图书简介
Presenting in a coherent and accessible fashion current results in nanomagnetism, this book constitutes a comprehensive, rigorous and readable account, from first principles of the classical and quantum theories underlying the dynamics of magnetic nanoparticles subject to thermal fluctuations.
Starting with the Larmor-like equation for a giant spin, both the stochastic (Langevin) equation of motion of the magnetization and the associated evolution (Fokker–Planck) equation for the distribution function of the magnetization orientations of ferromagnetic nanoparticles (classical spins) in a heat bath are developed along with their solution (using angular momentum theory) for arbitrary magnetocrystalline-Zeeman energy. Thus, observables such as the magnetization reversal time, relaxation functions, dynamic susceptibilities, etc. are calculated and compared with the predictions of classical escape rate theory including in the most general case spin-torque-transfer. Regarding quantum effects, which are based on the reduced spin density matrix evolution equation in Hilbert space as is described at length, they are comprehensively treated via the Wigner–Stratonovich formulation of the quantum mechanics of spins via their orientational quasi-probability distributions on a classically meaningful representation space. Here, as suggested by the relevant Weyl symbols, the latter is the configuration space of the polar angles. Hence, one is led, by mapping the reduced density matrix equation onto that space, to a master equation for the quasi-probability evolution akin to the Fokker–Planck equation which may be solved in a similar way. Thus, one may study in a classical-like manner the evolution of observables with spin number ranging from an elementary spin to molecular clusters to the classical limit, viz. a nanoparticle. The entire discussion hinges on the one-to-one correspondence between polarization operators in Hilbert space and the spherical harmonics allied to concepts of spin coherent states long familiar in quantum optics.
Catering for the reader with only a passing knowledge of statistical and quantum mechanics, the book serves as an introductory text on a complicated subject where the literature is remarkably sparse.
Introductory Concepts: Introduction; Motion of Magnetic Moments: Classical Treatment; Stochastic Motion of the Magnetization; Magnetization Relaxation Times; General Principles of Escape-Rate Theory for Classical Spins; Switching-Field Curves and Surfaces; Ferrofluids; Quantum Treatment of the Motion of Spins; Phase-Space Formulation of Magnetization Relaxation; Conclusion and Summary; Stochastic Dynamics of Classical Spins: Introduction; Reversal Time of the Magnetization at Very Low Damping: The Mean-First-Passage Time (MFPT) Approach; Magnetization Reversal Time in Nanomagnets with Non-Circularly Symmetric Potentials: Kramers’ Escape-Rate Theory Approach; Magnetization Relaxation in Uniaxial Nanomagnets; Magnetization Relaxation in Nanomagnets with Non-Circularly Symmetric Anisotropy; Nonlinear Stationary AC Response of Nanomagnets; Dynamic Magnetic Hysteresis; Spin-Transfer Torque Effects; Antiferromagnetics; Finite Barrier Correction for the Ferromagnetic Resonance Frequency; Magnetization Dynamics of Two Interacting Spins in an External Magnetic Field; Concluding remarks; Quantum Effects in the Magnetization Relaxation of Nanomagnets: Density Matrix and Phase-Space Formulations of Relaxation Phenomena in Spin Systems; Equilibrium Phase-Space Distribution Functions for Spins; Master Equation in Phase Space for Circularly Symmetric Systems; Master Equation in Phase Space for Non-Circularly Symmetric Systems; Appendix Special Functions, Operators, etc.: Relevant Special Functions and Associated Formulas; Spin and Polarization Operators; Derivation of the Master Equation for a Uniaxial Paramagnet Subjected to a DC Magnetic Field; Characteristic Times of Relaxation and Correlation Functions;
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