Adaptively time stepping the stochastic Landau-Lifshitz-Gilbert equation at nonzero temperature: Implementation and validation in MuMax3

摘要

Thermal fluctuations play an increasingly important role in micromagnetic researchrelevant for various biomedical and other technological applications. Until now, it wasdeemed necessary to use a time stepping algorithm with a fixed time step in order toperform micromagnetic simulations at nonzero temperatures. However, Berkov andGorn have shown in [D. Berkov and N. Gorn, J. Phys.: Condens. Matter,14, L281,2002] that the drift term which generally appears when solving stochastic differentialequations can only influence the length of the magnetization. This quantity is howeverfixed in the case of the stochastic Landau-Lifshitz-Gilbert equation. In this paper, weexploit this fact to straightforwardly extend existing high order solvers with an adaptivetime stepping algorithm.We implemented the presented methods in the freely availableGPU-accelerated micromagnetic software package MuMax3 and used it to extensivelyvalidate the presented methods. Next to the advantage of having control over the errortolerance, we report a twenty fold speedup without a loss of accuracy, when usingthe presented methods as compared to the hereto best practice of using Heun’s solverwith a small fixed time step. ? 2017 Author(s). All article content, except whereotherwise noted, is licensed under a Creative Commons Attribution (CC BY) license.