Relaxation Processes in Micromagnetics (International Series of Monographs on Physics)

Contents......Page 16
Preface......Page 8
Notations and conventions......Page 18
1.1 Introduction......Page 20
1.2 Equations of motion......Page 23
1.2.1 Damping......Page 28
1.3 Approaching the Curie temperature......Page 30
2.2 Models of small motions......Page 36
2.2.1 Distributive damping......Page 38
2.2.2 Instabilities and spin wave condensates......Page 40
3.2 Magnetostrictive coupling......Page 50
3.2.1 Small samples......Page 51
3.2.2 Large, homogeneous samples......Page 54
3.3 Loss torque in magnetic metals......Page 62
3.3.1 Eddy current damping......Page 63
3.3.2 Direct coupling of conduction electrons to the magnetization field......Page 68
3.4 Fluctuations in medium properties......Page 76
3.5 Relaxation due to weakly coupled magnetic impurities......Page 79
3.5.1 Slow relaxation......Page 80
3.5.2 Corrections to the adiabatic limit......Page 83
3.6 Appendix 3A. Inclusion of displacement current in Section 3.3.1......Page 86
4.1 Introduction......Page 90
4.2 Fluctuation-dissipation theorem......Page 93
4.3 Langevin equation, and generalized Langevin equation......Page 96
4.4 Fokker-Planck equation–cartesians......Page 104
4.4.1 Fokker-Planck equation in polar angles......Page 107
4.4.2 Fokker-Planck equation in the absence of well-defined canonical variables......Page 108
5.1 Introduction......Page 116
5.2 General observations......Page 117
5.3 Reversal in 2d......Page 121
5.3.1 Reversal in the long time limit......Page 128
5.3.2 Intermediate time scales......Page 133
5.3.3 Applied field and anisotropy axis misaligned......Page 137
5.3.4 Relation to first-passage type theories......Page 138
5.4 Rotation in 3d......Page 141
6.1 Introduction......Page 144
6.2 Relaxation due to magnetic moment interaction in a sparse medium......Page 146
6.2.1 Equations of motion for dipolar interaction......Page 147
6.2.2 A single pair......Page 149
6.3 More dense arrays of many interacting particles......Page 158
6.3.1 The Arnold web......Page 160
6.3.2 Relevance to magnetic relaxation and reversal......Page 162
6.3.3 Effective single-variable relaxation from causes other than chaos......Page 164
6.4 Magnetization reversal and the magnetization process in large, dense systems......Page 165
6.4.1 Simple model of magnetization reversal by domain wall motion......Page 168
6.4.2 Motion of a Bloch domain wall......Page 179
6.4.3 Magnetostatics and the magnetization process. Pre-existing domain walls......Page 182
6.5 Appendix 6A: Vortex solutions in cylinder and disc: stability considerations......Page 195
References......Page 204
N......Page 208
Z......Page 209