NONLINEAR ADIABATIC DYNAMICS OF SMALL FERROMAGNETIC PARTICLES

Abstract

The purpose of this work is to present an analytical description of dynamics of small ferromagnetic particles with uniaxial anisotropy and the slowly varying magnetic field applied at an arbitrary angle to the anisotropy axis. Considerable attention is given to the nonlinear aspects of adiabatic dynamics. Theoretical analysis based on the consideration of the Landau–Lifshitz–Gilbert equation employs an asymptotic expansion similar to the famous semi-classical WKBJ solution of quantum mechanics equations. The small parameter of the expansion is the ratio of characteristic frequency of the applied magnetic field to the precession frequency. The nonlinear equation describing the slow dynamics of small ferromagnetic particles is derived. The applicability conditions of the developed theory are presented. The nonlinear corrections to the precessional frequency are derived. It is shown that in numerical simulation using the Landau–Lifshitz–Gilbert equation it is not possible to neglect precessional terms at long simulation times due to the nonlinear dynamic correction to a position of the orbit center.