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TLFeBOOK ELECTRONIC STRUCTURE AND MAGNETO-OPTICAL PROPERTIES OF SOLIDS TLFeBOOK This page intentionally left blank TLFeBOOK Electronic Structure and Magneto-Optical Properties of Solids by Victor Antonov Institute of Metal Physics, Kiev, Ukraine Bruce Harmon Ames Laboratory, Iowa State University, Iowa, U.S.A and Alexander Yaresko Max-Planck Institute for the Chemical Physics of Solids, Dresden, Germany KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW TLFeBOOK eBook ISBN: Print ISBN: 1-4020-1906-8 1-4020-1905-X ©2004 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print ©2004 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: and Kluwer's eBookstore at: http://kluweronline.com http://ebooks.kluweronline.com TLFeBOOK Contents Preface Acknowledgments ix xv THEORETICAL FRAMEWORK 1.1 Density Functional Theory (DFT) 1.1.1 Formalism 1.1.2 Local Density Approximation 1.2 Modifications of local density approximation 1.2.1 Approximations based on an exact equation for Exc 1.2.2 Gradient correction 1.2.3 Self-interaction correction 1.2.4 LDA+U method 1.2.5 Orbital polarization correction 1.3 Excitations in crystals 1.3.1 Landau Theory of the Fermi Liquid 1.3.2 Green’s functions of electrons in metals 1.3.3 The GW approximation 1.3.4 Dynamical Mean-Field Theory (DMFT) 1.4 Magneto-optical effects 1.4.1 Classical optics 1.4.2 MO effects 1.4.3 Linear-response theory 1.4.4 Optical matrix elements 4 10 12 15 23 26 26 30 33 35 39 40 48 61 67 MAGNETO-OPTICAL PROPERTIES OF d FERROMAGNETIC MATERIALS 2.1 Transition metals and compounds 2.1.1 Ferromagnetic metals Fe, Co, Ni 71 71 71 TLFeBOOK vi ELECTRONIC STRUCTURE AND MO PROPERTIES OF SOLIDS 2.2 2.1.2 Paramagnetic metals Pd and Pt 2.1.3 CoPt alloys 2.1.4 XPt3 compounds (X=V, Cr, Mn, Fe and Co) 2.1.5 Heusler Alloys 2.1.6 MnBi 2.1.7 Chromium spinel chalcogenides 2.1.8 Fe3O4 and Mg2+ -, or Al3+ -substituted magnetite Magneto-optical properties of magnetic multilayers 2.2.1 Magneto-optical properties of Co/Pd systems 2.2.2 Magneto-optical properties of Co/Pt multilayers 2.2.3 Magneto-optical properties of Co/Cu multilayers 2.2.4 Magneto-optical anisotropy in Fen /Aun superlattices 75 99 121 127 135 138 141 158 159 178 193 203 MAGNETO-OPTICAL PROPERTIES OF f FERROMAGNETIC MATERIALS 3.1 Lantanide compounds 3.1.1 Ce monochalcogenides and monopnictides 3.1.2 NdX (X=S, Se, and Te) and Nd3 S4 3.1.3 Tm monochalcogenides 3.1.4 Sm monochalcogenides 3.1.5 SmB6 and YbB12 3.1.6 Yb compounds 3.1.7 La monochalcogenides 3.2 Uranium compounds 3.2.1 UFe2 3.2.2 U3 X4 (X=P, As, Sb, Bi, Se, and Te) 3.2.3 UCu2 P2 , UCuP2 , and UCuAs2 3.2.4 UAsSe and URhAl 3.2.5 UGa2 3.2.6 UPd3 229 229 230 239 248 265 273 286 308 320 322 327 332 338 341 346 XMCD PROPERTIES OF d AND f FERROMAGNETIC MATERIALS 4.1 3d metals and compounds 4.1.1 XPt3 Compounds (X=V, Cr, Mn, Fe, Co and Ni) 4.1.2 Fe3O4 and Mn-, Co-, or Ni-substituted magnetite 4.2 Rare earth compounds 4.2.1 Gd5 (Si2 Ge2 compound) 4.3 Uranium compounds 4.3.1 UFe2 357 358 359 379 395 397 401 404 TLFeBOOK vii Contents 4.3.2 4.3.3 4.3.4 4.3.5 4.3.6 4.3.7 4.3.8 US, USe, and UTe UXAl (X=Co, Rh, and Pt) UPt3 URu2 Si2 UPd2 Al3 and UNi2 Al3 UBe13 Conclusions 412 420 428 434 438 444 451 Appendices 453 A Linear Method of MT Orbitals 453 A.1 Atomic Sphere Approximation 453 A.2 MT orbitals 455 A.3 Relativistic KKR–ASA 456 A.4 Linear Method of MT Orbitals (LMTO) 460 A.4.1 Basis functions 460 A.4.2 Hamiltonian and overlap matrices 462 A.4.3 Valence electron wave function in a crystal 463 A.4.4 Density matrix 463 A.5 Relativistic LMTO Method 464 A.6 Relativistic Spin-Polarized LMTO Method 466 A.6.1 Perturbational approach to the relativistic spin-polarized 467 LMTO method B Optical matrix elements 469 B.1 ASA approximation 469 B.2 Combined-correction term 475 References Index 477 527 TLFeBOOK This page intentionally left blank TLFeBOOK Preface In 1845 Faraday discovered [1] that the polarization vector of linearly polarized light is rotated upon transmission through a sample that is exposed to a magnetic field parallel to the propagation direction of the light About 30 years later, Kerr [2] observed that when linearly polarized light is reflected from a magnetic solid, its polarization plane also becomes rotated over a small angle with respect to that of the incident light This discovery has become known as the magneto-optical (MO) Kerr effect Since then, many other magnetooptical effects, as for example the Zeeman, Voigt and Cotton-Mouton effects [3], have been discovered These effects all have in common that they are due to a different interaction of left- and right-hand circularly polarized light with a magnetic solid The Kerr effect has now been known for more than a century, but it was only in recent times that it became the subject of intensive investigation The reason for this recent development is twofold: first, the Kerr effect is relevant for modern data storage technology, because it can be used to ‘read’ suitably stored magnetic information in an optical manner [4, 5] and second, the Kerr effect has rapidly developed into an appealing spectroscopic tool in materials research The technological research on the Kerr effect was initially motivated by the search for good magneto-optical materials that could be used as information storage media In the course of this research, the Kerr spectra of many ferromagnetic materials were investigated An overview of the experimental and theoretical data collected on the Kerr effect can be found in the review articles by Buschow [6], Reim and Schoenes [7], Schoenes [8], Ebert [9], Antonov et al [10, 11], and Oppeneer [12] The quantum mechanical understanding of the Kerr effect began as early as 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245 Ni fcc, 75 orbital polarization correction, 23 Pd diluted alloys, 83 fcc, 77 Pt diluted alloys, 97 fcc, 84 self-interaction correction (SIC), 13 Sm monochalcogenides, 265 SmS, 265, 270 SmSe, SmTe, 267 SmB6 , 275 sum rules, 48, 55, 59 Tm monochalcogenides, 249 TmS, 249 TmSe, 257 TmTe, 263 U3 X4 X=P, As, Sb, Bi, 327 X=Se, Te, 331 UAsSe, 338 UBe13 , 444 UCu2 P2 , 333 UCuAs2 , 336 UCuP2 , 334 UFe2 , 323, 404 UGa2 , 341 UNi2 Al3 , UPd2 Al3 , 439 UPd3 , 347, 434 UPt3 , 429 URhAl, 340 TLFeBOOK 528 ELECTRONIC STRUCTURE AND MO PROPERTIES OF SOLIDS URu2 Si2 , 435 US, USe, UTe, 412 UXAl (X=Co, Rh, Pt), 420 Yb4 As3 , 296 XPt3 , (X=V, Cr, Mn, Fe, Co), 121, 359 YbMCu4 , 286 YbB12 , 279 TLFeBOOK ... Whereas optical and MO spectra are often swamped by too many transitions between occupied and empty valence states, x-ray excitations have the advantage that the core state has a purely local wave.. .ELECTRONIC STRUCTURE AND MAGNETO- OPTICAL PROPERTIES OF SOLIDS TLFeBOOK This page intentionally left blank TLFeBOOK Electronic Structure and Magneto- Optical Properties of Solids by Victor Antonov... Antonov Institute of Metal Physics, Kiev, Ukraine Bruce Harmon Ames Laboratory, Iowa State University, Iowa, U.S .A and Alexander Yaresko Max-Planck Institute for the Chemical Physics of Solids,