Micromagnetics simulation of high energy density permanent magnets

A finite element approach is used to calculate the influence of different grain boundary phases on the reversal process of sintered Nd-Fe-B magnets. To calculate equilibrium states of the magnetic polarization the total Gibbs´ free energy is minimized with a quasi-Newton conjugate gradient method. It was found that the grain boundary phases influence the coercive field significantly. For a perfect microstructure the numerical results agree well with the Stoner-Wohlfarth theory. A reduction of the magnetocrystalline anisotropy near grain boundaries leads to a linear decrease of the coercive field. In contrast to the Stoner-Wohlfarth theory the coercive field will decrease with increasing alignment of the easy axies if the anisotropy is reduced near grain boundaries. The finite element simulations confirm the experimental results that nonmagnetic Nd-rich phases at grain boundary junctions significantly increase the coercive field