A numerical solution of the magnetization reversal modeling in a permalloy thin film using fifth order Runge–Kutta method with adaptive step size control

The Landau–Lifshitz–Gilbert (LLG) equation is the fundamental equation to describe magnetization dynamics in microscale and nanoscale magnetic systems. In this paper we present a brief overview of a time-domain numerical method related to the fifth order Runge–Kutta formula, which has been applied to the solution of the LLG equation successfully. We discuss advantages of the method, describing the results of a numerical experiment based on the standard problem #4. The results are in good agreement with the ones present in literature. By including thermal effects in our framework, our simulations show magnetization dynamics slightly dependent on the spatial discretization.