Colored-noise magnetization dynamics: from weakly to strongly correlated noise

TL;DR

This paper develops and compares models for magnetization dynamics under colored noise with varying correlation times, demonstrating their equivalence even for strongly correlated noise.

Contribution

It introduces a non-Markovian integration model for magnetization dynamics and validates its consistency with existing formalisms across different noise correlation regimes.

Findings

Models remain equivalent for weakly correlated noise.

Validation of models for strongly correlated noise.

Extension of the applicability of the formalism.

Abstract

Statistical averaging theorems allow us to derive a set of equations for the averaged magnetization dynamics in the presence of colored (non-Markovian) noise. The non-Markovian character of the noise is described by a finite auto-correlation time, tau, that can be identified with the finite response time of the thermal bath to the system of interest. Hitherto, this model was only tested for the case of weakly correlated noise (when tau is equivalent or smaller than the integration timestep). In order to probe its validity for a broader range of auto-correlation times, a non-Markovian integration model, based on the stochastic Landau-Lifshitz-Gilbert equation is presented. Comparisons between the two models are discussed, and these provide evidence that both formalisms remain equivalent, even for strongly correlated noise (i.e. tau much larger than the integration timestep).