Linear and nonlinear superparamagnetic relaxation at high anisotropy barriers

TL;DR

This paper derives compact, practically exact formulas for superparamagnetic relaxation times and susceptibilities of uniaxial particles at high anisotropy barriers, improving upon previous models and applicable to textured or random assemblies.

Contribution

It introduces asymptotic series solutions to the micromagnetic Fokker-Planck equation, providing new formulas for relaxation and susceptibilities at high anisotropy barriers.

Findings

Formulas are compact and nearly exact at low frequencies.

Angular dependencies enable analysis of textured and random particle assemblies.

Advances previous two-level models for nonlinear superparamagnetic relaxation.

Abstract

The micromagnetic Fokker-Planck equation is solved for a uniaxial particle in the low-temperature limit. Asymptotic series in the parameter that is the inverse barrier height-to-temperature ratio are derived. With the aid of these series, the expressions for the superparamagnetic relaxation time and the odd-order dynamic susceptibilities are presented. The obtained formulas are both quite compact and practically exact in the low (with respect to FMR) frequency range that is proved by comparison with the numerically-exact solution of the micromagnetic equation. The susceptibilities formulas contain angular dependencies that allow to consider textured as well as randomly oriented particle assemblies. Our results advance the previous two-level model for nonlinear superparamagnetic relaxation.