Preface vii
Notations and conventions xvii
1 The Classical Magnetization Field 1
1.1 Introduction 1
1.2 Equations of motion 4
1.2.1 Damping 9
1.3 Approaching the Curie temperature 11
2 Small motions of the Magnetization 17
2.1 Introduction 17
2.2 Models of small motions 17
2.2.1 Distributive damping 19
2.2.2 Instabilities and spin wave condensates 21
3 Intrinsic Damping 31
3.1 Introduction 31
3.2 Magnetostrictive coupling 31 Preface vii
Notations and conventions xvii
1 The Classical Magnetization Field 1
1.1 Introduction 1
1.2 Equations of motion 4
1.2.1 Damping 9
1.3 Approaching the Curie temperature 11
2 Small motions of the Magnetization 17
2.1 Introduction 17
2.2 Models of small motions 17
2.2.1 Distributive damping 19
2.2.2 Instabilities and spin wave condensates 21
3 Intrinsic Damping 31
3.1 Introduction 31
3.2 Magnetostrictive coupling 31
3.2.1 Small samples 32
3.2.2 Large, homogeneous samples 35
3.3 Loss torque in magnetic metals 43
3.3.1 Eddy current damping 44
3.3.2 Direct coupling of conduction electrons to the
magnetization field 49
3.4 Fluctuations in medium properties 57
3.5 Relaxation due to weakly coupled magnetic impurities 60
3.5.1 Slow relaxation 61
3.5.2 Corrections to the adiabatic limit 64
3.6 Appendix 3A. Inclusion of displacement current in
Section 3.3.1 67
4 Fluctuations 71
4.1 Introduction 71
4.2 Fluctuation-dissipation theorem 74
4.3 Langevin equation, and generalized Langevin equation 77
4.4 Fokker-Planck equation-cartesians 85
4.4.1 Fokker-Planck equation in polar angles 88
4.4.2 Fokker-Planck equation in the absence of well-defined
canonical variables 89
5 Magnetization Reversal in a Very Dilute Array of Small
Particles 97
5.1 Introduction 97
5.2 General observations 98
5.3 Reversal in 2d 102
5.3.1 Reversal in the long time limit 109
5.3.2 Intermediate time scales 114
5.3.3 Applied field and anisotropy axis misaligned 118
5.3.4 Relation to first-passage type theories 119
5.4 Rotation in 3d 122
6 Magnetization Reversal in Arrays of Particles and
Continuous Media 125
6.1 Introduction 125
6.2 Relaxation due to magnetic moment interaction in
a sparse medium 127
6.2.1 Equations of motion for dipolar interaction 128
6.2.2 A single pair 130
6.3 More dense arrays of many interacting particles 139
6.3.1 The Arnold web 141
6.3.2 Relevance to magnetic relaxation and reversal 143
6.3.3 Effective single-variable relaxation from causes other than
chaos 145
6.4 Magnetization reversal and the magnetization process in
large, dense systems 146
6.4.1 Simple model of magnetization reversal by domain wall
motion 149
6.4.2 Motion of a Bloch domain wall 160
6.4.3 Magnetostatics and the magnetization process.
Pre-existing domain walls 163
6.5 Appendix 6A: Vortex solutions in cylinder and disc: stability
considerations 176
References 185
Subject Index 189