Nonlinear ac stationary response and dynamic magnetic hysteresis of quantum uniaxial superparamagnets

The nonlinear ac stationary response of uniaxial paramagnets and superparamagnets - nanoscale solids or clasters with spin number S ~ 10^0 - 10^4 - in superimposed uniform ac and dc bias magnetic fields of arbitrary strength, each applied along the easy axis of magnetization, is determined by solving the evolution equation for the reduced density matrix represented as a finite set of three-term differential-recurrence relations for its diagonal matrix elements. The various harmonic components of the magnetization, dynamic magnetic hysteresis loops, etc. are then evaluated via matrix continued fractions indicating a pronounced dependence of the nonlinear response on S arising from the quantum spin dynamics. In the linear response approximation, the results concur with existing solutions.Comment: 28 pages, 10 figures, 33 refererence

Reversal time of the magnetization of magnetic nanoparticles at very low damping

The magnetization reversal time of ferromagnetic nanoparticles is investigated in the very low damping regime. The energy-controlled diffusion equation rooted in a generalization of the Kramers escape rate theory for point Brownian particles in a potential to the magnetic relaxation of a macrospin, yields the reversal time in closed integral form. The latter is calculated for a nanomagnet with uniaxial anisotropy with a uniform field applied at an angle to the easy axis and for a nanomagnet with biaxial anisotropy with the field along the easy axis. The results completely agree with those yielded by independent numerical and asymptotic methods.Comment: An extended version: 28 pages; 5 figures; Mathematica Program

Investigation of the Thickness Mode in Surface Stabilized Ferroelectric Liquid Crystal Cells

Dielectric properties of surface stabilized ferroelectric liquid crystal (SSFLC) cells have been investigated both experimentally and theoretically. The thickness mode is found to consist of two relaxation processes. A decomposition of an analytical solution of the complex dielectric permittivitye(v) in terms ofthese processesis given. Theexperimental results showagreement with theory and lead to the conclusion that the thickness mode can be separated into two processes. It has been found that the ratio of the dielectric strengths for the two processes depends on the cell thickness, and that the ratio of their frequencies is approximately equal to 10. The lower frequency process is assigned to the relaxation within the bulk and the higher frequency process is assigned to the ¯uctuations of molecules at the two surfaces of the cell. The latter process is seen only in thicker cells for the reason that anchoring at surfaces predominantly controls the behaviour of thinner cells

Phase space master equations for quantum Brownian motion in a periodic potential: comparison of various kinetic models

The dynamics of quantum Brownian particles in a cosine periodic potential are studied using the phase space formalism associated with the Wigner representation of quantum mechanics. Various kinetic phase space master equation models describing quantum Brownian motion in a potential are compared by evaluating the dynamic structure factor and escape rate from the differential recurrence relations generated by the models. The numerical solution is accomplished via matrix continued fractions in the manner customarily used for the classical Fokker-Planck equation. The results of numerical calculations of the escape rate from a well of the cosine potential are compared with those given analytically by the quantum-mechanical reaction rate theory solution of the Kramers turnover problem for a periodic potential, given by Georgievskii and Pollak (1994 Phys. Rev. E 49 5098), enabling one to appraise each model

Dynamique de l'aimantation des particules superparamagnétique avec anisotropie triaxiale

Dans ce travail, nous avons effectué des études théoriques sur le processus de relaxation de l aimantation des nanoparticules superparamagnétiques avec une anisotropie triaxiale (orthorhombique). Dans le contexte du modèle de Néel-Brown, nous avons obtenu les solutions numériques et analytiques de l équation de Fokker-Planck-Brown qui décrit la dynamique de l aimantation de la particule monodomaine. Le processus de relaxation magnétique est caractérisé par le temps de relaxation de l aimantation le plus long, les temps intégraux et effectifs. Dans le domaine des fréquences, il est caractérisé par les composantes longitudinale et transversales du tenseur de la susceptibilité magnétique. Les résultats des calculs numériques nous ont donnés la possibilité d évaluer ces grandeurs importantes avec beaucoup d habilités pour les valeurs typiques de la constante de dissipation a, de la température T, des constantes d anisotropie et la pulsation en absence ou en présence d un champ magnétique uniforme extérieur H0. En utilisant l approche de Kramers-Brown-Coffey, nous avons déduit les équations analytiques pour les temps de relaxation de l aimantation et pour les composantes longitudinale et transversale de la susceptibilité magnétique. Ces équations sont en accord complet avec les résultats du calcul numérique. Elles ont des formes simples et nous permettent de comprendre le comportement qualitatif des temps de relaxation de l aimantation et des spectres de la susceptibilité magnétiques dans toute la gamme de variation des paramètres physiques (température, pulsation, champ extérieur, et constante de dissipation).In this thesis, a theoretical study of the dynamics of the magnetization of superparamagnetic nanoparticles with triaxial (orthorhombic) anisotropy has been carried out using the Néel-Brown model. Numerical and analytical solutions of the Fokker-Planck equation given by Brown, which describes the relaxation of the magnetization in the nanoparticles, have been obtained in order to facilitate this study. The process of relaxation of the magnetization is characterized by the longest relaxation time, integral relaxation time, and, in the frequency domain, by the longitudinal and transverse components of the magnetic susceptibility tensor. The numerical solutions allows us to evaluate these characteristics for typical values of the dissipation constant a, temperature T, anisotropy constants with and without a uniform external magnetic field H0. By using the approach of Kramers-Brown-Coffey, analytical equations for the magnetization relaxation times and for the longitudinal and transversals components of the magnetic susceptibility have been deduced. These analytical equations are in complete agreement with the results of our numerical calculations. They have simple analytical forms and allow one to quantify the dependence of the relaxation times and the magnetic susceptibility on the temperature T, angular frequency , strength of the external field H, and dissipation constant a. Moreover they can be used to estimate the relaxation times and the magnetic susceptibility in wide ranges of variation of T,, H, and a. The results obtained may be considered as a complete solution of the problem of relaxation of the magnetization in nano particles with triaxial anisotropyPERPIGNAN-BU Sciences (661362101) / SudocSudocFranceF