Explaining Browns paradox in NdFeB magnets from micromagnetic simulations

Abstract

We present the results of a systematic investigation into how the coercivity and maximum energy product of NdFeB permanent magnets are affected by magnetic and geometric microscopic properties. The results are based on numerical micromagnetic simulations carried out with the open source numerical framework MagTense. We considered artificially generated realistic microstructures for which we can control the number of crystal grains as well as the thickness of the intergrain region. Based on variations of the exchange constant, easy axis orientation, grain boundary width and intergrain material properties, the results indicate that while all of these can contribute to a reduction of coercivity, the easy axis orientation has the largest influence. For this, if the easy axis orientation is distributed within a cone with an opening angle of 15°, that is enough to reduce the coercivity by 1 T. Regarding the maximum energy product, the width of the grain boundary layer as well as the easy axis orientation were seen to have the largest influence, with the exchange constant only very weakly influencing the maximum energy product. Our analysis thus methodically clarifies the different factors contributing to the reduction of the value of the coercivity and maximum energy product when compared to the theoretical limit, a discrepancy known as Brown’s paradox.