For hundreds of years, models of magnetism have been pivotal in the understanding and advancement of science and technology, from the Earth's interpretation as a magnetic dipole to quantum mechanics, statistical physics, and modern nanotechnology. This book is the first to envision the field of magnetism in its entirety. It complements a rich literature on specific models of magnetism and provides an introduction to simple models, including some simple limits of complicated models. The book is written in an easily accessible style, with a limited amount of mathematics, and covers a wide range of quantum-mechanical, finite-temperature, micromagnetic and dynamical models. It deals not only with basic magnetic quantities, such as moment, Curie temperature, anisotropy, and coercivity, but also with modern areas such as nanomagnetism and spintronics, and with 'exotic' themes, as exemplified by the polymer analogy of magnetic phase transitions. Throughout the book, a sharp line is drawn between simple and simplistic models, and much space is devoted to discuss the merits and failures of the individual model approaches.
Author(s): Ralph Skomski
Series: Oxford Graduate Texts
Publisher: Oxford University Press, USA
Year: 2008
Language: English
Pages: 366
Contents......Page 8
List of abbreviations......Page 13
List of panels and tables......Page 15
Preface......Page 16
1 Introduction: The simplest models of magnetism......Page 18
1.1 Field and magnetization......Page 19
1.2 The circular-current model......Page 21
1.3 Paramagnetic spins......Page 23
1.4 Ising model and exchange......Page 25
1.5 The viscoelastic model of magnetization dynamics......Page 27
Exercises......Page 30
2 Models of exchange......Page 32
2.1 Atomic origin of exchange......Page 34
2.1.1 One-electron wave functions......Page 35
2.1.2 Two-electron wave functions......Page 38
2.1.3 Hamiltonian and spin structure......Page 39
2.1.4 Heisenberg model......Page 42
2.1.5 Independent-electron approximation......Page 44
2.1.6 Correlations......Page 46
2.1.7 *Hubbard model......Page 49
2.1.8 *Kondo model......Page 51
2.2.1 Atomic orbitals......Page 53
2.2.2 Angular-momentum algebra......Page 56
2.2.4 Spin and orbital moment......Page 58
2.3.1 Exchange in oxides......Page 61
2.3.2 Ruderman-Kittel exchange......Page 63
2.3.3 Zero-temperature spin structure......Page 65
2.4 Itinerant magnetism......Page 68
2.4.1 Free electrons, Pauli susceptibility, and the Bloch model......Page 71
2.4.2 Band structure......Page 75
2.4.3 Stoner model and beyond......Page 80
2.4.4 *Itinerant antiferromagnets......Page 83
Exercises......Page 86
3 Models of magnetic anisotropy......Page 90
3.1 Phenomenological models......Page 91
3.1.1 Uniaxial anisotropy......Page 92
3.1.2 Second-order anisotropy of general symmetry......Page 93
3.1.4 Cubic anisotropy......Page 95
3.1.5 Anisotropy coefficients......Page 96
3.2 Models of pair anisotropy......Page 97
3.2.1 Dipolar interactions and shape anisotropy......Page 98
3.2.2 Demagnetizing factors......Page 99
3.2.4 The Néel model......Page 100
3.3 Spin-orbit coupling and crystal-field interaction......Page 101
3.3.1 Relativistic origin of magnetism......Page 102
3.3.3 Crystal-field interaction......Page 104
3.3.4 Quenching......Page 106
3.3.5 Spin-orbit coupling......Page 107
3.4.1 Rare-earth anisotropy......Page 108
3.4.2 Point-charge model......Page 112
3.4.3 The superposition model......Page 114
3.4.4 Transition-metal anisotropy......Page 115
3.5.1 Magnetoelasticity......Page 117
3.5.2 Anisotropic exchange......Page 118
3.5.3 Models of surface anisotropy......Page 119
Exercises......Page 121
4 Micromagnetic models......Page 124
4.1 Stoner-Wohlfarth model......Page 127
4.1.1 Aligned Stoner-Wohlfarth particles......Page 128
4.1.2 Angular dependence......Page 129
4.1.3 Spin reorientations and other first-order transitions......Page 130
4.1.4 Limitations of the Stoner-Wohlfarth model......Page 132
4.2 Hysteresis......Page 133
4.2.1 Micromagnetic free energy......Page 134
4.2.2 *Magnetostatic self-interaction......Page 135
4.2.3 *Exchange stiffness......Page 136
4.2.4 Linearized micromagnetic equations......Page 137
4.2.5 Micromagnetic scaling......Page 139
4.2.6 Domains and domain walls......Page 140
4.3 Coercivity......Page 145
4.3.1 Nucleation......Page 147
4.3.2 Pinning......Page 152
4.3.3 Phenomenological coercivity modeling......Page 156
4.4.1 Boundary conditions......Page 158
4.4.2 Spin structure at grain boundaries......Page 160
4.4.3 Models with atomic resolution......Page 161
4.4.4 Nanojunctions......Page 162
Exercises......Page 163
5 Finite-temperature magnetism......Page 166
5.1 Basic statistical mechanics......Page 167
5.1.1 Probability and partition function......Page 169
5.1.2 *Fluctuations and response......Page 170
5.1.3 Phase transitions......Page 172
5.1.4 Landau theory......Page 173
5.2 Spin-Space modeling......Page 176
5.2.1 Heisenberg models......Page 177
5.2.2 Ising, XY, and other n-vector models......Page 178
5.2.3 *Other discrete and continuum spin models......Page 179
5.2.4 Ionic excitations......Page 180
5.2.5 Spin fluctuations in itinerant magnets......Page 181
5.3 Mean-field models......Page 184
5.3.1 Mean-field Hamiltonians......Page 185
5.3.2 Basic mean-field predictions......Page 186
5.3.3 *Ornstein-Zernike correlations......Page 188
5.3.4 Magnetization and Curie temperature......Page 189
5.3.5 *Mean-field Curie temperature of n-vector models......Page 190
5.3.6 Two-sublattice magnetism......Page 191
5.3.7 Merits and limitations of mean-field models......Page 195
5.4 Critical behavior......Page 196
5.4.1 One-dimensional models......Page 197
5.4.2 Superparamagnetic clusters......Page 198
5.4.3 *Ginzburg criterion......Page 200
5.4.4 Fluctuations and criticality......Page 201
5.4.5 Renormalization group......Page 204
5.5 Temperature dependence of anisotropy......Page 207
5.5.1 Callen and Callen model......Page 208
5.5.2 Rare-earth anisotropy......Page 210
5.5.3 Sublattice modeling......Page 212
Exercises......Page 213
6.1 Quantum dynamics and resonance......Page 216
6.1.1 Spin precession......Page 218
6.1.2 Uniform magnetic resonance......Page 219
6.1.3 Spin waves......Page 220
6.1.4 Spin dynamics in inhomogeneous magnets*......Page 223
6.2 Relaxation......Page 225
6.2.1 Damped precession......Page 226
6.2.2 *Physical origin of relaxation......Page 227
6.2.3 *A mechanical model......Page 228
6.3 Coarse-grained models......Page 230
6.3.1 Master equation......Page 231
6.3.2 Fokker-Planck equations......Page 233
6.3.3 Langevin models......Page 235
6.4 Slow magnetization dynamics......Page 237
6.4.2 Superposition model of magnetic viscosity......Page 240
6.4.3 Asymptotic behavior*......Page 242
6.4.4 Energy-barrier models......Page 243
6.4.5 *Linear and other laws......Page 244
6.4.6 Superparamagnetism......Page 245
6.4.7 *Fluctuations......Page 246
Exercises......Page 250
7.1 Disordered magnets and spin glasses......Page 254
7.1.1 Atomic disorder and electronic structure......Page 255
7.1.2 *Green Functions......Page 256
7.1.3 Ferromagnetic order in inhomogeneous magnets......Page 259
7.1.4 Spin glasses......Page 261
7.2 Soft matter, transport, and magnetism......Page 264
7.2.1 Random walks, polymers, and diffusion......Page 265
7.2.2 *The n=0 vector-spin model......Page 266
7.2.3 Polymers and critical dimensionality......Page 267
7.2.4 Percolation......Page 269
7.2.5 Diffusive transport......Page 272
7.2.6 Gases in magnetic metals......Page 273
7.2.7 Magnetoresistance......Page 275
7.2.8 Other transport phenomena involving magnetism......Page 278
7.3.1 Static and dynamic properties......Page 280
7.3.2 *Parameterization......Page 282
7.3.3 *Self-consistent materials equations......Page 283
7.3.5 *Percolation in the Bruggeman model......Page 284
7.4 Nanostructures, thin films, and surfaces......Page 285
7.4.1 Length scales in nanomagnetism......Page 287
7.4.2 Nanomagnetic effects of atomic origin......Page 288
7.4.3 Random anisotropy......Page 291
7.4.4 *Cooperative magnetization processes......Page 294
7.4.5 Two-phase nanostructures......Page 296
7.5 Beyond magnetism......Page 299
7.5.1 Metallurgy......Page 300
7.5.2 Biology and medicine......Page 302
Exercises......Page 303
A.1.1 Units systems and notation......Page 306
A.2.1 Linear equations......Page 307
A.2.2 Eigenmode analysis......Page 309
A.2.3 Real 2 X 2 matrices......Page 310
A.2.4 Vector and functional calculus......Page 312
A.3 Basic quantum mechanics......Page 314
A.3.2 Eigenvalues and eigenfunctions......Page 315
A.3.3 Perturbation theory......Page 316
A.3.4 Quantum statistics......Page 317
A.3.5 Relativistic quantum mechanics......Page 319
A.4.1 Maxwells equations......Page 321
A.4.2 Simple magnetostatic solutions......Page 323
A.4.3 Simple dynamic solutions......Page 325
A.5 Magnetic materials......Page 326
A.5.1 Transition-metal elements and alloys......Page 327
A.5.3 Rare-earth magnets......Page 331
A.6 Forgotten and reinvented......Page 332
References......Page 336
A......Page 352
C......Page 353
D......Page 354
E......Page 355
F......Page 356
G......Page 357
I......Page 358
M......Page 359
N......Page 360
P......Page 361
S......Page 363
T......Page 365
Z......Page 366
