A direct method to solve quasistatic micromagnetic problems

Abstract Micromagnetic simulations are employed for predicting the behavior of magnetic materials from their microscopic properties. In this paper we focus on hysteresis loops, which are computed by assuming quasistatic conditions: i.e. the magnetization distribution remains at equilibrium while the applied magnetic field is slowly varied. The dynamic behavior of micromagnetic systems is governed by the Landau-Lifshitz equation. In order to apply the dynamic equation to a quasistatic problem, it is necessary to artificially decouple the relaxation dynamics from the time-scale of the variation of the applied field. This decoupling is normally done in an iterative fashion: the field is considered fixed until the equilibrium point is reached, and subsequently updated. However, this approach is indirect and also has the potential issue that a system might switch to a different equilibrium configuration before the previous equilibrium becomes unstable, which is a behavior not possible in the quasistatic regime. Instead, here we derive the differential equation, which directly describes the evolution of the equilibrium states of the Landau-Lifshitz equation as a function of the external field, or any other externally varied parameter. This approach is a more rigorous description of quasistatic processes and inherently enforces the system to follow a given equilibrium configuration until this disappears or becomes unstable. We demonstrate this approach with simple examples and show it to be as or more stable than the previously used approaches.