Micromagnetic modeling of magnetization reversal in permanent magnets

Micromagnetic numerical 3D calculation is presented in this paper to investigate the effect of a soft magnetic heterogeneity on the magnetization reversal of a single hard magnetic grain. Both equilibrium and transient magnetization configurations are obtained by solving the dynamic Landau-Lifshitz-Gilbert (L.L.G.) equation. A modified forward difference method is used to integrate the time dependent L.L.G. equation without conflicting with the constraint of constant magnetic moment. A continuum view of the material medium is adopted and the spatial finite difference method is used to describe the system as a set of cubic elements. In each element the magnetization is interpolated with quadratic polynomial functions and constrained to follow the Brown condition at the surface. A multigrid approach is developed to calculate the magnetic potential and the resulting stray field associated with a given microstructure. The calculated properties are compared to actual properties of NdFeB sintered magnets. Assuming a soft nucleus of 160 Angstrom diameter and 80 Angstrom depth, the calculated coercive field is about 1.45T, close to experimental values and the calculated angular dependence of H-c ressembles experimental beheviors.