Stable and fast semi-implicit integration of the stochastic Landau–Lifshitz equation

Abstract

We propose new semi-implicit numerical methods for the integration of the stochasticLandau–Lifshitz equation with built-in angular momentum conservation. The performanceof the proposed integrators is tested on the 1D Heisenberg chain. For this system, ourschemes show better stability properties and allow us to use considerably larger time stepsthan standard explicit methods. At the same time, these semi-implicit schemes are also ofcomparable accuracy to and computationally much cheaper than the standard midpointimplicit method. The results are of key importance for atomistic spin dynamicssimulations and the study of spin dynamics beyond the macro spin approximation.