Non-Markovian magnetization dynamics for uniaxial nanomagnets

TL;DR

This paper introduces a stochastic model for nanomagnet magnetization dynamics that accounts for finite autocorrelation time of noise, bridging existing approximations, and validates it through numerical comparisons.

Contribution

It develops a unified stochastic framework interpolating between Landau-Lifshitz-Gilbert and Landau-Lifshitz-Bloch models, incorporating colored noise effects.

Findings

Hierarchy of magnetization moments can be closed with a truncation scheme.

The model's predictions agree with numerical solutions of Langevin equations.

Finite autocorrelation time influences magnetization response significantly.

Abstract

A stochastic approach for the description of the time evolution of the magnetization of nanomagnets is proposed, that interpolates between the Landau-Lifshitz-Gilbert and the Landau-Lifshitz-Bloch approximations, by varying the strength of the noise. Its finite autocorrelation time, i.e. when it may be described as colored, rather than white, is, also, taken into account and the consequences, on the scale of the response of the magnetization are investigated. It is shown that the hierarchy for the moments of the magnetization can be closed, by introducing a suitable truncation scheme, whose validity is tested by direct numerical solution of the moment equations and compared to the averages obtained from a numerical solution of the corresponding colored stochastic Langevin equation. This comparison is performed on magnetic systems subject to both an external uniform magnetic field and an internal one-site uniaxial anisotropy.