 1 ! ) o f the magnetic superzone gap produced b y the periodic structures along the c-axis, due to the increase o f Pres.
HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2+x PHASES
271
The temperature dependence of the magnetic resistivity term in the basal plane Pm,b(T), is best fitted through a combination Pm,b(T) e( ATn+ BT 2 exp(-A/kBT), where the first term predominates at low temperatures (T « A/kB) and possibly signifies the presence of an AF excitation, while the second term is due to magnon excitation in anisotropic ferromagnets. Both the power n and the spin-wave excitation gap A decrease in the hydrogenated crystals, i.e. from n ~ 5 to 2.5 and from A/kB ~ 38 K to 6 K, for x gõing from 0 to 0.1. There also exist susceptibility measurements on two non-magnetic «*-phase solid solutions. In (x*-ScHx, Volkenshtein et al. (1983) fotmd X decreasing by nearly a factor of 2 between pure Sc and x = 0.36, illustrating the decrease of the density of electrons responsible for the measured paramagnetism. In ct*-LuHx, Stierman and Gschneidner (1984) observed, for the same reasons, a regular decrease of x for 0.01 ~<x ~ 1.3 b 4.1; 6.8 3.1; 6.2 3.3; 4.3 3.3 (1.7); 5; 6.2 n.o./> 0.35 4.0 3.1 n.o. ~> 1.8 4.1 3.35 2.0 2.5 n.o. ~> 1.5 n.o. ~> 1.5 n.o. ~> 1.5 3.3 n.o./> 2 6.6 6.0 5.3 2.65 2.9; 4.5 (1.75); 2.95 (2.15); 2.25 3.5 9.6 9.6 8.0 n.o. >/1.5 15.8 18.3 16.3
Tral (IC) 14.5 16 17.5 21 16
6.0 (~5) 5.5
Tm~ (IC) 42.5 42 42 33 26
28 16.5 12.5
4.5 4.3 (5.5)
9.5 12.2
10.2 10.8
13.5 12.6
Ref. 1,2 1,2 1,2 1,2 1,2 1,2 1,2 3,4 3,4 3,4 3,4 3,4 3,4 5,6 5,6 5,6 5,6 5,6 5,6 5,6 3,7 3,7 8,9 8,9 8,9 8,9 8,9 8,9 8,9 8,10 5,11 5,11 5,11 5,11 12,13 12,13 14
continued on next p a g e
HYDROGEN 1N RARE-EARTH METALS, 1NCLUDING RH2+~ PHASES
273
Table 23a, notes a TNj stands for several TN (TN1, TN2, etc.).
b n.o. >/ . . . . not observed above . . . .
References (1) Vajda et al. (1990a) (2) Burger et al. (1991) (3) Abeln (1987); Arons et al. (1987b) (4) Schefer et al. (1984) (5) Vajda et al. (1989a)
(6) Daou et al. (198%) (7) Arons et al. (1987a,c) (8) Senoussi et al. (1987) (9) Daou et al. (1992) (10) Drulis and Stalinski (1982)
(11) (12) (13) (14)
Vajda et al. (1989b) Drulis and Stalinski (1989) Bischof et al. (1983) Drulis (1993)
et al. (1988a). It was noted that the overall variation ofpm followed the de Germes factor but that their absolute values were much smaller than those for the corresponding pure R-metals. This implies not only modifieations of the electronic band structure but also a significant reduction of the exchange interaction between conduction and f-electron spins. Deviations of the ground-state resistivities Pm, GS at the ordering temperature T = TN, from the theoretical free-ion values are shown to originate from orten large crystal-field (CF) effects. The values of Pm and of the ground-state magnetic moments #es are given in table 22. A theoretical basis for the CF-analysis in the RH2+x-systems has been given in the work of Lea et al. (1962) who had calculated the splitting of the (2J+ 1) degeneracy of the ionic ground state in a cubic environment. The interaction of these CF-exeitations with magnetism ean be observed principally by inelastic neutron scattering and also in the elassical measurements of specific heat, resistivity or susceptibility. (A detailed discussion is given by Arons 1991.) Table 23a assembles the various characteristic temperatures for magnetie transitions as observed by different experimental techniques. We have separated the light RH2+x-systems (table 23a) from the heavy ones (table 23b), since the situation in the latter is often more complicated. Furthermore, this allows us to present a typical selection of coherent data covering a representative x-interval using the most recent and reliable results. Tc,N are the Curie and the Néel-temperatures (sometimes several TNi) for transition towards the FM and the AF stares, respectively; TM1 and Tml are the positions of the low-temperature maxima and minima in resistivity, corresponding to incommensurate ordering transifions and/or short-range ordered spin fluctuations (or Kondo effects for CeH2+x or YbH2+x); TM2 and Tm2 are the respective positions for a second possible higher-temperature magnetic transformation. The various TM,m are sometimes seen as additional kinks or shoulders in susceptibility and specific-heat measurements. 6.2.1. Specißc RH2+xhydrides The magnetic phase diagram of the CeH2+x-system is rather eomplex and has been established mainly from neutron diffraction (Schefer et al. 1984, Abeln 1987), susceptibility (Abeln 1987, Arons et al. 1987b) and resistivity measurements (Vajda et al. 1990a, Burger et al. 1991). There are two AF transitions in the pure dihydride CED1.95 (Abeln 1987) or CeH2.00 (Vajda et al. 1990a, Burger et al. 1991): TN1 =6.2K or 6.9K, TN2=5K or 4.2 K, possibly followed by another magnetic configuration at even lower temperatures, 1.7K or 2.4K. Neutron-seattering experiments on single crystals (Arons et al. 1987b)
274
P. VAJDA Table 23b Characteristic magnetic temperatures in heavy RH2+x-systems TM1 (K)
Tml (K)
23.7
53.7
1
1.98+0.14
11.5
60.3
1
1.96+0.17
14.5
36.6
1.97 + 0.21
(16)
R Gd
2+x
Tc,Nia (K)
1.94
18.3
1.97 + 0.04
17.75
Tb
1.96
9.5 12
3.7; 5.0
1.97+0.02
3.7; 5.0
1.98+0.10 1.97+0.13
65
105
30.5 32.5
38.5
52
38
52.5
2.55
32.5
42
36
42
4
5.5
5
12 (10)
5 5
8.6
(10.5)
16
10.7
20.5
5
10.7
18.7
5 6
5.4
2.00 + 0.095 2.00+0.175
6 8.2
2.00 + 0,23 3.2 3.5; 4.7
3 4 4
3.4; 5.5
2.00 + 0.047
3
5 ~~ 1.5 b
1.80
n.o./>4
10 30
10
11 11 11 11 9 12 13
2.25
3.9
13
2.37
3.9
13
2.41
4
13
a T~i stands for several T N (Tm, Tr~» etc.),
b n.o. >/ . . . . not observed above . . . .
References (1) Vajda et al. (1991a) (2) Carlin et al. (1980) (3) Vajda et al. (1987a) (4) Vajda et al. (1993) (5) Vajda and Daou (1992a)
(6) Boukraa et al. (1993a) (7) Carlin and Krause (1981a) (8) Daou and Vajda (1994) (9) Shaked et al. (1984)
(10) Vajda and Daou (1994) (11) Boukraa et al. (1993b) (12) Burger et al. (1986a) (13) Drulis et ak (1988b)
permitted the analysis of the AF structure below Tm as MnO-type, with AF-coupted FM-planes modulated along [1101; the propagation vector is rm = 11111] + ½[110], cf. fig. 54a. The introduetion of excess H atoms x on O sites first induces the disappearance of the AF order (for x = 0.05), and then the appearance of FM order (for 0.05 ~<x < 0.6), followed by another AF order up to the highest concentrations measured (x = 0.96). The latter AF strucmre is close to that observed for x = 0, simplified by the lack of the [110] modulation (fig. 54b) caused by the absence of the RKKY-mediating conduction electrons. All magnetic transformatiõns are strongly influenced by the ordering state of the x-atoms (cf. sect. 3). Thus, a quench from room temperature into liquid nitrogen, conserving the random distribution of the octahedral H atoms, drastically modifies the magnetic manifestations, sometimes even leading to their disappearance, cf. e.g. fig. 55 for x = 0.1 and 0.2 (Burger et al. 199 t). The same is true for the Kondo transition observed in these systems (Vajda et al. 1990a): the coherent-incoherent transformation temperature shifts from 17.5 to 2 2 K after a quench, while the two magnetic transitions at T N I and
276
P. VAJDA
«0
~.-'-~5~--I 4--/Y
Fig. 54. (a) Magnetic structure of CeDI.95. The AF-coupled (111) planes show a modulation along [li0]. (b) Magnetic structure of CeDz91 . The modulation shown in (a) is suppressed (Abeln 1987).
ss ~ j ~
/
i,f----"
~0.2
50
°
4
~
o~~' «
I, ° " ~ ~ - ~
J
i
~
n
45
',-o.,
40
35
35
3O
25 5
II
I
I
10
30
50
J
7 0 T(K)
Fig. 55. Thermal variation of the resistivity of CeHzl and CeH2.2 in the relaxed (open symbols) and quenched (solid symbols) state. The arrows indicate the Kondo minima and maxima between 15 and 35 K, together with the magnetic anomalies at lower temperatures. Note the suppression of magnetism in the quenched specimens (Burger et al. 1991).
TN2 vanish (cf. fig. 35 in sect. 5.21 and the related discussion). Figure 56 summarizes the data in the form of a magnetic phase diagram.
HYDROGEN IN RARE-EARTH METALS, INCLUDING RHz+x PHASES 0.2
0.4
g
0.6
0.8
277
1
"
4
2
0Ö
I
I 0.2
I
I 0.4
I
I 0.6
_1
I 0.8
I
x(at.H/at.Ce)
Fig. 56. Magnetic phase diagram for CeH2+x, constructed from resistivity (Burger et al. 1991), susceptibility (Abeln 1987) and neutron scattering data (Schefer et al. 1984).
The pure Pr dihydride PrH1.97 possesses a TN = 3.35 K (Abeln 1987, Vajda et al. 1989a) and exhibits - like CeH2 - a resistivity minimum (Daou et al. 1989b) which is not related to an incommensurate magnetic structure. In the case of CeH2.00, it has been connected to a Kondo effect (Vajda et al. 1990a), while in PrH1.97 it is due to a CF effect. It was shown (Burger et al. 1990) that the experimental situation can be well reproduced assuming a magnetic ground stare, F5 in this case, and a non-magnetic first excited stare, F1, so that the contribution of spin-disorder scattering to p decreases first in a certain interval with increasing temperature, before increasing again due to the taking over by the phonon scattering. The progressive disappearance of the p-minimum and of the magnetic ordering for x > 0 (cf. fig. 57 and table 23a) can thus be explained by a splitting of the degenerate F5-triplet through the non-cubic CF symmetry. Investigations of CF-levels in PrH(D)2+x were performed by inelastic neutron scattering (Knorr et al. 1978, Arons et al. 1987c), specific heat (Drulis 1985) and by proton NMR (Belhoul et al. 1991); the latter results nieely confirm the above interpretation of the p-data through an orthorhombic CF distortion giving a singlet ground state. The magnetic structure of PrD2 was determined by neutron diffraction (Arons and Cable 1985, Abeln 1987) and is similar to that of CeD2 (fig. 54a), except for a different propagation vector: rm = 11111]- ½[112]. NdH2, apart from the orthorhombic semiconducting EuH2 (see below), is the only pure (x = 0) R-dihydride ordering ferromagnetically (Te ,-~6.5 K), see Carlin et al. (1982), Bohrt and Arons (1982), Senoussi et al. (1987). Upon introduction of x-hydrogen atoms, the FM is gradually suppressed, evolving for x ) 0 . 5 towards complex AF structures (Daou et al. 1992) and behaving for still higher x (>0.65-0.7) like a spin glass (Senoussi et al. 1987). This effect is due to an interplay between RKKY-exchange interactions and the random uniaxial anisotropy energy, which appears for x > 0, and is sensitive to the concentration and the ordering state of the exeess hydrogens x. Thus, similar to CeH2+x (see above, fig. 55) a quench aeross the 200K region can completely suppress the magnetic ordering and turn the sample spin-glass like (e.g. fig. 58 for x=0.65).
278
P. VAJDA 0
10
20
30
[
[
I
K
40
55
EB
T2
T1 ~1oo~ .... /
54,'
Pr H2. x 0.15
t
32
T3
54
28
oo!.
~F
651 0
.
~1
°oo
--
I 10
.
o
.
2
.
.
.
4K
[ 20
~~~~_
T I 30
10.5
T/K
40
Fig. 57. Thermal variation of the resistivity of several PrH2+x speeimens, showing the characteristic temperatures for magnetic transitions (Vajda et al. 1989a).
This effect becomes more pronounced when coming close to the M-S transition (and the y-phase region) near x=0.7 (of. sect. 5.2.2), a clear indication for a modification of the electronic band structure. A similar flattening of the initially k-type peaks for the magnetic transitions was seen in specific-heat measurements (Drulis and Stalinski 1982) when approaching x ,~ 0.7. A tentative magnetic phase diagram in fig. 59 (Daou et al. 1992) summarizes the experimental situation, possibly involving a two-phase region around x ~ 0.6 (cf. sect. 3, fig. 15). The pure dihydride SmH2 has an AF structure of the MnO type, with a propagation vector r m = ½ [ l l l ] (Arons and Schweizer 1982); it orders at TN=9.6K. For x > 0 , TN decreases progressively (down to 8K for x=0.16) and disappears completely for x > 0.25. Again, like the lighter RH2+x-systems (see above), structural disorder in the x-sublattice exerts a strong influence upon the magnetism. A striking example is given in fig. 60 where the (now possibly incommensurate) magnetism seems to have reappeared in the quenched x = 0.26 specimen. These phenomena are probably related to perturbations of the CF, which may lead to a splitting of the F8 ground-level quartet. Indications for this were noted, for x > 0, in the anomalous temperature variations of the resistivity (Vajda et al. 1989b) and the complex behaviour of the specific heat (Opyrchal and Bieganski 1978). In the latter experiment, their SmHz00 speeimen contained a non-negligible amount
HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2+« PHASES I
T(K
!
I
PM
I
279
I
NdH2+ x
--4.0 4
« 3.9
2.1 B
X = 0.65 R
~L
2.0 1.94
I
5
~ , I 2 ~, 2.5 K ! 12"17K I
10
o
o.2
t
I ?"~ 0.4
+
S 0.6 0.8 x (at.H / at.Nd)
Ndl-I2+x system, from resistivity (solid circles, Daou et al. 1992)and magnetisationdata (crosses, Senoussi et al. 1987).
2.25K
I 1.5
o
I
Fig. 59. Tentative magnetic phase diagram in the
1.9 1.90
\
2 -- FM I
15 T(K)
Fig. 58. Thermal variation of the resistivity of relaxed
(R, solid circles) and quenehed (Q, solid triangles) NdHz65 in the magneticregion (Daou et al. 1992).
ofx-hydrogen atoms, which is reflected in a rather low TN ---6.75 K and a bump near 10 K, whieh was not mentioned by the authors, and possibly corresponding to the TM1 of the p-measurements (cf. table 23a). The orthorhombic EuH2 is (like YbH2) an insulator, since the divalent europium has lost both its valence electrons upon hydriding. The Eu 2+ ion has seven unpaired spins and is strongly magnetic, resulting in a FM transition at Tc = 16-18K (Mustachi 1974, Bischof et al. 1983, Drulis and Stalinski 1989, Drulis 1993). The magnetic structure of pure GdH2 (like that of SmH2) is AF of MnO type, with a propagation vector ~m = ½[111] (Arons and Schweizer 1982). Additional x-hydrogens on O sites lead to incomrnensuracy, the structure becomes helicoidal, with an axis along [111]. Simultaneously, the TN, which was 18.3 K for x = 0, decreases regularly to TN = 11.5 K for x=0.14, the situation becoming more complicated for higher x (Vajda et al. 1991a). Thus, a second maximum at TM2 appears in the p-curves for x=0.16 (cf. fig. 43 in sect. 5.2.2) which grows in amplitude at the expense of the first maximum at TM1 until the complete vanishing of the latter for x near the phase boundary at x~max~ 0.30. The extreme sensitivity to x-sublattice ordering is shown in the quench experiments. The maximum at TM2, which is evidently related to the ordered H structure, has disappeared to the benefit of a strong emergence of the maximum at TM1, which is obviously conneeted to the disordered (random) x-hydrogen atoms. Gd being a pure S ground state ion (L = 0), one does not expect any significant interaction with the CF; therefore, the strong variations of the magnetic manifestations have to be attributed to profound modifications of the Fermi surface and its nesting conditions. Figure 61 presents, as a summary, the tentative magnetic phase diagram of GdH2+x in the relaxed and in the quenched stare of the x-
280
P. VAJDA 0
10
105f
20
T/K
30
11 Sm H2+x I. ."
104 5'
: ..
•
1;:I~-::°i~oio:~~'~~i°°~ i:
95 90
~°~°°°°°
5•oooo ~,~-/-~
69.
.."
~
+
~oooo°°~.. x~o,°
,Fr
4.5
j
37"
1
• °* o*
36.5
35
34.5
36
2~ «
o
oO°
~° o o°°° .
.
.
~ x = O
.
o:R
20.
201 0
I
I
10
20
T/K
30
Fig. 60. Thermal variation of the resistivity of several SmH2+x specimens in the relaxed (open symbols) and quenched (solid symbols) stare. Note the reappearance of magnetism after a quench for x=0.26 (Vajda et al. 1989a,b).
/ -
/ /
•~~ f T : ~
80
+/4/ / /
iC 2
60 p-
•
40
IC
.~ Tml "~+ i"' icl
20 -
AF
0
hel ]
0.1
• o/
/
I
I
0.2 0.3 x(at,H(D)/at.Gd)
Fig. 61. Tentative magnetic phase diagram of GdH2+x(open symbols) and GdD2+x (solid symbols) in the relaxed (solid lines) and in the quenched (dotted lines) stare obtained from resistivity studies (Vajda et al. 1991a). icl,» incommensurate or magnetically SRO phases; hel, helieoidal phase• For the various critical temperatures, see text and table 23b.
HYDROGEN IN RARE-EARTHMETALS, INCLUDINGRHz+x PHASES
/
(a) /
;/
(b) k= [1/4, 1/4 ,3/4]Æ [113] /
/
/
,/ ,
281
k'= [1/8. 1/8,3/4 ]//[116]
/
/
/
Fig. 62. Magnetic structures of TbDz00; (a) commensuratephase observed for T < 16 K; (b) incommensurate phase in the interval 14.8~0.05, only suppression OfPmag
284
P. VAJDA
t
r
~
~
~
J
J
,
~
57
B',~ /\~.~\,/x=o.o~ ,~ õô
Ê23
25
"~ 7
x=o.o2
4,65 J~'\
~ , 2 \ T\
~
4 /x=O
~ 2
0
~.~~ i 1
1 2
I 3
I ~ 4 T(K)
i 6
I 7
I 8
Fig. 66. Resistivity of various Hort2+« specimens in the magnetic region showing the evolution of the critieal temperatures as a function ofx (Daou and Vajda 1994).
TI is l e r as a manifestation of magnetism in the form of a slope maximum near 6 K in p and as a flat maximum in X (Boukraa et al. 1993a). On the other hand, a second structure develops as a hump above T ~ 25 K for concentrations x > 0.12 (el. also fig. 46 in sect. 5) which could be due to the appearance of a new magnetic phase caused by the LRO in the x-sublattice, similar to GdH2+x and TbH2+x. The magnetic structure of ErH2, the heaviest of the magnetically ordering dihydrides, is a complex AF below TN = 2.15-2.30 K (Bieganski and Stalinski 1976), with a mixture of both eommensurate and incommensurate components down to 1.5 K (Shaked et al. 1984). The incommensurate structure lines in the neutron diffraction pattern are at the same positions as those of the intermediate structures in TbD2, DyD2 and HoD2, showing their close relationship to each other. It should, in fact, be interesting to investigate ErH2 down to even lower temperatures in view of an eventual observation, by analogy, of the pure commensurate structure, since the measured "mixed" spectra might be representative only for the overlap region between the two phases such as noted in TbD2 (Vajda et al. 1993). This close relationship is also evident in the behaviour of the superstoichiometrie ErH2+x-system, in that it is similar to other heavy RH2+x compounds: a decrease of TN for small x and the appearance of a new magnetic structure at higher temperatures for x high enough to form a H sublattice (figs. 67 and 48). The tentative phase diagram for the characteristic temperatures in the magnetically ordering range (fig. 68) was constructed from the available resistivity (Vajda and Daou 1994) and susceptibility data (Boukraa et al. 1993b, Carlin and Krause 1981b). Again, as for DyH2+x, neutronscattering measurements are required to determine the precise SRO and LRO magnetic configurations.
285
HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2+x PHASES 0.02 121 x = 0.088 " ~
29.5
~~
+
_
29
119 117
r
L 3!
L
I
0,1 I ....
Er H2+x
g ~ pM
~ \x=oo7 2.5
~-2~
12.0
1.5
1 0
0.6 0
0.06
I
I 1
I 2
I 3
I
1 _l 0.04 x(at.H/at.Er)
f 0.08
I 4 T(K)
Fig. 67. Resistivity of various ErH2+x speeimens in the magnetie region showing the evolution of the transition temperature with increasing x (Vajda and Daou 1994).
Fig. 68. Tentative magnetic phase diagram of ErH2+« indicating the different coexisting eommensurate and incommensurate phases as well as the SRO domains, constructed from resistivity (solid triangles, solid inverted triängles, Vajda and Daou 1994) and suseeptibility data (solid cireles, solid squares, Boukraa et al. 1993b; crosses, Carlin and Krause 1981b).
No magnetic transitions have been observed in TmH2 down to 1.5 K. An analysis of the spin-disorder resistivity, Pm, shows that the ground stare (F2) is non-magnetic but separated from the first excited magnetic state (F~2)) by AE ~ 170K - a Van Vleck paramagnet (Burger et al. 1986a, Shaltiel et al. 1991a). The only low-temperature investigation undertaken up to now in the TmI-I2+x system coneerned Tm-169 Mössbauer studies on samples with ill-defined eompositions by Waibel et al. (1980) who interpreted the spectra as evidence for the presence of two non-magnetic phases. Further thorough experiments should, however, be interesting in view of the great sensitivity of such a Van Vleck compound to minor changes in the surroundings of the Tm-ions. For example, it was shown in EPR-linewidth measurements of substitutional Gd and Er impurities (0.01 at.%) in TmH2 that the latter reduced the first CF-level separation AE by nearly a factor of two (Shaltiel et al. 1991b). Even greater effeets should be expected from interstitial type defects such as the oetahedral x-hydrogens. The orthorhombic YbH2 is non-magnetic because of the divalency of the yb2+-ion, which becomes an analog of Lu 3+. In the fee superstoiehiometric dihydrides with x > 0.25, the presence of yb3+-ions, yielding a mixed-valence system, seems to lead to Kondolattiee behaviour, with a eoherent-incoherent transition near 4 K (Drulis et al. 1988b, but: cf. also the note in sect. 5.2.2).
286
R VAJDA
7. Summary and outlook
This review of experimental data concerning hydrogen in rare earths, both in the form of solid solutions and of hydrides, shows - as a first general result - the great influence of the initial metal purity upon the characterization of the fmal specimen and its physical and physico-chemical properties. A thorough control of the preparation conditions is a further (related) requirement for obtaining unambiguous and reproducible results. Among the general regularities along the R-series, one can note the evolution of eertain dimension-dependent properties, for example a decreasing solubility in the B-phase (i.e. a narrowing of the pure R-phase region). On the other hand and for the same reasons, the solubility in the low-temperature «*-phase increases, as the eventual preeipitation of the B-phase is retarded in lattices with smaller unit cells. Similarly, for the J-dependent magnetic properties, such as the transition temperatures TN and the spindisorder resistivities Pmag, the B-RH2hydrides follow the de Gennes factor, just as in the pure metals. As to the more prominent properties, one has to mention the hydrogen sublattice ordering occurring below room temperature both in the «*-phase solid solutions and in the [3-phase RHz+x systems. In the former case one observes zig-zagging chains along the c-axis made of H-H pairs on tetrahedral sites of the hcp lattice, and in the latter, the excess hydrogen atoms x on octahedral sites of the fluorite type fee lattice form a tetragonal DO22 configuration, at least in the heavy RH2+x compounds. This ordering has a striking influence on the magnetie manifestations, via modification of the Fermi surfaee and/or the crystal-field symmetry. Also related to the above x-sublattice ordering are the recently observed metalsemiconductor transitions near room temperature in the heavy superstoichiometric dihydrides GdH2+x, HoH2+x, ErH2+x and in YH2+x for x dose to the R-phase boundary (0.1< Xmax ~ < 0.3). Another M-S transition oecurring in these systems at lower temperatures (20-12010 seems to be due to carrier localization caused by atomic disorder. Analogous effects were noted in the light substoichiometric trihydrides (also in the B-phase) LaHz+x and CeH2+x in the range 0,7 < x < 0.9. As to future developments, one expects a more intense neutron-scattering work both for the determination of structural phase diagrams (mainly concerning the H sublattice) and of magnetic phase diagrams, in particular the complex ineommensurate configurations in the heavy RHz+x compotmds. Inelastic neutron-scattering studies are required for the investigation of phonon-dispersion relations and of H local modes. Also, further work is needed for the determination of the precise electronic mechanism responsible for the M-S transitions. And, finally, little is known of the low-T properties of the y-phase trihydrides because of their inherent chemical instability. Last but not least, a major effort should be devoted to the growth of monoerystalline hydride specimens other than CeH2+x, a prerequisite for the study of short-range-ordered configurations.
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HYDROGEN IN RARE-EARTH METALS, INCLUDING RH2÷x PHASES Vajda, R, and J.N. Daou, 1991, Phys. Rev. Lett. 66, 3176. Vajda, P., and LN. Daou, 1992a, Phys. Rer. B 45, 9749. Vajda, P., and J.N. Daou, 1992b, Mod. Phys. Lett. B 6, 251. Vajda, R, and J.N. Daou, 1993a, in: Proc. Int. Conf. on Metal-Hydrogen Systems, Uppsala, Sweden, i992, Z. Phys. Chem. NF 179, 403. Vajda, R, and J.N. Daou, 1993b, The rare-earth hydrogen systems, in: Metal-Hydrogen Systems, Vol. 1, eds A. Aladjem and RA. Lewis (VCH, Weinheim) ch. 3a. Vajda, R, and J.N. Daou, 1994, Phys. Rev. B, to be published. Vajda, E, J.N. Daou and P. Moser, 1983a, J. Phys. (Paris) 44, 543. Vajda, R, J.N. Daou, E Radhakrishna and G. Chouteau, 1983b, J. Phys. F 13, 2359. Vajda, E, J.N. Daou, J.E Burger and A. Lucasson, 1985, Phys. Rer. B 31, 6900. Vajda, E, J.N. Daou, J.R Burger, K. Kai, K.A. Gsehneidner Jr and B.J. Beaudry, 1986, Phys. Rev. B 34, 5154. Vajda, E, J.N. Daou and J.R Burger, 1987a, Phys. Rev. B 36, 8669. Vajda, R, J.N. Daou, J.R Burger, C. Schmitzer and G. Hilscher, 1987b, J. Phys. F 17, 2097. Vajda, E, J.N. Daou, A. Lucasson and J.R Burger, 1987c, J. Phys. F 17, 1029. Vajda, R, J.N. Daou and J.E Burger, 1989a, Z. Phys. Chem. NF 163, 637. Vajda, R, J.N. Daou and J.R Burger, 1989b, Phys. Rev. B 40, 500. Vajda, R, J.N. Daou, J.R Burger, G. Hilseher and N. Pillmayr, 1989e, J. Phys. Cond. Matter 1, 4099. Vajda, R, J.E Burger and J.N. Daou, 1990a, Europhys. Lett. 11,567. Vajda, R, J.N. Daou, R Moser and R Remy, 1990b, J. Phys.: Condens. Marter 2, 3885.
291
Vajda, R, J.N. Daou and J.R Burger, 1991a, J. LessCommon Met. 172-174, 271. Vajda, R, J.N. Daou and J.R Burger, 1991b, J. Phys. Cond. Matter 3, 6267. Vajda, R, J.N. Daou, R Moser and R Remy, 1991c, J. Less-Common Met. 173, 522; Solid State Commun. 79, 383. Vajda, R, J.N. Daou and G. André, 1993, Phys. Rer. B, to be published. Viallard, R., and J.N. Daou, 1972, in: Hydrogène dans les Métaux, Vol. 1 (Science et Industrie, Paris) p. 76. Volkenshtein, N.V., E.V. Gatoshina, M.E. Kost and T.S. Shubina, 1983, Phys. Status Solidi b 117, K47. Völkl, J., H. Wipf, B.J. Beaudry and K.A. Gschneidner Jr, 1987, Phys. Status Solidi b, 144, 315. Vorderwisch, P., S. Hautecler and W. Wegener, 1980, J. Less-Common Met. 74, 117. Waibel, F., A. Strauss, W. Potzel, EE. Wagner and G. Wortmarm, 1980, J. Phys. (Paris) 41(Suppl.), C1231. Weaver, J.H., R. Rosei and D.T. Peterson, 1979, Phys. Rev. B 19, 4855. Wegener, W., P. Vorderwisch and S. Hautecler, 1980, Phys. Status Solidi b 98, Kl71. Wiesinger, G., and G. Hilscher, 1991, Magnetism of hydrides, in: Handbook of Magnetic Materials, Vol. 6, ed. K.H.J. Buschow (North-Holland, Amsterdam) ch. 6. Zarnir, D., R.G. Barnes, N. Salibi, R.M. Cotts, T.T. Phua, D.R. Torgeson and D.T. Peterson, 1984, Phys. Rev. B 29, 61. Zogal, O.J., 1987, J. Less-Common Met. 130, 187. Zogal, O.J., and R UHéritier, 1991, J. Alloys & Compounds 177, 83. Zogal, O.J., Ch. Jäger, H. Döhler and B. Schnabel, 1984, Phys. Status Solidi a 82, K153.
Handbook on the Physics and Chemistry of Rare Earths VoL 20 edited by K.A. Gschneidner, Jr. and L. Eyring © 1995 Elsevier Science B.V.. All rights reserved
Chapter 138 MAGNETIC PROPERTIES OF INTERMETALLIC COMPOUNDS* D. G I G N O U X
a n d D. S C H M I T T
Laboratoire de Magndtisme Louis N~el, C.N.R.S., B P 166, 38042 Grenoble Cddex 9, France
Contents List of symbols and abbreviations 1. Introduction 2. 3d Magnetism 2.1. Onset of magnetism in Co- and Nibased alloys 2.1.1. Collective electron metamagnetism (CEM) 2.1.1.1. The WohlfarthRhodes model 2.1.1.2. RCo2 2.1.1.3. ThCo 5 2.1.1.4. Further CEM systems 2.1,1.5, Strong magnetoelastic effects 2.1. t .6. Spin fluctuation effects 2.1.1.7. A new model of CEM 2.1.2. Very weak itinerant ferromagnetism (VWIF) 2.1.3. Cobalt antiferromagnetism 2.2. 3d Magnetocrystalline anisotropy 2.2.1. Experimental characteristics 2.2.2. Theoretical interpretations 2.3. Instability and frustration of Mn magnetism in RMn 2 compounds 2.3.1. Topological frustration 2.3.2. Mn moment instability and complex magnetic structures
294 295 296 297 298 298 299 301 302
303 304 306 308 309 310 310 313 316 316 317
* In memory of Remy Lemaire. 293
2.3.3. Large Mn anisotropy 2.3.4. Giant spin fluctuations 2.3.5. Theoretical approaches 2.4. Lanthanide-3d transition-metal compounds where both carry a well defined magnetic moment 2.4.1. General characteristics 2.4.2. Curie temperatures and 3d-4f exchange interactions 2.4.3. High-field magnetization processes, 3d-4f interaction and magnetocrystalline anisotropy 3. 4f Magnetism 3.1. Crystal-field and exchange interactions in ferromagnetic compounds 3.2. Metamagnetism and associated phase diagrams 3.2.1, General considerations 3.2.1.1. Demagnetizing field effects and hysteresis 3.2.2. CEF metamagnetic systems 3.2.3. Quadrupolar metamagnetic systems 3.2.4. Ferromagnetic metamagnetic systems 3.2.5. Weakly anisotropic metamagnetic systems
322 323 325
327 327 328
331 337 338 345 345
347 350 355 359 363
294
D. GIGNOUX and D. SCHMITT
3.2.6. Spin-flip metamagnetic systems: simple antiferromagnets 3.2.7. Modulated metamagnetic systems 3.2.8. Spin-flip metamagnetism: long-period commensurate systems 3.2.9. Spin-slip metamagnetism: long-period commensurate systems 3.2.10. Complex multistep metamagnetism: long-period commensurate systems 3.2,11. Planar metamagnetic systems 3.2.12. Multiaxial metamagnetic systems 3.3. Quantitative analysis of incommensurate magnetic systems 4. Summary and conclusion 5. Appendix: Definitions and/or descriptions of magnetic terms or phenomena 5.1. Antiferroquadrupolar and ferroquadrupolar ordering 5.2. Amplitude-modulated structure
5.3. Antiphase structure 5.4. Collinear and noncollinear structures 5.5. Commensurate and incommensurate structures 5.6. Equal-moment structure 5.7. Exchange interaction J(/j) and Fourier transform J(q) 5.8. Fan structure 5.9. Flopside structure 5. i 0. Frustration 5.11. Helical structure 5.12. Helifan 5.13. Multiaxial structure 5.14. Multistep metamagnetic process 5.15. Multi-Q structure (double, triple. . . . ) 5.16. Quadrupolar moment 5.17. RKKY (Ruderman, Kittel, Kasuya, Yosida) exchange interaction 5.18. Single-Q structure 5.19. Spin-flip transition 5.20. Spin-flop transition 5.21. Spin fluctuations 5.22. Spin-slips (or spin discommensurations) 5.23. Spin-reorientation transition References
367 369
373
378
380 390 394 399 406 408 408 408
409 409 409 410 410 410 411 411 412 413 413 413 413 413 414 415 415 415 416 416 417 417
List of symbols and abbreviations a, b, e a*, b*, c* AM B B~ C phase CEF
basis vectors of the unit cell basis vectors of the reciprocal unit cell amplitude modulated magnetic induction crystal field parameters commensurate phase crystalline electric field
CEM EM F FOMR Gj
collective electron metamagnetism equal moment free energy first-order magnetic reorientation tetragonal quadrupolar parameter
G2 gj H
trigonal quadrupolar parameter Land~ factor magnetic field
7-( I phase INS
Hamiltonian incommensurate phase inelastic neutron scattering
J J1
Jz J(ij) J(q) J(0) kB K K~ L LMTO M M
total kinetic moment operator exchange interaction between nearest neighbours exchange interaction between second-nearest neighbours exchange interaction between moments i andj Fourier transform of the exchange interactions paramagnetic exchange parameter Boltzmann constant reciprocal lattice vector second-order anisotropy constant of tmiaxial systems orbital kinetic moment operator linear muffin tin orbital chemical symbol for 3d transition metals magnetization
MAGNETIC PROPERTIES OF INTERMETALLICCOMPOUNDS Ms M-NM n, n n(/?F)
Na N NMR O~ PF model Q q R Ri RKKY RPA S S SCR Tc
component of the total kinetic
Tt~
moment
TQ
magnetic-nonmagnetic bilinear exchange coefficient density of states at the Fermi level demagnetizing field factor number of moments per magnetic unit cell nuclear magnetic resonance Stevens operators periodic field model propagation vector of magnetic structure vector of the reciprocal space chemical symbol for rare earth, lanthanide position of atom i Ruderman-Kittel-Kasuya-Yosida random phase approximation Stoner enhancement factor spin kinetic moment operator self-consistent renormalization Curie temperature
TR TsF Tt, TI, T2, ... TEC U VWIF W Fi
y eF )~ ~ #B ~tSR r X Z~)
295
Nrel temperature quadrupolar ordering temperature spin reorientation temperature spin fluctuation temperature transition temperatures thermal expansion coefficient Coulomb repulsion or exchange energy very weak itinerant ferromagnetism bandwidth irreducible representation of a symmetry group electronic specific heat coefficient Fermi energy spin orbit coupling constant wavelength Bohr magneton muon spin resonance incommensurate component of the magnetic propagation vector magnetic susceptibility third-order paramagnetic susceptibility
1. Introduction This chapter is devoted to the magnetic properties o f rare earth intermetallic compounds investigated during the last fifteen years. The earlier works in this field have been described by Kirchmayr and Poldy (1979) in a previous chapter o f this Handbook series (volume 2, chapter 14), During the last 15 years, research in magnetism can be characterized by a b o o m in the field o f rare-earth (R)-based materials, in particular the metallic ones. Currently, rare earth intermetallics are in a prominent situation not only from a fundamental point o f view but also for the large number o f technological applications, in particular in the field o f permanent magnets. Rare-earth intermetallics play an important role in a large range o f current research fields, in particular those devoted to heavy fermions, valence fluctuations, Kondo lattices, magnetostrictive materials, permanent-magnet materials, spin glasses and random anisotropy systems. Since these aspects o f magnetism in rare-earth intermetallics are treated elsewhere, they will not be discussed here. In this chapter we are mainly concerned with the basic properties o f intermetallic compounds with normal lanthanides, i.e. those with a well localized 4 f shell. This means that most o f the Ce and Yb materials are excluded. Furthermore, rather than giving an exhaustive report on magnetic properties with many physical values reported
296
D. GIGNOUXand D. SCHMITT
in tables, we prefer to emphasize what we consider to be the major steps in this field of research during the period under consideration. This chapter is divided into two major parts. The first part is devoted to systems in which the obtained results led to a better knowledge of 3d magnetism. Four major aspects will be considered. First (sect. 2.1), the onset of magnetism in Co and Ni, in which the major part is devoted to the systems where collective electron metamagnetism has been observed. The understanding of the large 3d magnetocrystalline anisotropy of many intermetallic compounds is treated in sect. 2.2. In the cubic Laves phase RMn2, the instability of Mn magnetism together with the topological frustration of antiferromagnetic interactions lead to quite original properties which are at the origin of new physical concepts and theoretical approaches. The magnetic properties of these fascinating compounds are presented in sect. 2.3. The last section of this part is devoted to rareearth-3d transition-metal compounds where both carry a well defined magnetic moment. These compounds generally are excellent materials for permanent-magnet applications, but only the last results obtained concerning their intrinsic properties are presented. The second part of this chapter concerns the magnetic properties of compounds in which only the lanthanide atom is magnetic. After a description (sect. 3. I) of recent progress made in the quantitative knowledge of the main interactions (exchange and crystal field) in the small number of lanthanide-based series which are ferromagnetic, the main purpose of this part is devoted to the compounds which exhibit metamagnetic processes of quite different origins (sect. 3.2). Because of the long range and oscillatory character of the indirect RKKY exchange interaction the majority of these compounds order antiferromagnetically with complex magnetic-field-temperature phase diagrams often characterized by the competition between commensurate and incommensurate magnetic structures. Dramatic progress has been made in the knowledge of these systems during the last decade due to the improvement of experimental devices, the increasing number of single crystals of good quality and the evolution of theoretical models. Parallel to the experimental advances in this field, theoretical models have been proposed to quantitatively analyze these complex phase diagrams, in particular the incommensurate magnetic systems, which is the purpose of the last section (sect. 3.3) of this part. In this chapter a large number of experimental results and theoretical approaches, already presented in previous review papers, are assumed to be known. The reader will find useful information in the reports on rare-earth-based intermetallic compounds by Buschow (1977a, 1979, 1980, 1988) and by Kirchmayr and Poldy (1979).
2. 3d Magnetism The R-M systems, where M is a 3d transition metal, form an outstanding tool for the study of 3d band magnetism and in particular the interactions, instabilities and anisotropies of such magnetism. In the majority of cases, for a given M element, a series of compounds with different rare earths crystallize in the same crystallographic structure and thus have practically the same band structure. It is then possible to study the 3d magnetism under
MAGNETIC PROPERTIES OF INTERMETALLIC COMPOUNDS
297
several conditions depending on the rare earth (nonmagnetic or magnetic, isotropic or not, different sign of the magnetocrystalline anisotropy parameters . . . . ). Many studies are devoted to these systems and it is impossible to describe all the results obtained. We focus on the most original advances in 3d magnetism discovered in R-M intermetallic compounds during the last decade. 2.1. Onset of magnetism in Co- and Ni-based alloys These compounds are formed by the association of the 3d band of the M element with the 5d band of R (4d for Y) with higher energy. The electronegativity difference between the constituents causes a transfer of 5d (4d) electrons towards the unfilled 3d band. Since the screening of the nuclear potentials by the electrons is modified, the two bands approach each other leading to 3d-5d (or 3d-4d) hybridized states (Cyrot and Lavagna 1979, Shimizu et al. 1984). The Fermi level of the compounds often lies in this region of the density of states. This itinerant description of 3d magnetism is the most appropriate for Co and Ni in which, due to the width of the 3d band, the Un(ev) product (U is the Coulomb repulsion or exchange energy between up and down spins, and n(eF) the density of states at the Fermi level) is smaller than unity (with Mn and Fe this ratio is closer to unity and accordingly magnetism is more localized). Starting from pure Ni or Co, the progressive increase of the R percentage leads first to a decrease of the density of states at the Fermi level n(eF). For a critical concentration range (around RCo2 for cobalt and RNi5 for nickel) alloys are close to the conditions required for the onset of magnetism (Stoner criterion) and magnetic instabilities can be observed, each behaviour strongly depending on the fine structure of n(e) near eF. However, resurgence of 3d magnetism appears for a slightly larger R amount and then disappears altogether as shown in fig. 1. e--
o~ 6~-e,l (.9 ~.-__
1.5 "
,
I
I
+
.-~
go I
I
+
g
• Yxcol-x
,-~ ~,',ec
~r v
o
, 1.0
LaxCOl_ x
YxN,l_ x
g,
Iii
k)
~+I om 'I ~
...1
g +'
t~
5-
u
c,4
I +
0.5
~; ~,
' t, t--,
0
0.1
0.2
~ ~
o c9
0.3
0.4
0'.5 x ~-
Fig. 1. Mean value of the 3d moment as a function of the rare earth concentration in the compounds of the La-Co, Y-Co and Y-Ni systems (Gignoux and Schmitt 1991).
298
D. GIGNOUX and D. SCHMITT
Three types of characteristic behaviours are mainly observed for R concentrations near or larger than the critical ones, namely collective electron metamagnetism (CEM), very weak itinerant ferromagnetism (VWIF) and Co antiferromagnetism. 2.1.1. Collective electron m e t a m a g n e t i s m (CEM) 2.1.1.1. The Wohlfarth-Rhodes model. Collective electron magnetism (CEM), predicted in 1962 by Wohlfarth and Rhodes (1962), refers to the transition from a nonmagnetic to a magnetic state when the field acting on the band is larger than a critical value HM. Using a Landau-type expansion of the magnetic free energy of the d-electrons, such as F = AM 2 + BM 4 + CM 6 + ....
(1)
MH,
the theory led to the following expressions for the first lower-order coefficients
1 (2)
A - 4n,gF,---~ o,ot)
1 B-=-64n3(eF)
2] 3n(eF------)- \ n(eF) J J '
(3)
where S = (1 - Un(eF)) -1 is the Stoner enhancement factor, n, n' and n" are the density of states and its first and second derivatives at the Fermi level. CEM occurs when the magnetization dependence of F has the upper variation shown in fig. 2a in zero field and it becomes the lower curve of this figure above the critical field HM. The corresponding expected low-temperature magnetization curve is shown in fig. 2b. The above formulae show that such a behaviour can occur when: (1) A is weakly positive, i.e. when the Stoner criterion for the onset of ferromagnetism is almost satisfied, and (2) B is negative, which implies another minimum for a nonzero value of M. This latter condition requires n"(eF) to be large enough, which means that the density of states at the Fermi level has a strong positive curvature. The system is now a Pauli paramagnet in low field and the thermal and field dependences of its susceptibility are given by X = SXo
[,7~2(.BH(EF) Rt(EF)2) 1 - --~S
T2+
S3(Bt"(EF)_nt(EF)2"~H2 ] + • ...
(4)
This formula shows that a maximum in the thermal variation of the susceptibility, having the same origin, is also predicted (fig. 3b). Because of this increase of the susceptibility with temperature, the shape of the magnetization curves changes with temperature; the magnetization discontinuity tends to decrease and even to disappear above a given temperature. The high magnetization state is then reached continuously (fig. 3a). This behaviour, which was assumed only to occur on Co in RCo2, but had not been directly observed until the late seventies, has since clearly shown up in several rareearth-transition-metal alloys. The best examples are RCo2 and ThCo5 which are presented below.
MAGNETIC PROPERTIESOF 1NTERMETALLICCOMPOUNDS z~F (a)
M
299
(b)
H=0
HE i
/M= H H~
HM
H~
Fig. 2. Collective Electron Metamagnetism. (a) Variation of the difference between the free energy of the ferromagnetic and paramagnetic states as a function of magnetization at different fields; (b) variation of magnetization with increasing field (Barbara et al. 1988).
M~ (a)
0
X
HM
I~
(b)
T2
Fig. 3. Schematic representation of the Collective Electron Metamagnetism. (a) M vs. H at various temperatures; Co)thermal variation of the initial susceptibility (Gignoux et al. 1983).
2.1.1.2. RCo2. As shown in fig. 1, RCo2 compounds are at the limit o f the onset o f Co magnetism. In these cubic Laves-phase compounds Co atoms belong to one crystallographic site. With magnetic rare earths the compounds are ferromagnetic (with light lanthanides) or ferrimagnetic (with heavy lanthanides) and, below the Curie temperature, Co is magnetic with a moment close to I#B. Conversely in YCo2 and LuCo2, Co is nonmagnetic (Lemaire 1966). These latter compounds are enhanced Pauli
300
D. GIGNOUX and D. SCHMITT 20
A 18 ol
YCo2 ........... v- 12 ,.J
-~ ~o n
U8 ~
6
,6o
26o
Fig. 4. Thermal variationof the susceptibility of YCo2 and LuCo2 (Gignoux et al. 1983).
36o
TEMPERATURE (K)
Y(C°I"xAtx)2 0.5
4.2K
'
~
¢,O0'6 ..~
t/oo, I/t= 10
B
20 (T)
LuCU°
J r-,..
~ ~ - - ~ " 1
LJ
0
'
30
Fig. 5. Magnetization curves of Y(Col_xAlx)2 at 4.2 K (Sakakibara et al. 1987).
T=IO K
0,
z,o
20
40
60
80
100
H(T)
Fig. 6. Magnetization curves of YCo2 and LuCo2 at 10 K in pulsed ultra-high magnetic field up to 94 T (Gignoux and Schmitt 1991, after Goto et al. 1990). The magnetizationdata measured in a long pulse field are also plotted as dots. paramagnets but the field and thermal effects indicate the possibility o f CEM. Indeed, in YCo2 and LuCo2 the susceptibility exhibits a broad m a x i m u m around 230 K and 370 K, respectively (fig. 4). Moreover, at 4.2 K the superimposed susceptibility o f YCo2 increases by about 20% between 0 and 35 T (Bloch et al. 1975), whereas in LuCo2 this effect is much smaller (Schinkel 1978). Actually, CEM was not observed because this m a x i m u m magnetic field was smaller than the critical field HM o f the metamagnetic transition. With
MAGNETICPROPERTIESOF 1NTERMETALLICCOMPOUNDS
301
magnetic rare earths the high magnetization state was reached owing to the molecular field contribution of the rare earth. Moreover, the first-order transition observed at the Curie temperature in some of these compounds, namely DyCo2, HoCo2 and ErCo2, has been ascribed to the collapse of the Co magnetic moment at this temperature (Lemaire 1966, Petrich and M5ssbauer 1968, Givord and Shah 1972). In 1977, polarized neutron diffraction studies on TmCo2 and HoCo2 carried out by Gignoux et al. (1977) showed that HM should be smaller than 100T (around 70T with Tin). From a theoretical point of view, the first calculations (Bloch et al. 1975) led to a much larger value of Hr~ (142 T). Later, more realistic band structure calculations led to H ~ values around 80 T (Cyrot et al. 1979, Yamada et al. 1985, 1987, Yamada and Shimizu 1985, 1990). In order to directly observe the metamagnetic transition in this system, a large effort was undertaken to depress the critical field by substitution effects, and in 1987 this was obtained by substituting a small amount of A1 for Co in YCo2 and LuCo2 (Sakakibara et al. 1987) where the transition occurs below 40 T (fig. 5). In the Y(Col-xFex)2 system, although less dramatic, the CEM has been observed for 0.04 ~<x
="
-5
_ ~ '
/1""~
/
S (a.u.)
-10
,m
-20 -40
g ._= ,4 0 for holes (n > 5). The anisotropy constant is KI = Eso, ± - Eso, [I = ,~(L± - Lrl) S = -~. z ~ . S, if one assumes that the spin is independent of the direction. Then KI is proportional to AL with the same sign for n > 5 and with opposite sign for n < 5. The large anisotropy in many R-3d intermetallic compounds arises from the large orbital moment and hence its large anisotropy. In principle the Coulomb repulsion U between electrons depends on the orbitals occupied by the two electrons, and this could be important for the calculation of orbital effects. However it has been established that this has little effect on the anisotropy energy. In conclusion, the large magnetocrystalline anisotropies in rare-earth-3d intermetallics arise from the orbitally selective 3d band energy dispersion due to the particular character of the 3d atoms surrounding, associated with the presence of the rare earth, this effect being much larger than the usual crystal field effects. 2.3. Instability and frustration of Mn magnetism in RMn2 compounds It is well known that exchange interactions in metallic Mn-based systems are negative. Moreover, when two nearest neighbours of an atom can be nearest neighbours to each other (e.g. triangular lattices or atoms on the tops of a regular tetrahedron) one is faced with frustrated magnetic systems. Such a topological frustration occurs in the RMnl2, R6Mn23 and RMnz series. Among them, the RMnz compounds are especially fascinating because the Mn moment is close to the instability of band magnetism. So, magnetism is complex and presents exotic features which have attracted much attention during the last ten years and have been investigated by using macroscopic techniques (such as magnetization and thermal expansion measurements) as well as microscopic techniques (e.g. neutron and X-ray diffraction, nuclear magnetic resonance (NMR) and Mrssbauer measurements).
2.3.1. Topologicalfrustration For light lanthanides or for heavy ones, that is for large or small R atoms (R = Pr, Nd or Er, Tm, Lu), the RMn2 compounds crystallize in the hexagonal C14 Laves phase. ThMn2 and ScMn: also crystallize in this C14 phase. For intermediate R atoms (R= Gd, Y, Tb, Dy) the RMn2 compounds crystallize in the cubic (f.c.c.) C15 Laves phase. A dimorphism is observed for R = Sm or Ho. As shown in fig. 20, in both structures Mn atoms are at the tops of regular tetrahedra. These tetrahedra are stacked in chains along the six-fold axis in the hexagonal phase and they are packed in the diamond arrangement, connected by sharing vertices, in the cubic structure. In both structures, the topology of the packing ensures that any antiferromagnetic ordering will be highly frustrated.
MAGNETIC PROPERTIES OF INTERMETALLIC COMPOUNDS
,
C15
7
I .
....
o-- .-o 0
0
317
.
.
.
q
' - ~ C
14
Fig. 20. Crystallographic structures of f.c.c. CI5 and hexagonal C14 Laves phases. Left, projection in (001) plane; right, stacking of Mn tetrahedrons.
2.3.2. Mn moment instability and complex magnetic structures A characteristic signature of the magnetic instability of manganese in the RMn2 intermetallics is well illustrated by the large magnetovolume anomalies observed (fig. 21) for some R atoms. In fact, as shown (Wada et al. 1987a and references therein, Shimizu 1985) through thermal expansion and NMR measurements (fig. 22), such anomalies occur depending upon the Mn-Mn interatomie distances. A critical distance (de = 2.66 A) for the onset of a Mn moment appears to exist, which allows us to divide the compounds into three different subsets of magnetic behaviours. When the Mn-Mn distance is significantly lower than de, as in ScMnz, ErMn2 and HoMn2, Mn is nonmagnetic. ScMn2 is a Pauli paramagnet and its thermal expansion coefficient (TEC) is small. ErMn2 and HoMn2 exhibit ferromagnetic ordering characteristic of the rare-earth moment only (Feleher et al. 1965). The paramagnetic TEC is large but no volume discontinuity appears at TN. (The situation of HoMn2 is not quite clear and NMR seems to indicate that, depending on the preparation, some Mn sites could be magnetic.) When the Mn-Mn distance is larger than de, as in PrMn2, NdMn2, SmMn2 and GdMn2, the Mn magnetism is well stabilized with large values of the Mn moment (about 2.7/~B). Magnetic Mn ordering is accompanied by a large volume discontinuity and a paramagnetic TEC is as large as in the compounds with Er and Ho. Collinear antiferromagnetic structures with moments parallel to [120] have been determined by neutron diffraction in PrMn2 (TN = I15K) and NdMn2 (TN = 104K). However, in the latter, below 50 K, some Mn moments and all Nd moments progressively rotate toward the [100] axis due to the magnetocrystalline anisotropy ofNd (Ballou et al. 1988a, Ouladdiaf 1986). The magnetic structure of GdMn2 bears some similarities [same propagation vector
318
D. GIGNOUX and D. SCHMITT
J
YMn2
I
•
L :17:--_-:;
PrM n 2
.
c
1,
....
J
0
]
100
J
I
~
200 TEMPERATURE (N)
'
2
ditcttometer
I
300
Fig. 21. Thermal expansion curves of RMn2 obtained by X-ray diffraction measurements (circles) and dilatornetric measurements (dashed lines). Open and solid circles show the processes with decreasing and increasing temperature, respectively. Solid lines are guides for the eye (Wada et al. 1987a). 2 3, 2 0)] with the virgin magnetic structure of TbMn2 (Ouladdiaf 1986). The magnetic (3, structure of SmMn2 is still unknown. The most dramatic properties are observed in the other compounds, where Mn is close to the magnetic instability and where magnetism is very sensitive to external parameters such as temperature, pressure, magnetic field and alloying. When temperature is increased, YMn2 shows a first-order transition (with a large hysteresis) at TN accompanied with a giant volume drop of about 5%, which is ascribed to a substantial reduction of the Mn moment at TN. The TEC above TN is the largest of the series (50× 10-6 K -1 at 300 K). The magnetic structure of YMn2, determined from neutron diffraction, is helimagnetic (fig. 23) with a long period (~380 ]~). On the other hand NMR spectra have shown that the helix is not regular but distorted owing to a large Mn magnetic anisotropy which favours
319
MAGNETIC PROPERTIES OF INTERMETALLIC COMPOUNDS
4
(o)
% zL ~3
Fir
T o
2
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i
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10
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INTERATOMIC DISTANCE, d~r~M#t R.T. (~,) Fig. 22. Variations of Mn moment, volume change at T~ and thermal expansion coefficient (TEC) with interatomic distance, dMn_Mn(Wada et al. 1987a). (a) Mn moment, /~Mn, at 4.2K in RMn2 as a function of dMn_Mn; CO) volume change at T N (AV/V) at T= T~ (solid circles) and the average TEC between 200 K and 300 K (open circles) plotted against dMn-Mnat room temperature. Lal0 and La25 represent Y09oLaoloMnz and Y0.75Lao25Mn2, respectively.
one of the local two-fold axes (110) (Ballou et al. 1987). The substitution of a small amount of Sc for Y shrinks the lattice, leading to nonmagnetic Mn atoms (Nakamura et al. 1988a). In Y0.97Sc0.03Mn2 a complete paramagnetic state at 4.2 K has been observed and the absence of Mn moment has been confirmed by NMR. However, a large TEC, as in YMn2, is observed. For a Sc amount smaller than 2% the coexistence of the magnetic state with a Mn moment mMn ~ 2.7/UB and nonmagnetic state is observed. On the contrary, the substitution of La for Y expands the lattice and enhances the stability of the antiferromagnetism. In particular, in Y0.75La0.25Mn2 the volume discontinuity at TN is about 2% and the TEC at room temperature is 40× 10--6 K -I, smaller values than in pure YMn2 (Nakamura et al. 1988b). In the Yl-xCexMn2 pseudo-binary alloys, the decrease of the cell volume with Ce content and the destruction of the magnetic ground state for x ~> 0.05 are surprising as Ce has a larger ionic volume than Y in both the 3+ and the
320
D. GIGNOUX and D. SCHMITT
2N-I
~
~"/
22N !
2N+2
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~J~+
~' ~ >?:
b I
, / ~-/
')
y /'
>
/
! ,.i ....
!
b
0~. I .....
..............
....,j
Fig. 23. Magnetic structure of YMnz. Only Mn atoms are shown. (a) Collinear antiferromagnetic structure previously reported (Nakamura et al. 1983), open and solid circles represent Mn atoms with up and down spins, respectively. The propagation vector is Q = (0, 0,1); (b) helimagnetic structure deduced from neutron diffraction studies using a long wavelength. In the tetrahedron layers (solid lines) the antiferromagnetic arrangement is collinear as in (a). The propagation vector is Q=(r,0,1) with r=0.02. A and z~' are the two easy directions of Mn moments. Inset: in both models, the Heisenberg exchange interactions do not cancel between pairs of atomic layers 2N - 1,2N, but do cancel between pairs of atomic layers 2N, 2N + I. Magnetic structures are then formed of highly correlated layers of tetrahedra with weak coupling between these layers. (Ballou et al. 1987). 4+ state. This property has b e e n ascribed to a strong hybridization o f the C e - 4 f and M n - 3 d b a n d s ( M o n d a l et al. 1992). In T b M n 2 , the m a g n e t i c field structure in zero applied field is complex, with all m a n g a n e s e atoms i n the m a g n e t i c state. However, a " m i x e d structure" with coexisting m a g n e t i c a n d n o n m a g n e t i c M n atoms (fig. 24) is i n d u c e d b y an applied field o f 4.5 T at 25 K or b y chemical pressure i n d u c e d b y the substitution o f smaller Fe atoms
MAGNETICPROPERTIESOF INTERMETALLICCOMPOUNDS
321
Mn(lb)~ Mn(3d)~ Tb~ Fig. 24. Magnetic structure of Tb0Vlno.96Fe0.04)2below 30 K, or the S2-typestructure of TbMn2 induced by an applied field of 4.5 T at 25 K (Brown et al. 1992). for a small amount (~4%) of Mn atoms as shown by neutron diffraction (Brown et al. 1992) and by M6ssbauer measurements (Oddou et al. 1993). In this magnetic structure, although all the Mn sites are chemically equivalent, only 25% of them bear a magnetic moment. Note that in TbMn2, as well as in YMn2, the variation of the N6el temperature with hydrostatic pressure reaches a huge value, namely - 3 6 K/kbar (Voiron et al. 1990, Oomi et al. 1987). DyMn2 is the first compound in which, in the absence of applied field, a mixed magnetic-nonmagnetic Mn state was evidenced by NMR (Yoshimura and Nakamura 1984, Yoshimura et al. 1986a). The magnetic structure, as determined from neutron diffraction (Ritter et al. 1991), is similar to that of TbMn2 in an applied field when considering the Mn sublattiee only. Because thorium is tetravalent, the M n - M n distance in ThMn2 cannot be compared with dc determined for trivalent R elements; however in this compound, due to the larger filling of the 3d band, Mn is also close to the magnetic instability. ThMn2 orders antiferromagnetically at TN=ll5 K (Buschow 1977b) in a mixed structure, shown in fig. 25, in which magnetic Mn atoms form a triangular structure resulting from the topological frustration of antiferromagnetic interactions (D6portes et al. 1987a). Note that in all these mixed states the nonmagnetic Mn atoms are those which are subjected to a
322
D. GIGNOUXand D. SCHMITT
In 2
Fig. 25. Projection into the basal plane of the ThMn2 magnetic structure. Only Mn atoms of the 6h site are magnetic (Drportes et al. 1987a). total field smaller than the critical value necessary to induce a magnetic state of higher energy. In particular, in ThMn2 the molecular field on nonmagnetic atoms is strictly zero. However the cancellation of Mn moment on some sites is really a nonmagnetic state and not a paramagnetic one which would have resulted from a simple cancellation of the field on localized moments. Indeed, the susceptibility does not increase at decreasing temperatures as expected for local moments in paramagnetic state in an applied field. Consequently the splitting of the local band is cancelled. 2.3.3. Large Mn anisotropy Although it cannot be measured directly because of the complex frustrated structures, a large local magnetocrystalline anisotropy of Mn moments has been shown in the RMn2 compounds. It manifests itself clearly in YMn2 and NdMn2. In the former, a quantitative analysis of the tilt of the moments with respect to a perfect helix, inferred from NMR and neutron diffraction experiments (Ballou et al. 1987), leads to a local anisotropy of the same order of magnitude as generally observed in uniaxial 3d intermetallics, in particular those containing cobalt (see sect. 2.2). In NdMn2 this anisotropy, of the same order of magnitude as that of Nd in the plane perpendicular to c, is responsible for the noncollinear magnetic structure observed at low temperature (Ballou et al. 1988a).
MAGNETIC PROPERTIES OF INTERMETALLIC COMPOUNDS
323
2.3.4. Giant spin fluctuations Most physical properties of the RMn2 series bear witness to the importance of spin fluctuations in these frustrated systems, which are dramatically enhanced in the compounds close to the Mn magnetic instability, in particular in YMn2. As cited above, the large volume change at TN and the large TEC above this temperature in this compound is ascribed to a substantial reduction of the Mn local moment mMn and then to its rapid recovery with temperature in the paramagnetic state. Indeed, a phenomenological theory of magnetovolume effects (Shiga 1981) has shown that the magnetic contribution to the TEC is proportional to the square amplitude of the local spin fluctuations or, in other words, the square of the local moment. The lattice contribution to the TEC has been taken as that of the Y(Mnl-xAlx)2 compounds for x > 0.1; there it has been established from different measurements (lattice parameter as a function of the AI content, NMR experiments, Yoshimura et al. 1986b) that mMn is stable and takes the maximum local value of about 3/~B which is temperature independent. From this weak contribution to the TEC, it has been possible to deduce the thermal variations of local spin fluctuations, i.e. (m2n), in the different RMn2 compounds. They are schematically shown in fig. 26. Curve (e) is the local moment limit (Y(Mnl_xAlx)2 compounds with x > 0.1, Shiga et al. 1987, Motoya et al. 1988) whereas, at the opposite, curve (a) is the Pauli paramagnetic type limit (ScMn2). In YMn2 the Mn moment, which reaches 2.7#B at low temperature, is reduced to about 1/tB just above TN and recovers to 2#B at room temperature. This result has been confirmed from neutron diffraction experiments below TN and from paramagnetic scattering measurements using polarized neutrons (D@ortes et al. 1987b, Freltoft et al. 1988). The results revealed that the amplitude of the local magnetic moment of Mn atoms drops by more than 30% at TN and then slowly increases with increasing temperature. Moreover, up to 6TN, the paramagnetie scattering was strongly enhanced about the staggered antiferromagnetic wavevector. The thermal variation of the magnetic susceptibility of YMn2 is also quite unusual (fig. 27) and its increase with temperature above TN is further evidence for the increase of the local spin-fluctuation amplitude with temperature. In the nonmagnetic Y0.97Sc0.03Mn2 compound, the TEC as large as in pure (e__])
( PrMn~ Ndt,,tn ,j--F~--~, ts~Mr~2 ' ~u t |GdMn 2 ~ ~c
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~(c)
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D
-I V
~
Mn2
}HoMn)
Er~4n-
)
(O)
T EMPERATURE
i~ xSC2xi,An
ScMn 2
"ID
Fig. 26. Schematic representation of the temperature variation of ( ~ 2 n ) of RMn2. Curve (a) shows the Pauli paramagnetic type and (e) the local moment limit. The type of spin fluctuations changes from (b) to (d) in RMn 2 with increasing dMn_Mn(Wada et al. 1987a).
324
D. GIGNOUXand D. SCHMITT
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,
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100
i
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200
i
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~
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,
I
i
300 t~00 500 T(K} Fig. 27. Temperaturedependenceof the susceptibilityof Y(MnI_~Alx)2 for 0 ~<x ~. 0 uJ Z IJJ
; °
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'
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I 1.89 2.59
'
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.... L . _ + 0
1'o MAGNETIC
1'8 FIELD ( T )
2'0
Fig. 43. Magnetic field dependence of the CEF energies obtained for PrNis~Cu point contacts for fields along the [100], [120] and [001] axes (different symbols are used for different contacts) after Reiffers et al. (1989). The solid curves are the calculated variations with the refined parameters. The sequence of the lowest CEF levels at zero field is F3 (ground state), F 1 (38.3 K), F~I~(4I .6 K) and F6 (42.2 K). The numbers are proportional to the calculated transition probabilities from the ground state at 10 T and 20 T and are given in the same order as the calculated energy levels. The dashed curves show the calculated energy of the first excited F t level with the CEF parameters given by Barthem et al. (1988). (Zero energy corresponds to the ground state).
field were observed. In particular it has been possible to follow the field dependence o f the first excited F] CEF level whereas the transition from the ground state to this level cannot be observed directly in zero field. This experiment confirmed that the sets o f parameters previously determined were reasonably correct (Andres et al. 1979, Alekseev et al. 1980, Barthem et al. 1988) and at the same time allowed them to be refined. The knowledge o f CEF parameters allowed one to predict a highly original high-field magnetization behaviour arising from the existence o f the nonmagnetic singlet ground state, namely transitions associated with the field-induced "crossing" and "anticrossing" o f the two lowest states along the [100] and [120] directions, respectively. In quantitative agreement with prediction, metamagnetic transitions have been observed at low temperature (T ~< 5 K ) from magnetization measurements in fields up to 38T; associated with "crossing" these become steeper and steeper as temperature decreases,
342
D. GIGNOUX and D. SCHMITT
~: 15
©
5
0
0
20
40
60
80 T(K)
O0
Fig. 44. Specific heat of ErNis: black dots are the experimentalpoints(Radwanskiet al. 1992b),the solid line is the calculationwithparametersgivenby Zhang et al. (1994).
whereas those associated with "anticrossing" are nearly temperature independent (Ball et al. 1992a) (see sect. 3.2.2). In TbNis, in addition to the above quoted experiments, the spin waves and single-ion type magnetic excitations have been studied by inelastic neutron scattering at 4 K on a single crystal along the (q, 0, 0) and (0, 0, q) propagation directions (Gignoux and Rhyne 1986). One dispersive accoustic mode and two nondispersive modes were observed, from which J(q) along these two directions has been deduced; this resulted in improvement of the CEF parameters proposed earlier (Gignoux et al. 1979, Goremychkin et al. 1984). As quoted above, in ErNi5 the latest set of parameters (Zhang et al. 1994) gives particularly good fits for all the experiments, in particular the low-temperature high-field magnetization measurements along the hard axes of the basal plane (see sect. 3.2.4) and the specific heat characterized by a large Schottky anomaly around 35 K (Radwanski et al. 1992b; fig. 44). The microscopic aspects of the magnetization processes along the [120] and [100] axes, calculated with the refined set of parameters, exhibit quite interesting features as shown in fig. 45: (i) There is a large decrease of the value of the Er moment during the rotation process from the easy c axis toward the applied field direction, the minimum value corresponding to the field at which moments become parallel to [120] and [100] (i.e. 19 T and 22 T), respectively. (ii) Above 22 T, the reduction of the magnetization measured in the basal plane (compared to that measured along [001]), arises from a huge anisotropy of the magnetization and not from the fact that moments would not be parallel to the applied field. As with the reduction of the Er moment during the rotation, this is a consequence of the fact that the moments in the basal plane are induced by the applied field. As for ErNi5, the calculation with the refined parameters allows us to understand the magnetization processes. For instance, in NdNi5 (fig. 46), the anisotropy energy between the a ([100]) and b ([120]) axes (hatched area in the figure) is weak: a field of 11 kOe applied along b is large enough to align the moments in this direction. It is worth noting that in higher fields the magnetization difference between both axes arises from a large anisotropy of the magnetization which strongly increases with the field up to 130kOe and reaches 12% in 150kOe. When the field is applied along the hard
MAGNETIC PROPERTIES OF INTERMETALLIC COMPOUNDS
343
10 Q ~
~ 0
Q 0
Q I
Q Q ~ ~
Z LU
,o
H//[120] . . . . . .
~3
ErNi
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v 4-a C-
o~o~O~
5
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./.
o
-_
7 /
E
/".
f
° ~" ~
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/"
o
/ / / / /
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100
~
~
I
I
1
J
I
;
I
I
[
I
i
I
I
I
I
I
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(19 (1) Ob
80
(1)
q~
H//[120]
60
v
H//[100] o o
40
o o .o ~o
20
® ®® 0
0
10
20
30
H(Tesla)
40
Fig. 45. ErNis: calculated field dependences of the moment amplitude (upper part) and of the angle between moments and the [001] axis (lower part) when the field is applied along the [120] and [100] axes of the hard plane. Dashed lines in the upper part represent the calculation of the moment amplitude when moments are forced to be either along [120] or [100] (after Zhang et al. 1994).
c axis, the observed variation of the magnetization corresponds to a slow rotation o f the Nd moments associated with a gradual decrease o f their amplitude. Besides, in zero field the Nd moments are perpendicular to c and reach 2.01/ZB, in an internal field o f 150 kOe the moment amplitude is only 1.40/~B and moments still make an angle of 29 ° with the field (Barthem et al. 1989a). From these quantitative studies in this hexagonal series and earlier studies in cubic ferromagnetic compounds it has been possible to compare the exchange parameters along the series. As for the previously reported analysis of the R - M exchange coupling, Belorizky et al. (1988) analyzed the R - R coupling in different series. The variation OfnRM in all the studied series had been ascribed to a variation of the 4f-5d exchange interaction arising from the increasing distance between the 4fand 5d shells going from light to heavy R elements. As the same 4f-5d exchange interactions are involved in any metallic system containing magnetic R elements, it was natural to study the R - R interactions in systems where they are not masked by dominant R - M interactions, i.e. in the absence o f magnetic M atoms. The RA12, RZn and RNi5 series are quite suitable for such a study. As shown
344
D. GIGNOUX and D. SCHMITT
% z 113 z
._..,_____..-----J
~
rn :3.
-~
lib
NdNi 5 1.5K
MNd = 1.&.0 PB
HIIc
~°=29" "
Nd
L ~ M N d =2.01PI~
0
50
160
Hi(kOe )
150
Fig. 46. Internal field (applied field corrected for the demagnetizing field) dependences of the magnetization at 1.5 K in NdNi 5. Black dots are the experimental values. Solid lines are the calculated variations (Barthem et al, 1989a).
5 000
4 000 I
~ " 3 ooo
~l ~
m~ 20OO
\\\\ k\
~x \\ \ \ ".
U 1000 \
\ ~,~
0 Lo.Ce
K
I
I
Pr Nd,
I
I
Sm
~O I
I
I
I
I
I
I
Gal.Tb Dy Ho Er Tm
I
t
Lu
Fig. 47. Molecular field coefficients nSR in the RA12 (open circles), RZn (solid circles) and RNi 5 (open triangles) series (Belorizky et al. 1988).
MAGNETICPROPERTIESOF INTERMETALLICCOMPOUNDS
345
in fig. 47 there is a large increase of the R-R interactions across a given series from heavy to light R atoms. This increase is still larger than for the R-M interactions (see figs. 31 and 32). In particular it has been observed that the increase of nSg is similar to that of (nSM)2. Knowing that the ne,g coupling involves three stages, namely the 5d-4f, 5d-5d and again the 5d-4f interactions, the observed variation has the same origin as that of nSM and confirms that, according to Campbell (1972), the exchange interaction involving R atoms are essentially mediated by the 4f-5d exchange. The same conclusions have been derived from the analysis of the transferred hyperfine field at the nonmagnetic site like A1 and Zn in the RAI2 and RZn series (Belorizky et al. 1988 and references therein).
3.2. Metamagnetism and associated phase diagrams The concept of metamagnetism has spread considerably over the last decades, since Kramers introduced the term for the original property of a first-order phase transition between a simple antiferromagnetic structure with a low magnetization and the induced ferromagnetic state with a high magnetization, this transition being induced by the application of a magnetic field (see ref. 1 in Stryjewski and Giordano 1977). First limited to such single-step phase transitions, this concept has been progressively extended to a lot of processes breaking antiferromagnetic structures, and more generally to all types of field-induced magnetic phase transitions (Date 1990, Gignoux and Schmitt 1991). The aim of this section is to present an extensive review of the different types of metamagnetic processes occurring in the rare-earth intermetallic compounds in which only the rare earth is magnetic (the metamagnetism associated with 3d magnetism is not considered here). For each process, a number of examples as large as possible will be provided for illustrating the particular physics involved or the particular balance between the different couplings giving rise to the metamagnetic behaviour. After some general considerations, each type of metamagnetic process will be widely developed by order of increasing complexity.
3.2.1. General considerations First we have to specify exactly what the term metamagnetism will signify in the following. We will consider as metamagnetie behaviour any anomaly occurring during the magnetization process of a given compound, compared to the "normal" behaviour of a magnetization curve exhibiting a downward curvature (usual paramagnetic or ferromagnetic system). Such an anomaly is characterized by an upward curvature present in a limited field range. Two main classes of metamagnetic transitions can then be distinguished (see fig. 48): (i) a step-like behaviour where the magnetization jumps more or less suddenly between two well defined plateaus: class (1); (ii) an S-shaped behaviour where the magnetization increases smoother than in class-(1) systems, showing only an inflexion point at a given critical field He: class (2). It can be noticed that class-(1) transitions are often, but not always, associated with a first-order transition, which is never the case for class-(2) transitions; moreover, class-(1) transitions are generally sharper as the temperature is lowered, and they often evolve at high temperature towards class-(2)
346
D. GIGNOUX and D. SCHMITT M
M
(a)
(b)
class (1)
Hext
2)
Hext
Fig. 48. Schematic representation of: (a) a discontinuous (class (1)), and Co) a continuous (class (2)) metamagnetic transition.
behaviour. More subtle particularities may occur in both classes: for class-(1) materials, the transition can be discontinuous or can present a portion with a finite slope as a function of the external (applied) magnetic field, and this will be related to demagnetizing field effects in the presence of hysteresis (see below); for class-(2) compounds, the magnetization curve may exhibit an angular point at the critical field, i.e. a discontinuity of the slope dM/dH at the transition, or keep a smooth variation in the whole field range. Note that this smooth behaviour may be intrinsic or due to faults or inhomogeneities in the sample. It is worth noticing that some compounds may present both types of metamagnetic transitions, on the same magnetization curve or at different temperatures. The value of the transition field Hc generally depends on temperature, T, and sometimes on the direction of variation of the field (increasing or decreasing field). Moreover, some transitions may exist for one single direction of variation. By reporting the corresponding H - T values, more or less complex phase diagrams can be constructed, showing one or several distinct regions, each one associated with a particular spin structure, and separated by boundary lines which are generally first- or second-order transition lines (see fig. 49). In addition, these phase diagrams may exhibit several critical points on the transition lines, such as tricritical points (junction between first- and secondorder transition lines), triple points (junction between three first-order transition lines) and critical or bicritical endpoints (end of a second- or first-order transition line) (Stryjewski and Giordano 1977). Numerous examples will be shown throughout this section. The general topology of a phase diagram together with its associated details will reflect the underlying microscopic properties at the origin of the metamagnetic behaviour. The two main ingredients playing an essential role in these phenomena are the anisotropy and the interionic interactions. The former property, i.e. the crystalline electric field (CEF) coupling, plays a fundamental role by constraining the magnetic moments to lie along a given direction (axial anisotropy), or within a given plane (planar anisotropy), or anywhere in space (weak anisotropy). A particular situation of axial anisotropy will occur when there are several equivalent noncollinear easy magnetization directions, as for example the two-fold axes in hexagonal or tetragonal symmetry, or the three-fold axes in cubic symmetry. The one-ion magnetoelastic coupling must be included in this first category, being considered as the strain derivative of the CEF itself. The second
MAGNETIC PROPERTIES OF INTERMETALLIC COMPOUNDS
H
347
first order line " ~ , , , ~ tricrifical point X \
triple point
\
bicritical • endpoint
', I
second orderqine I
T
Fig. 49. Schematic view of a H - T magnetic phase diagram with some critical points.
fundamental ingredient includes all types of interionic interactions, namely the isotropic or anisotropic bilinear exchange coupling and the two-ion quadrupolar coupling, as well as their possible strain dependence, i.e. the interionic magnetoelastic couplings. These two basic microscopic properties appear to be the essential characteristics of a metamagnet. Their relative importance as well as the sign of the different parameters involved will lead the considered compound to belong to one of the families described below, keeping in mind that, sometimes, there is no obvious frontier between two different behaviours, and that an observed transition can result from the combined action of several phenomena. 3.2.1.1. Demagnetizing field effects and hysteresis. Special attention must be paid to the distinction between internal and external (applied) magnetic field, in particular as far as a first-order transition is concerned. For an ellipsoidal sample, it is well known that the magnetization is uniform as a function of the applied field Hext, but actually the magnetic ions experience an effective internal field, Hi, instead of Hext: Hi = Hext - Hd = Hext - NdM,
(22)
w h e r e N d is the demagnetizing field factor depending on the shape of the sample and on the direction of application of the field. The presence of this demagnetizing field Hd has an important consequence in the case of a first-order transition (Stryjewski and Giordano 1977). Let us consider such a first-order magnetic transition for the critical internal field H~ and without any hysteresis (see fig. 50a). Actually this field is defined by the crossing of the Gibbs free energy variation for both magnetic states under consideration. The magnetization M then should jump discontinuously from MB to Mc when the internal field reaches the critical value H~ (vertical line BC in fig. 50a). In external field, the transition starts for the critical value HCxt = H c + NdMm However, the transition cannot proceed all at once, because an increase of M would lead to a decrease of Hi below the value required to induce the transition. The transition therefore must take
348
D. GIGNOUX and D. SCHMITT
M
M (a)
~B
D
A-
A' C
Hi
M
(c)
E
(e)
J.,
Hexl
M
D
B
F
H~
D'
C;
Hi
C
A
M
(b)
H~
DF
(d)
A~
E'
D'
C'
F'
B~
Hi
Hext
M
E
!,'S
(f)
D' E
'
A'
A
Hext
M (g)
G A
D
C
E
M
(h)
E !
C I_ _
D'
G,I/t
B
A'
F Hi
F' Hext
Fig. 50. Schematic representation of a first-order metamagnetic transition in internal (a, c, e, g) or external (b, d, f, h) field, and without hysteresis (a, b), with a large hysteresis (c, d, g, h) or with a small hysteresis (e, f); the distinction between (c, d) and (g, h) arises from the way the domain structure is modified during the transition (see text).
MAGNETIC PROPERTIESOF INTERMETALLICCOMPOUNDS
349
place gradually, any change 6M occurring only for the corresponding change 6He×t which keeps Hi constant, i.e.: 5M
1
6Hext
Nd"
(23)
The result is an inclined portion in the magnetization process as a function of the applied field (line WC t in fig. 50b), the slope corresponding to the reciprocal demagnetizing field factor 1/Nd. During this portion, the sample breaks into domains of the two phases coexisting at the first-order transition, a behaviour similar to the initial magnetization process of a ferromagnet below its Curie temperature. This mixed-phase region is then associated with all first-order transitions between states of different magnetization but without any hysteresis. Let us consider now the case of a first-order magnetic transition with hysteresis. The crossing of the free energy of both states still defines the theoretical critical field H~. However, the magnetization does not jump for this critical field, but exhibits a hysteresis cycle between the two limits H u and H d (see fig. 50c). These fields correspond to the points where the change of magnetic configuration is initiated in increasing and decreasing field, respectively. This phenomenon arises when an energy barrier between both states prevents the system to carry out the transition at H~. The hysteresis width may range from small to relatively large values, as we will see in the following, depending on the origin of this barrier and on the temperature. The critical point H~ corresponds to the instability of the low-field state which may occur either within the whole sample or in some nucleation centers. In the former situation, and if the hysteresis is wide enough, the full system suddenly jumps from B to C on the cycle, experiencing a corresponding reduction of the internal field equal to N a ( M c - M B ) . This is possible because point C corresponds to a state allowed for the system, i.e. a stable state. This results in a vertical portion WC p in the magnetization process in external field (fig. 50d). The inverse process occurs in decreasing field (lines EF and E~Ft). As a consequence, the hysteresis width AHC×t in external field is reduced compared to the theoretical value Zk/-/ic = (H ui - H di ) in internal field: AH~xt = AH~ - Nd(Mc - MB).
(24)
In the case of a narrow hysteresis, namely AH~ smaller than N d ( M c - M s ) , the situation should be more complex, exhibiting both behaviours described above, and should lead to an unusual hysteresis cycle in external field, where the increasing critical field HeUt is lower than the decreasing one Hdxt (fig. 50e, f). Moreover, from the above considerations, it follows that a transition which follows the demagnetizing field factor in external field should always be associated with a first-order transition without hysteresis, while the existence of hysteresis should always produce a transition with vertical portions, at least in part. However this behaviour does not seem to be always the case in experiments, where transitions following the demagnetizing field factor in external field are often
350
D. GIGNOUXand D. SCHMITT
associated with a strong hysteresis. This means that, generally, the sample does not transit at once, i.e. the domains where the high-field state is nucleated do not extend suddenly to the whole crystal: the transition occurs progressively as in the first case described above, within a finite external field range where the sample is in a mixed-phase state (fig. 50g, h). The nucleation centers around which the transition is initiated may be any fault, inhomogeneous region or antiferromagnetic domain wall. In this latter case, the situation is necessarily different by increasing or decreasing field since the magnetic structure itself can be very different on both sides of the transition. This difference can play an important role in the occurrence and width of the hysteresis. Finally, the effective critical field H u for example may be smaller than the theoretical value corresponding to the instability of the low-field state, because of the presence of these nucleation centers, following the same process as in ferromagnets with a hysteresis, where the coercive field is generally far below the anisotropy field. 3.2.2. C E F metamagnetic systems The simplest systems where metamagnetism can occur are pure CEF ones, i.e. those where the CEF is the only interaction acting on the 4f shell. Indeed this single coupling is sufficient to induce field transitions under certain conditions of anisotropy and field direction. This effect was first predicted by Cooper (1966) for TmSb. This cubic compound exhibits a ['1 singlet as ground state, with a M j =4 main component. When an external field is applied along the hard magnetization direction [001], a crossing of F1 and of one of the levels issued from the F4 excited state (having a Mj = 5 component) is anticipated at about 40 T, giving rise to a step in the predicted magnetization becoming more and more pronounced as the temperature is lowered down to 0 K. A second crossing between F4 and one of the F~2) levels is predicted in still higher fields, resulting in a second step toward the saturated magnetization (Mj = 6). Due to the low availability of high magnetic fields at that time, this effect has not been observed experimentally1. Such a crossing of CEF levels has been observed several years later in Pr metal at a field of 31.5 T applied along the [001] hard direction of this double-hexagonal close-packed material (MeEwen et al. 1973). In this system, the ground state at both the cubic and hexagonal sites is a singlet, and the exchange interaction is undercritical so that there is no magnetic ordering down to very low temperatures. At 4.2 K and for a field of 31.5 T, the magnetization process along the hard direction exhibits a well-defined step (see fig. 51), which has been ascribed to a first-order transition on the hexagonal sites. The size of the magnetization jump is 2.08/~B per hexagonal site, and there is a noticeable hysteresis of about 0.2 T at 4.2 K, the transition being sharper and the hysteresis larger at lower temperature. This transition has been explained by the field-induced crossing of the F1 singlet ground state (Mj = 0) with the F3 excited level (Mj = 3 component) lying at about 50K above F1, in zero field. This has been confirmed later (Franse et al. 1990). 1 Note added in proof A field-inducedmetamagnetictransition associatedto a CEF level crossing has been observed very recentlyin TmSb along the [001] direction,for a field of about 48T, in reasonableagreement with the theoreticalpredictions(Nimoriet al. 1995).
MAGNETICPROPERTIESOF INTERMETALLICCOMPOUNDS
351
P£
o II10] . [001] o
0
2
o
o
o
o
o
0
c) ,-n ::::t.
0
/
F-..
g
Z LJ
o
•
C3 5-
•
eeo O~ooe
0
"
• s
• °
o 5
10
1
I
2O 30 z.0 INTERNAL FIELD (TESLA
Fig. 51. High-field magnetization data for paramagnetic Pr metal at 4.2K along two different directions; note the hysteresisof the first order transition at 31.5T (after McEwen et al. 1973).
A still more interesting example is provided by the hexagonal compound PrNi5 in which two different types of CEF metamagnetic transition occur, namely a crossing of CEF levels along the [100] direction and an anticrossing along the [120] direction (Ball et al. 1992a). Indeed, in this paramagnet the ground state is the F3 singlet followed by another singlet F1 around 30 K and two doublets F~1) and F6 at about 50 K. When the magnetic field is applied in the basal plane, the energy of the first excited level decreases much faster than that of the ground state so that these two levels should cross for a given field. However, according to group theoretical considerations, the ground level I"3 transforms into a F2 or 1"5 level under the application of a field along the [100] or [120] directions, respectively, while the first excited level keeps the Fl symmetry. It follows that the two levels actually cross each other in the first case, because they belong to different representations, while in the second case an anticrossing occurs because they both belong to the same representation (see fig. 52). This leads to a metamagnetic transition which becomes sharper and sharper in the first case when the temperature is lowered, finally reaching a stepwise behaviour at 0 K, while in the second case the transition remains smooth even at 0 K. Both transitions have been experimentally observed, for magnetic fields of 18.5 T and 12 T, respectively (fig. 53). It turns out that such behaviours (crossing or anticrossing) give useful information about the CEF level scheme because the value of the critical field of the metamagnetic transitions is directly related to the zero-field energy position of the excited level which crosses or anticrosses the ground state. This is particularly true in PrNis, where the composition of the 1`1 excited level forbids one to observe directly a transition from the ground state by neutron spectroscopy in zero field. However, this transition becomes possible for nonzero magnetic field and has been actually observed by point-contact spectroscopy (see sect. 3.1, fig. 43) (Reiffers et al. 1989). This allowed one to slightly adjust the CEF parameters determined previously (Ball et al. 1992a). In a general way, both types of CEF metamagnetic transitions occur when a nonor weakly magnetic ground state evolves into a stronger magnetic ground state as a function of the magnetic field, the continuous or discontinuous character of the transition depending on the symmetry of the levels, i.e. of the detailed composition in
352
D. GIGNOUXand D. SCHMITT 4
I
I
I
I
3 _
I
!
PrNi
PrNi s [1001
0
.
~
,
54.2K ......~~ i - 2 " 0
i ....
,
E
"
/~.~._¢~ 1.4K 4.2K / ~ . ~ . . . .
-
.f
"
-
1.4K and 0.3K
/
-
~
.__~~F
-100
(c)
1
[120]
]
e~ -120 -140 -160 -180
,
0
I
i
I
m
I
10 20 30 Applied Field (Tesla)
i
10 20 30 Applied Field (Tesla)
40
Fig. 52. Calculated field variations of the magnetizationand the energy of the first two CEF levels in PrNi5 along both symmetrydirections of the basal plane and at various temperatures; note the different behaviourof the metamagnetictransitions associatedwith the crossing or anticrossingof the levels(after Ball et al. 1992a). Mj components. According to the sequence of the CEF levels and to the direction of the applied field, one or several successive stepwise transitions can be expected, associated with several successive levels crossings or anticrossings (Mrachkov and Leyarovski 1988). In fact, the metamagnetic behaviour should be present as soon as the CEF ground state eigenfunction does n o t include the Mj = J component as its major part, for the considered field direction. There always exists a direction fulfilling this condition, even possibly along the easy magnetization direction, although the corresponding critical fields often are much too high to be reached experimentally. In addition, as seen above, the sharpness of the metamagnetic behaviour increases when the temperature decreases, so that a low temperature is often needed to observe them. That explains why both examples where these transitions were observed (see above) are paramagnets, having a nonmagnetic singlet as ground state, because this particular CEF configuration more easily allows the exchange interaction to be undercritical with regard to the occurrence of magnetic ordering. A measurement at low temperature can then be made without being disturbed by the latter. However, one can imagine that the increasing availability of both high magnetic fields and low temperatures in the future will allow one to use these properties to get information about the CEF level scheme under magnetic field,
MAGNETIC PROPERTIES OF INTERMETALLIC COMPOUNDS i
i
353
i
PrNi 1.4K 5
t120]/'~i /
................
.'°
[100]
J f
*°°°
/j/°
1
Go
,
I
,
I
,
I
q
PrNi 4.2K 5
3 °
[120]
O
O
o
o°
# o o
°
[lOO]
o o
o o• 8 °
[001]
s o eoeo*
0
I
0
I
I
10
I 20
,
I 30
Applied Field (Tesla)
40
Fig. 53. High-field magnetization curves in PrNi 5 along the two main symmetry directions of the basal plane at 1.5 K and 4.2 K (after Ball etal. 1992a).
similarly as neutron spectroscopy does in zero field. Moreover, and as already mentioned by Cooper (1966), the field-induced transition is generally associated with an anomaly of the temperature dependence of the magnetic moment, namely the presence of a maximum which is particularly strong for a magnetic field just below the critical field: this effect is obvious when the successive isothermal curves in fig. 52 are considered. It can be noticed that this maximum is not always present on the susceptibility curve itself, i.e. in the zero-field limit, in particular in the case of a level crossing. However, when the susceptibility variation exhibits such a maximum, it is generally associated with a change of sign of the third-order magnetic susceptibility (Morin et al. 1988): below the temperature where this maximum occurs, the third-order susceptibility becomes positive, i.e. the initial magnetization process exhibits a positive curvature which is the signature of a metamagnetic transition in higher field. Another interesting effect related to a CEF level crossing may appear in the presence of nonzero magnetic interactions and has been studied by Tsuneto and Murao (1971) in the case of a S = 1 system. R has been shown that, in the vicinity of the crossing point, small ferromagnetic exchange interactions may be at the origin of a field-induced second-order magnetic ordering. This can be explained as follows: within the mean-field picture, the usual magnetic ordering occurs when the initial susceptibility increases, by
354
D. GIGNOUX and D. SCHMITT
M
(a)
M
/
(b)
T'T: ~+.+ ; ~¢.-o---+,--+~--e.--
+
+ ¢,,--,,e-0-¢-
(b) T:'12 K' o__..-0
5
.
v ~r
,
i
i
i
(el) T=29 K'
c)'T=l~ K '
3
i
I
0
~
20
L
4.0
T(K)T~"~
i
i
r
i
0 20 H~ ( kOo )
/+0
i
60
Fig. 90. Magnetization process at various temperatures and along the main symmetry axes in tetragonal NdRuzSi2 (after Shigeoka et al. 1990).
P ____..o-----~
F
10
NdRu2Ge2 I
I
I
8
I
lo
-
H(kOe)
Fig. 91. Magnetic phase diagram of NdRu2Ge2 obtained on a polycrystal; AF refers to the modulated phase, P and F to the para- and ferromagnetic phases, respectively. Note that the borderline between P and F has no physical meaning, both phases being ferromagnetic (induced or spontaneous) (after Ivanov et al. 1992b).
o f compounds having this tetragonal crystallographic structure and a c easy magnetization direction, numerous new results can be expected in the future. The other very simple crystallographic structure having a strong uniaxial character is the hexagonal structure. However, few complex antiferromagnefic systems with this symmetry and a c easy axis have been thoroughly investigated. One recent example is provided by the simple A1B2-type compound HoA1Ga, which has been extensively studied by magnetization and neutron diffraction measurements on a single crystal. As quoted above (see sect. 3.2.7), this compound exhibits two different magnetic phases in zero field (Gignoux et al. 1991b): (i) an antiphase one below Tt = 18.5K, characterized by i 2) 1 and its third harmonics 3Ql =(0,0, ½); (ii) an amplitude the basic vector Q 1 - ( 3 I, 3,
386
D. GIGNOUX and D. SCHMITT
9
I
I
]
A
o "r :::L 6
oo
-
~tPI -~
~
I
I
\~
~ ~///
c axis
t(
~
T:I./Ga
/=~-~,
I 20
~
,
~
I
,
,
,
40
I
~
~
60
80
H(kOe) 60
. . . .
¢ 50
O
2Ql
v
I
. . . .
"15
"to
" 2Q2
I
. . . .
I
Fig. 92. Magnetization process at 1.7 K in hexagonal HoA1Ga along the c axis and associated magnetic structures as determined by neutron diffraction in fields of 0, 30 and 48 kOe; A, B and C denote lines of moments [3n,3n, z], [3n+l,3n+l,z] and [3n+2,3n+2,z], respectively (n integer) (after Ball et al. 1992b).
. . . .
HoAIGaJ/c
' 2Q2
X
'1- 40 30
.m
20 ~ \
\ f°-o'Q~'2Q, \ ~,3)
~Tt :185K
,.
\
II
i TN:31K
10
lo
20
30 T(K) 40
Fig. 93. Magnetic H-T phase diagram of HoA1Ga for the c direction; the propagation vectors observed by neutron diffraction are shown for each measured point (solid squares); the hatched region indicates the progressive vanishing of the lowtemperature periodicity associated with Q~ (see text) (after Ball et al. 1992b).
modulated structure between Tt and TN = 31 K with the single incommensurate vector Q2 = (½, ½, 0.481). It is worth noting that no anomaly could be detected by specific heat or susceptibility experiments at Tt; only neutron diffraction allowed us to determine the temperature of this transition. At low temperature, a three-step metamagnetic process is observed along the c axis (see fig. 92), with a hysteresis decreasing in increasing field, the two intermediate magnetizations reaching ~ i and ½ of the full moment. From the temperature dependence of the critical fields (see fig. 72, sect. 3.2.7), a magnetic phase diagram has been constructed (see fig. 93). It shows three ordered regions, the magnetic structures of which have been determined by neutron diffraction on a single crystal (Ball et al. 1992b). The first intermediate phase (Phase III) is characterized by: (i) the vanishing of the 3Q1 harmonics; (ii) the growing of the even harmonics 2Q1 and 6Q1 = Q0 = (0, 0, 0), this latter corresponding to the ferromagnetic component; (iii) the appearance of new propagation vectors, namely (0, 0, 1) and (½, ½, ½). The smallest common vector able to
MAGNETICPROPERTIESOF INTERMETALLICCOMPOUNDS
387
generate the observed ones being (½, ½, ~), a magnetic cell three times larger than the zerofield one and containing 18 moments has been considered. As shown in fig. 92, in the corresponding structure, a single line B (or equivalently C) is involved: along this line, a flipping of 32-of the initially antiparallel moments and an "antiflipping" of ½ of the parallel moments has occurred, in agreement with the value of the net magnetization. The second field-induced state at 1.7 K is characterized by the flipping of all the remaining antiparallel moments of line B, the magnetic unit cell recovering the same size as at zero field, i.e. it includes 6 moments. However, this structure does not appear fully consistent with the apparent absence of borderline detected by magnetic measurements within Phase II (Gignoux et al. 1991b), since the other extremity of this phase is associated with an incommensurate propagation vector. Effectively, such borderline has been determined by neutron diffraction, although the transition is not as strong as expected (see the hatched region in fig. 93). In fact, a broadening of the diffraction peaks at 1.7 K and 48 kOe is already present and suggests that a perfect arrangement with wavevector Q1 and its even harmonics is not fully achieved within this limited region, but presents faults reminiscent of the high-temperature propagation vector and illustrating the competition between both commensurate and incommensurate periodicities. Another crystal symmetry showing complex multistep metamagnetism is the ort h o r h o m b i c symmetry. In the RCu2 series, HoCuz, ErCu2 (Hashimoto et at. 1979) and more particularly NdCu2 exhibit a metamagnetic behaviour. In this latter compound, four successive antiferromagnetic phases have been detected in zero field below TN = 6.3 K, and magnetoresistance as well as magnetization measurements have revealed a quite complex phase diagram along the b easy direction, showing numerous antiferromagnetic and ferrimagnetic phases (see fig. 94; Svoboda et al. 1992). In the isomorphous I
I
I
I
a MvsT 0 RvsH D CysT 3
NdCu2 0
i
i
o
2
4
6
[-.
8
i
10
T [K] Fig. 94. Proposed magnetic phase diagram of orthorhombic NdCu2 along the b axis, deduced from magnetization,magnetoresistanceand specificheatmeasurements,A, antiferromagneticphases;F, ferrimagnetic phases; P, paramagneticphases. (AfterSvobodaet al. 1992.)
388
D. GIGNOUX and D. SCHMITT 120
z
t
o H~
PrZn2 100
0
0
cD _~
0
o H~ 80
80
O O
"I-~0 ZZ 20 0
0
®
®
®
0
® 0
8g
• i
00
~
5
i
10
0
15
-
-
20
25
T(K) Fig. 95. Magnetic phase diagram in orthorhombic PrZn 2 along the three main symmetry axes; a is the easy axis, and c is the least favoured axis (after Kaneko et al. 1992b).
.
.
.
.
i
,
,
,
,
i
.
.
.
.
i
:
0,
o-oxi5
o ~ o ~ O -
O0
50
100 H (kOe)
150
Fig. 96. Magnetization processes of orthorhombic CeZn~ at low temperature along the three main symmetry
axes (afterYamashitaet al. 1987). RZn2 series, several more or less sharp metamagnetic transitions have been observed along the three different symmetry axes of NdZn2 (Kitai et al. 1990) and DyZn2 (Abe et al. 1992). The same is true in PrZn2 for which the magnetic phase diagram has been determined for the three main symmetry directions (fig. 95; Kaneko et al. 1992b). This
MAGNETIC PROPERTIES OF 1NTERMETALLIC COMPOUNDS 80
I
_
0
I
i
I
t
[
_ -*--~.~...~
I
t
CeZn z b
60
389
axis
oa
.2
40
20
j
I
2
4 6 Temperature (K)
8
Fig. 97. Magnetic phase diagram of CeZn2 along the b easy direction (after Gignoux et al. 1992).
diagram suggests the existence of two zero-field magnetic phases, but no experimental data is available at the present time. The simple antiferromagnet CeZn2 (TN = 7 K) appears to be much more anisotropic than the other compounds of the same series, and exhibits a three-step metamagnetic behaviour along the single b easy axis (see fig. 96). The associated phase diagram is shown in fig. 97. Comparison with the substituted compound Ce(Zn0.9Cu0.1)2, which exhibits a similar behaviour and which has been investigated by neutron diffraction in magnetic fields using a single crystal (Gignoux et al. 1992), suggests that both intermediate phases correspond to the successive flipping of blocks of moments according to a magnetic periodicity first tripled, then doubled along the c axis. These changes of magnetic cell are consistent with the values of the net magnetization in both phases, i.e. g1 and ½ of the saturation magnetization. Within the other orthorhombic series RCu6, the NdCu6 compound appears as a complex metamagnetic system below TN = 6.1 K (Takayanagi et al. 1991). In zero field, up to three incommensurate magnetic phases have been found in a narrow temperature range below TN, the associated transition temperatures being successively 5.83, 5.74 and 5.58 K, and all having a propagation vector of the type (0, r, 1) (Mitsuda et al. 1991), while below 5.58 K the simple antiferromagnetic structure with Q=(0, 0, 1) is stabilized. The magnetization process at 1.3 K along the b easy axis shows four successive sharp metamagnetic transitions with noticeable hysteresis (see fig. 98). It is noted that the hysteresis is anomalous for the last two transitions, the critical fields being lower in increasing field than in decreasing field (see sect. 3.2.1). Furthermore, the large superimposed susceptibility in the first plateau can be resolved into two different phases with an additional intermediate step by lowering the temperature down to 0.6 K. The low-field corresponding phase diagram has been determined by high-resolution specific-heat measurements under field (see fig. 99). As often observed, the incommensurate phases of the low-field and high-temperature region seem to replace the simple antiferromagnetic one at high field and low temperature, but this fascinating compound clearly needs a lot of additional investigations to be well understood, in particular the determination of the structures of the numerous field-induced
390
D. GIGNOUXand D. SCHMITT ~
2.0
NdCue
1.3K
t
TI
HRb-axis
2
5.0~
4.0
/
E/
~
H//b
3.0
o
f
:Z
]E
1.0
I
JJ ~ ,r
~ 1.0 a
//"
i[l L
.~ 2.0 m
/ j ~ ...-/ " /. / "
c
t> j 0
4.5
5
5.5
Temperature [K]
6
6.5
Fig. 99. Magnetic phase diagram of NdCu6 along the b axis deduced from specific heat measurements (after Takayanagi et al. 1991).
50 100 I50 M'agne'tic Field ( kOe )
Fig. 98. Magnetizationcurves at 1.3 K in orthorhombicNdCu6 along the three main symmetrydirections. Note the peculiar hysteresis associated with the last two transitions (after (Jnuki et al. 1986). magnetic phases. As a conclusion of this long section devoted to the complex multistep metamagnetic behaviour of compounds having a strong uniaxial-type anisotropy, one may still expect a large number of new experimental results in the future, from magnetization measurements as well as neutron diffraction experiments performed on single crystals, allowing us to determine the microscopic aspects of the related complex phase diagrams.
3.2.11. Planar metamagnetic systems The previous section has shown the variety of behaviours which can be observed in uniaxial lanthanide systems having their magnetic moments confined along the highsymmetry direction in the presence of incommensurate magnetic structures. Much less spectacular and a priori more complex are the same systems where the crystal field anisotropy fixes the moments to remain perpendicular to this direction. Indeed, the onedimensional character of the possible structures has to be replaced by a two-dimensional problem, which either can be isotropic or may reveal new features related to the inplane anisotropy. Again, although the pure lanthanide metals are not the main subject of this review, it is worth making a few remarks about them, on account of the recent remarkable renaissance in the study of their magnetic structures in various conditions of field and temperature (Mackintosh and Jensen 1992). Most of the new features were revealed in high-resolution studies with both X-rays and neutrons, performed using highquality single crystals. First, new types of magnetic structures have been identified during the magnetization process of a helical structure with a magnetic field applied in the plane of the helix, as in Ho metal (Jensen and Mackintosh 1990). These helifan structures do not
MAGNETIC PROPERTIES OF 1NTERMETALLICCOMPOUNDS
391
require specific anisotropic interactions, and occur between the distorted helix observed in low field and the fan configuration present in high field. Secondly, as described above (see sect. 3.2.9), spin-slip transitions have been observed as a function of field or temperature, resulting from the in-plane anisotropy of Ho for example (Jensen and Mackintosh 1992). Finally, the presence of several equivalent symmetry directions in the plane may also favour multiple-Q magnetic structures as in Nd metal for example, which exhibits a fascinating hierarchy of 1Q, 2Q, 3Q and 4Q structures below its Nrel temperature TN = 19.9K, and where more than 10 phases have been revealed in its complex phase diagram (McEwen and Zochowski 1990). Some of these phases are characterized by the appearance of subharmonics of the fundamental modulation wavevector and present some analogy with the helifan structure quoted above. As a general rule, the existence of several equivalent easy directions within the basal plane of planar intermetallic lanthanide systems allow the magnetic moment configurations to become non-collinear during the magnetization processes. Such canted magnetic structures noticeably multiply the number of possible magnetic phases. From this point of view, the most favourable symmetry is the hexagonal one, showing 6 possible directions for the moments. In this context, the RGa2 series appears particularly promising to be studied, several compounds of this series exhibiting at least one incommensurate magnetic phase together with an easy axis within the basal plane. For example, the PrGa2 compound, which presents a low-field behaviour being of Ising-type along its [100] easy direction at low temperature, as described above (see sects. 3.2.8, 3.2.9), recovers a planar behaviour at higher fields and/or higher temperature, as shown in fig. 100 (Ball et al. 1993a). The associated metamagnetic process is characterized by a two-step behaviour along the [100] direction, and a three-step one along the [120] hard direction of the basal plane, in the field range 10-15kOe. Moreover, the intermediate phases present a large superimposed susceptibility, a feature which seems to be quite general in these planar processes. This feature can be definitely associated with the noncollinear arrangement of the moments and their ability to rotate more or less continuously within 3.2 ~ 2.4 = •~
/
1.5K
1.6
130
10
20
30 40 50 H (kOe)
613 70
80
Fig. 100. Magnetization curves of hexagonal PrGa~ at 1.5 K along the three main symmetry directions. Note the large superimposed susceptibility of the high-field intermediate phases along the [100] and [120] axes (above 10kOe) (after Ball et al. 1993a).
392
D. GIGNOUXand D. SCHMITT '
Z
[120]
'
I
3 Ol
=
2
NdGa 2
/~.~
1.5 K ....
.......
0
" t
I
i
I
i
20
40 60 80 H (kOe) Fig. 101. Magnetizationcurves of hexagonalNdGa2 at 1.5K alongthe three main symmetrydirections.Note the largesuperimposedsusceptibilityof the intermediatephases alongthe [100] and [120] axes(afterBall et al. 1994b). the basal plane. In addition, it can be seen that during such rotations, the moments may be temporarily locked into intermediate easy directions. A preliminary neutrondiffraction experiment in this high-field phase at 1.5 K along the easy axis has shown the resurgence of the incommensurate propagation vector Q = (0.148, 0.148, 0.023) which characterizes the high-temperature phase of this compound in zero field (between 3.5 K and TN = 7.2 K). The resulting H - T magnetic phase diagrams of PrGa2 along both directions [100] and [120] of the basal plane then include 5 and 6 distinct phases, respectively. In the neighbouring compound NdGa2 (TN = 9.5 K), the situation is quite similar. This compound exhibits two different incommensurate magnetic structures in zero field (Ball et al. 1992c), and a multistep metamagnetic behaviour along both directions of the basal plane (see fig. 101). Again, the intermediate phases exhibit a superimposed susceptibility which is still larger than in PrGa2, and the corresponding phase diagrams include 4 (6) distinct regions along the [120] ([100]) directions (Ball et al. 1994b). The compound CeGa2 as well as its derived solid solutions Ce(Gal-xAlx)2 exhibits also planar metamagnetic properties, with the presence of ferromagnetic and incommensurate magnetic structures in their H - T phase diagrams (Takahashi et al. 1988, Jerjini et al. 1988, Frrmy et al. 1989). However, the most complex system of the RGa2 series is certainly DyGa2, where three successive magnetic phases have been observed in zero field (Gignoux et al. 1991a). Below 6.1 K, the structure is simple antiferromagnetic, the propagation vector being Q=(0, ½,0). Between 6.1 K and' TN = 11 K, the structure is incommensurate (amplitude modulated) with Q=(2r, ½- r, 0) and 3=0.134. Within the modulated phase, there is an additional spin reorientation transition at 8.7 K, the easy magnetization direction being the [120] and the [100] axis below and above this temperature, respectively. At low temperature, the magnetization processes show a particularly complex multistep metamagnetic behaviour, with numerous field-induced transitions when the magnetic field is applied in the basal plane, suggesting a great number of intermediate magnetic phases (see fig. 102). Some transitions are very sharp, while others are more subtle. A hysteresis is associated with almost all transitions, their
MAGNETIC PROPERTIES OF INTERMETALLICCOMPOUNDS
393
10
8
~6
0
oi 0
7O
20
I
40
I
60
I
I
'
I
'
DyGa2 II b
© 60 •"v 50
80
H(kOe)
'~ ¢" 'VIII
-
Fig. 102. Magnetization curves of hexagonal DyGa2 at 1.5K along the three main symmetry directions; b represents the [120] easy direction and a the [100] hard direction in the basal plane (after Gignoux et al. 1991a).
|
4
\
4O 30 " t
IX",
2O Fig. 103. Magnetic phase diagram of DyGa2
10
Oo
2
4 T(K) 6T1
8 T2 10 TN 12
along the [120] axis; the magnetic structure is simple antiferromagnetic below T~ and amplitude modulated between T Z and TN (after Gignoux et al. 1991a).
amplitude decreasing with increasing field. Some intermediate phases are present only in decreasing field. Although the general features of the curves are similar for both directions in the basal plane, they slightly differ in detail, and lead to quite complicated magnetic phase diagrams (see fig. 103 for the [120] axis). Very likely, all the observed fieldinduced transitions are associated with a mixing of the different types of metamagnetism (spin-flip, spin-flop, change of periodicity, ... ), but only an extensive neutron study will allow us to determine all the microscopic aspects of these phase diagrams. It is worth noting that there are only a few examples of planar multistep systems available up to now in other symmetries than the hexagonal one, this latter remaining the most favourable. One orthorhombic compound however, namely Ce3Sn7 (TN=5.1 K), exhibits a two-step metamagnetic process along the c easy axis (Fillion et al. 1992). The small discontinuous field-induced transitions have been explained by the occurrence of various intermediate
394
D. GIGNOUXand D. SCHMITT
canted magnetic structures in the (a, c) plane, and these latter have been determined by using polarized and nonpolarized neutron scattering.
3.2.12. Multiaxial metamagnetie systems In the previous sections, a single axis or a single plane was involved in the metamagnetic processes, the symmetry of the anisotropic lanthanide systems being of uniaxial type. This last section is devoted to the systems where the whole space will be concerned, i.e., where the equivalent symmetry directions for the moments do not all belong to the same plane. This is the case of the cubic symmetry. The first example of metamagnetism associated with this symmetry can be found in cubic NaCl-type lanthanide pnictides, where some compounds exhibit, in an applied field, canted intermediate structures similar to the "topside" antiferromagnetie structure evidenced in HoP (Fischer et al. 1985). An early example is provided by DySb (Everett and Streit 1979), but similar behaviours have been also reported in other pnictides, such as HoSb (Brunet al. 1980), HoAs and HoBi (Hulliger 1978) and DyBi (Hulliger 1980). This latter compound undergoes a firstorder transition at TN = 11.2 K into a simple antiferromagnetic structure [Q = (½, ½, ½)] with magnetic moments aligned along the [001] direction. Under the application of a magnetic field along the three main cubic symmetry directions, i.e. [100], [110] and [111], there is in each case an abrupt metamagnetic transition, the corresponding critical fields being approximately in the ratio 2:x/~:v~, and the resulting intermediate magnetizations reaching respectively ½, l/x/2 and l/v/3 of the saturated value (see fig. 104). A second and last step occurs at a slightly higher field along the four-fold axis, while no further transition could be seen up to 200 kOe for the two other directions. All the relative values of the critical fields and intermediate magnetizations are consistent with the "topside" structure where the moments are oriented along two orthogonal (100) directions, keeping the same propagation vector (bi-axial structure). This behaviour requires first a strong anisotropy favouring the four-fold axes, and secondly strong negative two-ion quadrupolar interactions in order to stabilize such a canted structure (K_im and Levy 1982). A biquadratic coupling was also found to be important to explain the similar two-step metamagnetic processes observed in the S-state isomorphous compound EuSe (Fukuma et al. 1985). A strong antiferroquadrupolar coupling has been also shown to be fundamental to explain the spontaneous triple-Q magnetic structures observed at low temperature, as well as the occurrence of well-defined field-induced multi-axis magnetic structures in some other simple cubic CsCl-type systems, such as DyCu and DyAg (Morin et al. 1990). The compound DyCu orders at TN--62.8K within a simple antiferromagnetic structure characterized by the propagation vector Q = (½, ½, 0). A thorough study of its magnetoelastic properties, in particular the absence of any spontaneous magnetostriction at low temperature in spite of a large magnetoelastic coupling, led to the conclusion that the cubic symmetry is preserved in the ordered phase by developing a triple-Q structure with magnetic moments pointing along the four three-fold symmetry directions of the unit cell (A16onard et al. 1984b). This configuration is favoured by the existence of a negative
MAGNETIC PROPERTIES OF INTERMETALLIC COMPOUNDS
395
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2" [111]
5
..,
•
4 3 2
DyBi l
1
,j,:"
:
;
15K
.. •
f~
i
0
20
0
40
60
I
I
J H (kO)
80
Fig. 104• Magnetization curves in cubic DyBi at 1.5 K (after Hulliger 1980)•
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z O
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8
U
7Lu 2
z O ,