Yuri P. Kalmykov

Thermal fluctuations of magnetic nanoparticles: Fifty years after Brown

The reversal time, superparamagnetic relaxation time, of the magnetization of fine single domain ferromagnetic nanoparticles owing to thermal fluctuations plays a fundamental role in information storage, paleomagnetism, biotechnology, etc. Here a comprehensive tutorial-style review of the achievements of fifty years of development and generalizations of the seminal work of Brown [Phys. Rev. 130, 1677 (1963)] on thermal fluctuations of magnetic nanoparticles is presented. Analytical as well as numerical approaches to the estimation of the damping and temperature dependence of the reversal time based on Browns Fokker-Planck equation for the evolution of the magnetic moment orientations on the surface of the unit sphere are critically discussed while the most promising directions for future research are emphasized.

The relaxation time of the magnetization of uniaxial single-domain ferromagnetic particles in the presence of a uniform magnetic field

The relaxation time of the magnetization of uniaxial single-domain ferromagnetic particles is evaluated for magnetic field applied to an arbitrary angle to the easy axis in the entire dissipation range, i.e., for very low damping (VLD), intermediate-to-high damping (IHD), and crossover values. The calculations are based on the Mel’nikov-Meshkov method [J. Chem. Phys. 85, 1018 (1986)] for bridging the VLD and IHD Kramers escape rates for mechanical particles (the Kramers turnover problem) as extended by Coffey et al. [Adv. Chem. Phys. 117, 483 (2001); Phys. Rev. E 63, 021102 (2001)] to the analogous magnetic spin problem. It is shown that the analytical results are in complete agreement with the relaxation time calculated numerically from the solution of the stochastic Landau-Lifshitz-Gilbert equation.

Analytical solutions for rotational diffusion in the mean field potential: application to the theory of dielectric relaxation in nematic liquid crystals

A theory of dielectric relaxation in nematics is developed for a molecular dipole moment directed at an arbitrary angle to the molecular long axis. Both exact and simple approximate analytical formulae for the longitudinal and transverse components of the complex dielectric permittivity tensor are obtained for the non-inertial rotational Brownian motion of a molecule in the mean field potential of Maier and Saupe. It appears that both longitudinal and transverse relaxation processes are effectively described by two Debye type mechanisms with corresponding relaxation times and dielectric strengths expressed in terms of the order parameter. The generalization of the theory for an arbitrary axially symmetric mean field potential is given.

Analytic calculation of the longitudinal dynamic susceptibility of uniaxial superparamagnetic particles in a strong uniform DC magnetic field

Abstract A simple analytic equation which allows one to obtain a qualitative understanding of the physical processes underlying the behavior of the longitudinal complex susceptibility χ || ( ω ) of an assembly of noninteracting uniaxial superparamagnetic particles subjected to a strong external uniform DC magnetic field is derived in the context of Browns model of magnetic relaxation. It is shown that a knowledge of 3 time constants characterizing the magnetization relaxation, viz. the integral relaxation time τ , the effective relaxation time τ ef , and the inverse of the smallest eigenvalue λ 1 of the Fokker–Planck operator are sufficient to accurately predict the spectrum of χ || ( ω ) in all frequency ranges of interest as well as the behavior of the equilibrium correlation function of the longitudinal component of the magnetization C || ( t ) in the time domain at all values of the barrier and external field parameters.

Relaxation of the magnetization in uniaxial single-domain ferromagnetic particles driven by a strong ac magnetic field

The magnetization spectrum and reversal time of uniaxial single-domain ferromagnetic particles driven by an ac magnetic field of arbitrary strength applied along the easy axis are evaluated by solving the infinite hierarchy of recurrence equations for the Fourier components of the relaxation functions governing the frequency dependence of the magnetization. A simple analytic equation for the reversal time is also obtained via the mean first passage time method exhibiting pronounced nonlinear effects such as a rapid decrease in the reversal time as the strength of the ac field increases. For weak ac fields, the results agree with perturbation theory.

Nonlinear stationary ac response of the magnetization of uniaxial superparamagnetic nanoparticles

The nonlinear stationary ac response of the magnetization of assemblies consisting of (i) noninteracting uniaxial superparamagnetic nanoparticles with aligned easy axes and (ii) randomly oriented nanoparticles subjected to superimposed ac and dc bias magnetic fields of arbitrary strength and orientation is calculated by averaging Gilbert’s equation augmented by a random field. The magnetization dynamics of uniaxial particles driven by a strong ac field applied at an angle to the easy axis of the particle (so that the axial symmetry is broken) alters drastically leading to new nonlinear effects due to coupling of the thermally activated magnetization reversal mode with the precessional modes via the driving ac field. In particular, the high frequency response reveals significant nonlinear effects in the precessional motion with significant consequences for the dynamic hysteresis and ultra-fast switching of the magnetization following an ultrafast change in the applied field.

Recent advances in broadband dielectric spectroscopy

Introduction.- List of Contributors.- Dielectric Relaxation of Water in Complex Systems Y. Feldman et al.- High-Frequency Dielectric Response of Hydrogen-Bonded Liquids between 0.2 and 2.5 THz Y. Yomogida et al.- Anomalous Diffusion, Cole-Cole Relaxation, and the Space in which they Occur: Puzzles and Problems P. Ben Ishai et al.- Complex Dielectric Permittivity of Metal-Containing Nanocomposites: Non-Phenomenological Description M.A. Kozhushner, L.I. Trakhtenberg.- State of Water In Confinement Near Hydrophilic Surfaces below the Freezing Temperature A. Greenbaum et al.- Dielectric Properties and Applications of CVD Diamonds in Millimeter and Terahertz Ranges B.M. Garin et al.- Nonlinear Susceptibility Experiments in a Supercooled Liquid: Evidence of Growing Spatial Correlations to Tg C. Brun et al.- On the Calculation of the Dielectric Properties of Liquid Ionic Systems M. Sega et al.- Applications and Implications of Fractional Dynamics for Dielectric Relaxation R. Hilfer.- Spectral Definition of the Characteristic Times for Anomalous Diffusion in a Potential Y.P. Kalmykov et al.- High-Frequency Resonance Absorption as Evidence for Oscillation in a Well before Escape from a Metastable State in the Kramers Energy Controlled Diffusion Model W.T. Coffey et al.- Molecular Dynamics of Polymers at Nanometric Length Scales: From Thin Layers to Isolated Coils F. Kremer et al.- Fractional Klein-Kramers Equations: Subdiffusive and Superdiffusive Cases R. Metzler.- Index.-

Solution of the master equation for Wigner's quasiprobability distribution in phase space for the Brownian motion of a particle in a double well potential

Quantum effects in the Brownian motion of a particle in the symmetric double well potential V(x)=ax(2)2+bx(4)4 are treated using the semiclassical master equation for the time evolution of the Wigner distribution function W(x,p,t) in phase space (x,p). The equilibrium position autocorrelation function, dynamic susceptibility, and escape rate are evaluated via matrix continued fractions in the manner customarily used for the classical Fokker-Planck equation. The escape rate so yielded has a quantum correction depending strongly on the barrier height and is compared with that given analytically by the quantum mechanical reaction rate solution of the Kramers turnover problem. The matrix continued fraction solution substantially agrees with the analytic solution. Moreover, the low-frequency part of the spectrum associated with noise assisted Kramers transitions across the potential barrier may be accurately described by a single Lorentzian with characteristic frequency given by the quantum mechanical reaction rate.

Extended rotational diffusion and dielectric relaxation in liquid solutions

The complex dielectric permittivity for a dilute solution of polar molecules dissolved in a nonpolar solvent is calculated in the context of a generalized J-diffusion model. This model takes into account both inertial effects and finite duration of collisions. The theory is compared with experimental far-infrared absorption spectra of HCl and DCl in nonpolar solvents.

Calculation of orientational correlation functions for free anisotropic rotational diffusion revisited

A simple matrix method for evaluating the orientational correlation functions of arbitrary rank j pertaining to free noninertial anisotropic rotational diffusion of rigid Brownian particles is presented. The first- and second-rank correlation functions are calculated analytically for a diagonal diffusion tensor.