Thermal fluctuations and relaxation processes in nanomagnets / William T Coffey, Yuri P Kalmykov, Sergei V Titov.

Format:

Book

Author/Creator:

Coffey, William T., author.

Kalmykov, Yu. P., author.

Titov, Sergeĭ, 1951- author.

Language:

English

Subjects (All):

Magnetism.

Nanostructured materials--Magnetic properties.

Nanostructured materials.

Physical Description:

xxiii, 684 pages : illustrations ; 24 cm

Place of Publication:

Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., [2020]

Contents:

Machine generated contents note: ch. 1 Introductory Concepts

1.1. Introduction

1.2. Motion of magnetic moments: classical treatment

1.2.1. Larmor equation

1.2.2. Magnetic properties of solids

1.2.3. Magnetocrystalline anisotropy

1.2.4. Landau

Lifshitz and Gilbert equations

1.2.5. Bloch equation

1.3. Stochastic motion of the magnetization

1.3.1. Langevin equation for magnetic moment

1.3.2. Fokker

Planck equation for magnetic moments in configuration space

1.3.3. Spin-transfer torque (STT) effects in the magnetization dynamics

1.3.4. Method of statistical moments

1.3.5. Methods of solution of infinite sets of differential-recurrence equations

1.3.6. Calculation of observables

1.3.7. Langevin and Fokker

Planck equations for magnetic moments in energy space

1.3.8. Energy-controlled diffusion equation in the presence of STT

1.4. Magnetization relaxation times

1.4.1. Relaxation processes

1.4.2. Discrete orientation model

1.4.3. Mean first-passage time (MFPT)

1.4.4. MFPT for circularly symmetric free energy

1.4.5. MFPT in the VLD regime

1.4.6. MFPT in the VLD regime in the presence of STT

1.5. Escape-rate theory for classical spins

1.5.1. Transition state theory for spins

1.5.2. Kramers' escape rate for Brownian particles

1.5.3. Langer's treatment of the IHD regime

1.5.4. IHD escape rate for spins

1.5.5. VLD escape rate for spins by the Kramers method

1.5.6. Turnover escape rate for spins

1.6. Switching-field curves and surfaces

1.6.1. Stoner

Wolhfarth astroids

1.6.2. Effect of thermal agitation

1.7. Ferrofluids

1.8. Quantum treatment of the motion of spins

1.8.1. Early theories

1.8.2. Density matrix formulation of spin relaxation

1.8.3. Collision kernel in the Markov approximation

1.8.4. Method of statistical moments for quantum spins

1.9. Phase-space formulation of magnetization relaxation

1.9.1. Quasiprobability distribution functions for particles

1.9.2. The Wigner distribution function for particles

1.9.3. Application to transition state theory

1.9.4. Application to quantum Brownian motion

1.9.5. Quasiprobability distribution functions for spins

1.9.6. Spin phase-space distribution functions

1.9.7. Weyl symbols of some spin operators

1.9.8. Master equation and statistical moment equations for spin relaxation in phase space

1.10. Conclusion and Summary

ch. 2 Magnetization Relaxation And Resonance In Nanomagnets

2.1. Introduction

2.2. Reversal time of the magnetization at VLD: the MFPT approach

2.2.1. Reversal time for circularly symmetric potentials

2.2.2. VLD reversal time for uniaxial anisotropy with an oblique field

2.2.3. VLD reversal time for biaxial anisotropy

2.2.4. Comparison of analytical, asymptotic, and numerical results

2.2.5. STT effects on the magnetization reversal time at VLD

2.3. Magnetization reversal time in nanomagnets with noncircularly symmetric potentials: Kramers' escape-rate theory approach

2.3.1. Basic escape-rate equations for nanomagnets

2.3.2. Uniaxial nanomagnet in an oblique dc magnetic field

2.3.3. Biaxial nanomagnet in a uniform dc magnetic field applied along the easy axis

2.3.4. Reversal time for cubic anisotropy

2.3.5. Mixed anisotropy: breakdown of the paraboloid approximation

2.3.6. STT effects in the thermally assisted magnetization reversal

2.4. Magnetization relaxation in uniaxial nanomagnets

2.4.1. Longitudinal relaxation and dc field effect

2.4.1.1. Matrix solution

2.4.1.2. Matrix continued fraction solution

2.4.2. Characteristic times and magnetic susceptibility

2.4.3. Depletion effect in a biased bistable potential

2.4.4. Magnetic stochastic resonance in uniaxial nanomagnets

2.4.5. Transverse response: ferromagnetic resonance

2.5. Magnetization relaxation in nanomagnets with noncircularly symmetric anisotropy

2.5.1. Uniaxial nanomagnet in an oblique field

2.5.2. Cubic anisotropy

2.5.2.1. Complex susceptibility and relaxation times

2.5.2.2. Magnetic stochastic resonance in nanomagnets with cubic anisotropy

2.5.2.3. Effect of a dc bias field

2.6. Nonlinear stationary ac response of nanomagnets

2.6.1. Uniaxial nanomagnets

2.6.2. Biaxial nanomagnets

2.7. Dynamic magnetic hysteresis

2.7.1. DMH in uniaxial nanomagnets

2.7.2. DMH in biaxial nanomagnets

2.8. Spin-transfer torque effects

2.8.1. STT effects in the magnetization reversal

2.8.2. Nonlinear ac stationary response

2.8.3. Linear dynamic susceptibility

2.8.4. Nonlinear response

2.8.5. Dynamic magnetic hysteresis

2.9. Antiferromagnetic nanoparticles

2.10. Finite barrier correction for the ferromagnetic resonance frequency

2.10.1. FMR frequency for uniaxial anisotropy with a transverse magnetic field

2.10.2. FMR frequency for biaxial anisotropy

2.10.3. Mixed anisotropy: breakdown of the paraboloid approximation

2.11. Magnetization dynamics of two interacting spins in an external magnetic field

2.11.1. Exchange interaction

2.11.2. Dipole-dipole coupling

2.12. Concluding remarks

ch. 3 Quantum Effects In The Magnetization Relaxation Of Nanomagnets

3.1. Introduction

3.2. Equilibrium phase-space distribution functions for spins

3.2.1. Spins in a uniform external field

3.2.2. Uniaxial nanomagnet in an external field

3.2.3. Uniaxial nanomagnet in a transverse field

3.2.4. Biaxial anisotropy

3.2.5. Cubic anisotropy

3.2.6. TST reversal time

3.2.7. Switching-field curves

3.3. Master equation in phase space for circularly symmetric systems

3.3.1. Master equation for a uniaxial nanomagnet subjected to a dc magnetic field

3.3.2. Differential-recurrence relations for the statistical moments

3.3.3. Spin relaxation in a dc magnetic field

3.3.4. Quantum analog of the magnetic Langevin equation

3.3.5. Exact solution of the master equation for longitudinal relaxation

3.3.6. Nonlinear longitudinal relaxation time

3.3.7. Linear response

3.3.8. Single-mode approximation

3.3.9. Longitudinal relaxation of uniaxial nanomagnets

3.3.10. Analytic equations for the characteristic relaxation times and dynamic susceptibility

3.3.11. Nonlinear longitudinal relaxation in superimposed ac and dc magnetic fields

3.3.12. Dynamic magnetic hysteresis

3.3.13. Quantum effects in stochastic resonance

3.4. Master equation in phase space for noncircularly symmetric systems

3.4.1. Uniaxial nanomagnet subjected to a dc bias field of arbitrary orientation

3.4.2. Characteristic relaxation times and dynamic susceptibility

A.1. Relevant special functions and associated formulas

A.1.1. Gamma and related functions

A.1.2. Confluent hypergeometric (Kummer) functions

A.1.3. Error function

A.1.4. Hermite and Laguerre polynomials

A.1.5. Legendre polynomials

A.1.6. Modified Bessel functions of the first and second kinds

A.1.7. Spherical harmonics

A.1.8. Wigner's D-functions

A.1.9. Elliptic integrals and functions

A.1.10. Dirac-delta and Heaviside functions

A.2. Spin and polarization operators

A.3. Derivation of the master equation for a uniaxial paramagnet subjected to a dc magnetic field

A.4. Characteristic times of relaxation and correlation functions.

Notes:

Includes bibliographical references and index.

ISBN:

9811217270

9789811217272

OCLC:

1136874442