Closing the hierarchy for non-Markovian magnetization dynamics

TL;DR

This paper introduces a stochastic framework for modeling nanomagnet magnetization dynamics that bridges existing models, incorporates non-Markovian effects via colored noise, and validates a moment hierarchy closure through numerical comparisons.

Contribution

It develops a unified stochastic approach that interpolates between known magnetization models and accounts for finite autocorrelation times, closing the moment hierarchy with a validated truncation scheme.

Findings

The hierarchy closure is validated against numerical solutions.

Finite autocorrelation times significantly affect magnetization response.

The framework enables efficient coarse-grained simulations.

Abstract

We propose a stochastic approach for the description of the time evolution of the magnetization of nanomagnets, that interpolates between the Landau--Lifshitz--Gilbert and the Landau--Lifshitz--Bloch approximations, by varying the strength of the noise. In addition, we take into account the autocorrelation time of the noise and explore the consequences, when it is finite, on the scale of the response of the magnetization, i.e. when it may be described as colored, rather than white, noise and non-Markovian features become relevant. We close the hierarchy for the moments of the magnetization, by introducing a suitable truncation scheme, whose validity is tested by direct numerical solution of the moment equations and compared to the average deduced from a numerical solution of the corresponding stochastic Langevin equation. In this way we establish a general framework, that allows both coarse-graining simulations and faster calculations beyond the truncation approximation used here.