Colored-Noise Magnetization Dynamics: From Weakly to Strongly Correlated Noise

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, τ, 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 τ 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., τ much larger than the integration timestep).