This monograph presents a unified and coherent account of an important, focused area of rare-earth magnetism -- magnetic structures and excitations -- which both reflects the nature of the fundamental magnetic interactions and determines many of the characteristic properties of metals. The authors concentrate on the essential principles and their applications to typical examples, generally restricting the discussion to the pure elements and considering alloys and compounds only when they are instructive in illuminating particular topics. Both authors have been involved for some time in the effort that has been made in Denmark to study, both theoretically and experimentally, the magnetic structures and especially the excitations in the rare earths. This account of the subject represents the result of their experience, and it has been written in the hope that it will be useful not only to those who have a special interest in rare-earth magnetism, but also to a wider audience of physicists and condensed matter scientists interested in the techniques and achievements of modern research in magnetism.
Author(s): Jens Jensen, Allan R. Mackintosh
Series: International Series of Monographs on Physics
Publisher: Oxford University Press, USA
Year: 1991
Language: English
Pages: 413
PREFACE......Page 3
1. ELEMENTS OF RARE EARTH MAGNETISM......Page 11
1.1 A brief history......Page 12
1.2 Rare earth atoms......Page 18
1.3 The metallic state......Page 26
1.4 Magnetic interactions......Page 49
1.5 Rare earth magnetism......Page 60
2.1 Mean-field theory of magnetic ordering......Page 78
2.1.1 The high-temperature susceptibility......Page 81
2.1.2 The mean-field approximation......Page 84
2.1.3 Transversely ordered phases......Page 89
2.1.4 Longitudinally ordered phases......Page 93
2.1.5 Competing interactions and structures......Page 95
2.1.6 Multiply periodic structures......Page 99
2.2.1 Temperature dependence of the Stevens operators......Page 104
2.2.2 Anisotropic contributions to the free energy......Page 111
2.3 Magnetic structures of the elements......Page 121
2.3.1 Bulk magnetic structures......Page 122
2.3.2 The magnetization of Holmium......Page 135
2.3.3 Films and superlattices......Page 140
3.1 The generalized susceptibility......Page 144
3.2 Response functions......Page 147
3.3 Energy absorption and the Green function......Page 152
3.4 Linear response of the Heisenberg ferromagnet......Page 159
3.5.1 The generalized susceptibility in the RPA......Page 164
3.5.2 MF-RPA theory of the Heisenberg ferromagnet......Page 170
4. MAGNETIC SCATTERING OF NEUTRONS......Page 173
4.1 The differential cross-section in the dipole approximation......Page 174
4.2 Elastic and inelastic scattering......Page 183
5. SPIN WAVES IN THE FERROMAGNETIC HEAVY RARE EARTHS......Page 191
5.1 The ferromagnetic hcp-crystal......Page 192
5.2 Spin waves in the anisotropic ferromagnet......Page 196
5.3.1 The magnetic susceptibility and the energy gap......Page 208
5.3.2 The validity of the spin-wave theory......Page 216
5.4.1 Magnetoelastic effects on the energy gap......Page 221
5.4.2 The magnon-phonon interaction......Page 229
5.5 Two-ion anisotropy......Page 241
5.5.1 The dipole-dipole interaction......Page 242
5.5.2 General two-ion interactions......Page 250
5.6 Binary rare earth alloys......Page 257
5.7.1 The indirect-exchange interaction......Page 266
5.7.2 The mass-enhancement of the conduction electrons......Page 280
5.7.3 Magnetic contributions to the electrical resistivity......Page 285
6. SPIN WAVES IN PERIODIC STRUCTURES......Page 295
6.1 Incommensurable periodic structures......Page 296
6.1.1 The helix and the cone......Page 297
6.1.2 The longitudinally polarized structure......Page 310
6.2 Commensurable periodic structures......Page 315
7. CRYSTAL-FIELD EXCITATIONS IN THE LIGHT RARE EARTHS......Page 322
7.1 MF-RPA theory of simple model systems......Page 323
7.2 Beyond the MF-RPA theory......Page 332
7.3.1 Magnetoelastic effects and two-ion anisotropy......Page 344
7.3.2 Conduction-electron interactions......Page 352
7.3.3 Coupling to the nuclear spins......Page 359
7.4.1 Induced magnetic ordering......Page 362
7.4.2 The magnetic excitations......Page 371
8. PERSPECTIVES FOR RARE EARTH RESEARCH......Page 380
REFERENCES......Page 391
INDEX......Page 408
