Combined dynamics of magnetization and particle rotation of a suspended superparamagnetic particle in the presence of an orienting field: Semi-analytical and numerical solution

Abstract

The magnetization dynamics of suspended superparamagnetic particles is governed by internal Néel relaxation as well as Brownian diffusion of the whole particle. We here present semi-analytical and numerical solutions of the kinetic equation, describing the combined rotation of particle orientation and magnetization. The solutions are based on an expansion of the joint probability density into a complete set of bipolar harmonics, leading to a coupled set of ordinary differential equations for the expansion coefficients. Extending previous works, we discuss the spectrum of relaxation times as well as convergence and limits of applicability of the method. Furthermore, we also provide the numerical scheme in electronic form, so that readers can readily implement and use the model.