Fast numerical three-dimensional scheme for the simulation of hysteresis in ferromagnetic grains

Abstract

The magnetic behavior of ferromagnetic materials like iron is important for the improvement of performances of electromagnetic devices. This article deals with a three-dimensional model that computes the magnetic behavior of an iron grain under a varying applied field starting from its microscopic material parameters. The model can be used as a tool to determine the quantitative relations between the different microscopic parameters and their influence on the magnetic properties of the grain. The magnetization dynamics are computed for successive quasistatic applied fields. In each space point of the grain, the time variation of the magnetic dipole M is described by the Landau-Lifshitz equation. To integrate this equation, two time stepping schemes are proposed: a forward semianalytical and a predictor-corrector time stepping scheme. The two methods obey the two intrinsic properties of the Landau-Lifshitz equation: (1) preservation of the amplitude of the magnetic dipoles and (2) the decrease of the total free energy when a constant field is applied. They also have a good time and memory efficiency, while the predictor-corrector semianalytical scheme has the best precision and convergence properties. The optimal time stepping scheme and corresponding time stepping parameters are determined. The proposed model is adapted to several experiments, varying different microscopic parameters. In the numerical computations, the spatial discretization is obtained by finite different techniques and the magnetostatic field is computed using fast Fourier transforms.