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Nonequilibrium Magnons: Theory, Experiment and Applications

Overview

This much-needed book addresses the concepts, models, experiments and applications of magnons and spin wave in magnetic devices. It fills the gap in the current literature by providing the theoretical and technological framework needed to develop innovative magnetic devices, such as recording devices and sensors.

Starting with a historical review of developments in the magnon concept, and including original experimental results, the author presents methods of magnon excitation, ...

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Overview

This much-needed book addresses the concepts, models, experiments and applications of magnons and spin wave in magnetic devices. It fills the gap in the current literature by providing the theoretical and technological framework needed to develop innovative magnetic devices, such as recording devices and sensors.

Starting with a historical review of developments in the magnon concept, and including original experimental results, the author presents methods of magnon excitation, and several basic models to describe magnon gas. He includes experiments on Bose-Einstein condensation of non-equilibrium magnons, as well as various applications of a magnon approach.

In short, the focus is on

1) new principles of energy transformation from noise to a coherent oscillations (chapters 5,6, appendix G)

2) new method of computing - chapter 8.

Suitable for those who do not work directly with magnetic systems, this book can provide several ideas and analogies that can be useful in their work and research.

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Product Details

  • ISBN-13: 9783527411177
  • Publisher: Wiley
  • Publication date: 1/14/2013
  • Edition number: 1
  • Pages: 204
  • Product dimensions: 6.80 (w) x 9.70 (h) x 0.60 (d)

Meet the Author

Dr. Vladimir L Safonov , a multi-disciplined scientist, world level expert on magnetic dynamics, is Chief Scientist at Mag & Bio Dynamics and Expert at Skolkovo Foundation. He graduated from Moscow Institute of Physics and Technology and obtained his Ph.D. and D.Sc. (Habilitation) degrees from the Russian Research Center "Kurchatov Institute". He has collaborated with research groups in Russia, Ukraine, Germany, Japan and U.S.A. Dr. Safonov has authored over 110 scientific publications and patents and has received many awards, including the Kurchatov Prize. He is a Senior member of IEEE and a member of the American Physical Society.

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Table of Contents

Preface XI

1 Harmonic Oscillators and the Universal Language of Science 1

1.1 Harmonic Oscillator 1

1.1.1 Complex Canonical Variables 3

1.2 Classical Rotation 4

1.2.1 Classical Spin and Magnetic Resonance 5

1.3 Collective Variables and Harmonic Oscillators in k-space 8

1.3.1 Chain of Masses and Springs 8

1.3.2 Chain of Magnetic Particles 9

1.4 Discussion 11

2 Magnons in Ferromagnets and Antiferromagnets 13

2.1 Phenomenological Description 14

2.1.1 Magnons in a Ferromagnet 14

2.1.1.1 Holstein–Primakoff Transformation 16

2.1.1.2 The Spectrum of Magnons 19

2.2 Microscopic Modeling 21

2.2.1 Magnons in a Two-Sublattice Antiferromagnet 21

2.2.1.1 Hamiltonian 21

2.2.1.2 Spectrum of Magnons 25

2.2.2 Magnon–Magnon Interactions 26

2.3 Nuclear Magnons 28

2.4 Magnetoelastic Waves, Quasi Phonons 30

2.5 Discussion 33

3 Relaxation of Magnons 35

3.1 Master Equation 35

3.2 Relaxation of Bose Quasi Particles 37

3.2.1 Relaxation Process of Harmonic Oscillators 37

3.2.2 Magnon–Electron Scattering 39

3.3 Relaxation via an Intermediate Damped Dynamic System 43

3.4 Ferromagnetic Resonance Linewidth 46

3.5 Magnons and Macroscopic Dynamic Equation 49

3.5.1 Linearized Landau–Lifshitz Equation 50

3.6 Relaxation of Coupled Oscillations 51

3.6.1 Example 1: Nuclear Magnons 53

3.6.2 Example 2: Magnetoelastic Oscillations 54

3.7 Discussion 57

4 Microwave Pumping of Magnons 59

4.1 Linear Theory 60

4.1.1 Ferromagnetic Resonance 61

4.1.2 Threshold of Parametric Resonance 61

4.2 Parametric Resonance in a Resonator Cavity 63

4.3 Nonlinear SR Theory 67

4.4 Experimental Techniques 71

4.5 Experimental Results 73

4.5.1 Equivalent Circuit 74

4.5.2 SR Theory and Experiment 76

4.5.2.1 Modulation Response 79

4.6 Discussion 83

5 Thermodynamic Description of Strongly Excited Magnon System 85

5.1 Principal Equations 86

5.1.1 Hamiltonian 86

5.1.2 Unitary Transformation 87

5.1.3 Bogoliubov Transformation 88

5.1.4 Effective Temperature Teff D 0 90

5.1.5 Effective Temperature Teff ¤ 0 91

5.1.5.1 Maximum of Entropy 93

5.2 Exact Solutions 94

5.2.1 The Effective Temperature 96

5.2.1.1 Instantaneous Switching 96

5.2.1.2 Adiabatic Switching 97

5.2.1.3 Thermodynamic Stability 97

5.2.2 Collective Oscillations 98

5.3 Magnon Pumping in a Resonator 100

5.4 Discussion 101

6 Bose–Einstein Condensation of Quasi Equilibrium Magnons 103

6.1 Bose Gas of Magnons 103

6.1.1 Ideal Bose Gas 103

6.1.2 Mathematical Analogy with BEC 105

6.2 Quasi EquilibriumMagnons 105

6.2.1 Ideal Gas of Quasi Equilibrium Magnons 107

6.2.2 Example: Isotropic Spectrum 107

6.2.3 Kinetic Equations 109

6.2.3.1 The Case of Teff D T 111

6.2.4 Magnon System with Bose Condensate 113

6.2.5 Magnetodipole Emission of Condensate 114

6.3 Fröhlich Coherence 115

6.4 Discussion 118

7 Magnons in an Ultrathin Film 119

7.1 Model 120

7.1.1 Magnetic Energy 121

7.2 Magnons 122

7.2.1 Magnon Interactions 124

7.2.2 Effective Four-Magnon Interactions 125

7.3 Example 126

7.4 Discussion 129

8 Collective Magnetic Dynamics in Nanoparticles 131

8.1 Long-Lived States in a Cluster of Coupled Nuclear Spins 134

8.2 Electronic Spins 136

8.3 Spin-Echo Logic Operations 138

Appendix A Harmonic Oscillator in Quantum Mechanics 143

A.1 Operators of Creation and Annihilation 143

A.1.1 Uncertainty Principle 144

A.1.2 Coherent States and Uncertainties 145

Appendix B Dipolar Sums 147

Appendix C Unitary Transformations in Weakly Nonideal Bose Gases 151

C.1 One-Component Bose Gas 152

C.1.1 Three-Boson Annihilation 154

C.1.2 The Confluence and Decay Processes 155

C.2 Two-Component Bose Gas 156

C.3 Concluding Remarks 158

Appendix D Magnetization Dynamic Equation 159

Appendix E A Parametric Pair Single-Mode Realization 163

E.1 A Single-Mode Representation 164

E.2 Example 166

Appendix F Small Signal Amplification and Preventive Alarm Near the Onset of a Dynamic Instability 167

Appendix G Noisy Pumping of Coherent Parametric Pairs 173

G.1 Experimental Procedure 174

G.2 Results and Discussion 175

G.2.1 Discussion 177

References 179

Index 189

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