New paper: “Micromagnetics of shape anisotropy based permanent magnets”

I am pleased to announce our new paper, which can be downloaded from

Abstract: In the search for rare-earth free permanent magnets, various ideas related to shape anisotropy are being pursued. In this work we assess the limits of shape contributions to the reversal stability using micromagnetic simulations. In a first series of tests we altered the aspect ratio of single phase prolate spheroids, ranging from 1 (sphere) to 20. We start with a sphere with a radius of 4.3 Lex and kept the total magnetic volume constant as the shape is transformed. For a ferromagnet with zero magnetocrystalline anisotropy the maximum coercive field reached up to 0.5 Ms. Therefore, in materials with moderate uniaxial magnetocrystalline anisotropy, the addition of shape anisotropy could even double the coercive field. Interestingly due to non-uniform magnetization reversal there is no significant increase of the coercive field for an aspect ratio greater than 5. A similar limit of the maximum aspect ratio was observed in cylinders. The coercive field depends on the wire diameter. By decreasing the wire diameter from 8.7 Lex to 2.2 Lex the coercive field increases by 40 percent. In the cylinders nucleation of a reversed domain starts at the corners at the end. Smoothing the edges can improve the coercive field by about 10 percent.
In further simulation tests we compacted soft magnetic cylinders into a bulk like arrangement. There are various effects that reduce the coercivity in assemblies of rods: Misalignment, magnetostatic interactions, and direct coupling through exchange interactions. These cause a spread of 0.1 Ms in the switching field of the rods. Comparing the volume averaged hysteresis loops computed for isolated rods and the hysteresis loop computed for interaction rods, we conclude that magnetostatic interactions reduce the coercive field by up to 30 percent.