This advanced level textbook is devoted to the description of systems which show ordered magnetic phases. A wide selection of topics is covered, including a detailed treatment of the mean-field approximation as the main paradigm for the phenomenological description of phase transitions. The book discusses the properties of low-dimensional systems and uses Green's functions extensively after a useful mathematical introduction. A thorough presentation of the RKKY and related models of indirect exchange is also featured, and a chapter on surface magnetism, rarely found in other textbooks, adds to the uniqueness of this book. For the second edition, three new chapters have been added, namely on magnetic anisotropy, on coherent magnon states and on local moments. Additionally, the chapter on itinerant magnetism has been enlarged by including a section on paramagnons.
Author(s): Norberto Majlis
Edition: 2nd ed
Publisher: World Scientific
Year: 2007
Language: English
Commentary: 61195
Pages: 392
City: New Jersey
Contents......Page 10
1.1 Introduction......Page 16
1.2.1 L-S (Russel-Saunders) coupling......Page 19
1.2.2 Hund's rules......Page 21
1.2.3 Spin-orbit splitting......Page 22
1.3 The quantum theory of paramagnetism......Page 23
1.4 Crystal-field corrections......Page 26
1.4.1 Effects of crystal- field symmetry......Page 27
1.4.2 Stevens operator equivalents......Page 29
1.5 Quenching of L......Page 33
1.6 Time reversal and spin......Page 35
1.6.1 Kramers degeneracy......Page 36
1.7 Effective spin Hamiltonian......Page 37
1.7.2 Single-ion anisotropy energy......Page 38
References......Page 40
2.1 Weiss model of ferromagnetism......Page 42
2.1.1 Critical behaviour of Weiss model......Page 43
2.2 Microscopic basis of magnetism......Page 44
2.2.1 The direct exchange interaction......Page 45
2.2.2 The superexchange mechanism......Page 51
2.2.3 The RKKY interaction......Page 55
References......Page 56
3.1 Helmholtz free energy......Page 58
3.2 Mean field susceptibility......Page 65
3.3 Specific heat of ferromagnet......Page 67
3.4 The Oguchi method......Page 70
3.5 Modulated phases......Page 73
3.6 MFA for antiferromagnetism......Page 76
3.6.1 Longitudinal susceptibility......Page 78
3.6.2 Transverse susceptibility......Page 80
3.6.3 Spin-flop and other transitions......Page 83
3.7 Helimagnetism......Page 87
References......Page 91
4.1 Introduction......Page 94
4.2 Holstein-Primako transformation......Page 97
4.3 Linear spin-wave theory......Page 99
4.4 Semiclassical picture......Page 100
4.5 Macroscopic magnon theory......Page 103
4.6.1 Total spin deviation......Page 104
4.6.2 Non-linear corrections......Page 106
4.7.1 Introduction......Page 107
4.7.2 Antiferromagnetic spin-waves......Page 108
4.7.3 Sublattice magnetization......Page 112
4.7.4 Ground state energy of AFM......Page 114
References......Page 115
5.1 Introduction......Page 116
5.2 Microscopic origin of anisotropy......Page 119
5.3 Magneto-elastic coupling......Page 123
5.4 Magnetostriction......Page 126
5.5 Inverse magnetostriction......Page 128
5.6 Induced magneto-crystalline anisotropy......Page 130
References......Page 131
6.1 Definitions......Page 132
6.2 Spectral representation......Page 134
6.3 RPA for spin 1/2 ferromagnet......Page 137
6.4 Comparison of RPA and MFA......Page 141
6.5 RPA for arbitrary spin......Page 142
6.6.1 Paramagnetic phase......Page 144
6.6.2 Linear FM chain......Page 147
6.6.3 Square FM lattice......Page 148
6.7 FM with a finite applied field......Page 150
6.8 RPA for antiferromagnet......Page 151
6.8.1 Spin 1/2 AFM......Page 152
6.8.2 Arbitrary spin AFM......Page 153
6.8.3 Zero-point spin deviation......Page 154
6.8.4 Correlation length......Page 155
6.9 RPA susceptibility of AFM......Page 158
6.10 Spin-op transition......Page 161
6.11 X|| at low T......Page 163
6.12 Transverse susceptibility......Page 164
6.13 Single-site anisotropy......Page 165
6.14 Dynamic linear response......Page 168
6.15 Energy absorbed from external field......Page 171
References......Page 173
7.1 Dipolar Hamiltonian......Page 176
7.2 Dipole-exchange spin-waves......Page 181
7.3 Uniform precession (k = 0) mode......Page 185
7.4 Eigenmodes for k = 0......Page 189
7.5 Ellipticity of spin precession......Page 191
7.6 Effect of magnons on total spin......Page 192
7.7 Magnetostatic modes......Page 194
References......Page 195
8.2 Coherent states of bosons......Page 198
8.2.1 Overcompleteness of coherent states basis......Page 200
8.3 Magnon number distribution function......Page 201
8.4 Uncertainty relations......Page 202
8.5 Phase states......Page 203
8.6 Magnon states of well defined phase......Page 205
8.7 Properties of the single-mode number states......Page 206
8.9 Expectation value of local spin operators in a coherent state......Page 207
References......Page 208
9.2 Pauli paramagnetic susceptibility......Page 210
9.3 Stoner model of ferromagnetic metals......Page 211
9.4 Hubbard Hamiltonian......Page 213
9.5 Instability of paramagnetic phase......Page 214
9.6.1 The RPA susceptibility......Page 215
9.6.2 Singularities of the susceptibility......Page 219
9.7 Tc in Stoner model......Page 223
9.8 Metals with degenerate bands......Page 225
9.9 Spin-density wave......Page 228
9.10 Hartree–Fock description of SDW......Page 230
9.11 Effects of correlations......Page 237
9.11.1 Kinetic exchange interaction......Page 239
9.12 Paramagnetic instability and paramagnons......Page 243
9.12.1 Paramagnon contribution to the specific heat......Page 247
9.14 Magnetism and superconductivity......Page 249
References......Page 250
10.1 Introduction......Page 254
10.2 Effective s-d exchange interaction......Page 255
10.3 Indirect exchange Hamiltonian......Page 262
10.4 Range function and band structure......Page 263
10.5.1 Intrinsic semiconductors, high T......Page 271
10.5.2 Intrinsic semiconductors, low T......Page 272
10.6 Magnetic multilayer systems......Page 274
References......Page 275
11.2 Anderson model......Page 278
11.3 Hartree–Fock solution of Anderson Hamiltonian......Page 279
11.4 Kondo effect......Page 282
11.4.1 Calculation of resistivity......Page 283
11.4.2 Calculation of the collision time......Page 284
References......Page 290
12.1 Introduction......Page 292
12.2.1 Bogoliubov inequality......Page 293
12.2.2 Application to the Heisenberg model......Page 294
12.3 Dipolar interactions in low dimensions......Page 297
12.3.1 Dipole-exchange cross-over......Page 301
12.4 One dimensional instabilities......Page 302
12.5 Antiferromagnetic chain......Page 304
12.6.1 Exchange dominated regime......Page 306
12.6.2 Dipolar dominated regime......Page 309
12.7 Dipolar interaction in layers......Page 310
12.7.1 Monolayer......Page 312
12.7.2 Bilayer......Page 313
References......Page 317
13.1 Introduction......Page 320
13.2 MFA treatment of surfaces......Page 321
13.3 Surface excitations......Page 324
13.4 LRPA method......Page 325
13.5 Wave functions for bulk and surface......Page 331
13.6 Surface density of magnon states......Page 332
13.7 Surface phase-transitions......Page 334
13.8 Dipolar surface effects......Page 338
13.9 Surface magnetism in metals......Page 339
References......Page 342
14.1 Introduction......Page 344
14.2 Green's function formalism......Page 346
14.3 One dimension......Page 352
14.4 Two dimensions......Page 354
14.5 Summary of results......Page 355
14.6 Anisotropy effects......Page 356
References......Page 358
15.1 Introduction......Page 360
15.2 Two-magnon interaction......Page 362
15.3 Three-magnon processes......Page 364
15.4 Magnon-phonon interaction......Page 368
15.5 Bilinear magnon-phonon interaction......Page 370
References......Page 372
A.1 Definition of group......Page 374
A.2 Group representations......Page 375
A.2.1 Reducibility......Page 376
A.4 Projection operators......Page 377
A.5 Coordinate transformations......Page 378
A.6 Wigner-Eckart theorem......Page 379
A.7 Space groups......Page 380
A.8 Bloch's theorem......Page 381
B.1 Antilinear operators......Page 384
B.3 Time reversal......Page 386
Index......Page 390
