Magnetic relaxation of a system of superparamagnetic particles weakly coupled by dipole-dipole interactions

TL;DR

This paper investigates how long-range dipole-dipole interactions influence the thermal relaxation dynamics of superparamagnetic particles, providing a modified model for relaxation times in weakly coupled systems.

Contribution

It introduces a modified approach to estimate superparamagnetic relaxation times considering dipole-dipole interactions, extending previous models that neglected such correlations.

Findings

Derived a nonlinear Fokker-Planck equation for the system

Estimated relaxation time scale with dipole interactions

Provided a simple correction to existing relaxation asymptotes

Abstract

The effect of long range dipole-dipole interactions on the thermal fluctuations of the magnetization of an assembly of single-domain ferromagnetic particles is considered. If orientational correlations between the particles are neglected, the evolution of the magnetization orientations may be described by a nonlinear Fokker-Planck equation (FPE) reducing to the usual linear one in the limit of infinite dilution [W.F. Brown Jr, Phys. Rev. 130, 1677 (1963)]. The thermally activated relaxation time scale of the assembly is estimated, leading to a simple modification of the axially symmetric asymptotes for the superparamagnetic relaxation time.