Microscopic origin of coercivity enhancement by dysprosium substitution into neodymium permanent magnets

Neodymium (Nd) magnets (${\mathrm{Nd}}₂{\mathrm{Fe}}₁₄\mathrm{B}$), known as the strongest permanent magnets, are indispensable in realizing high efficiency in energy conversion devices. To enhance their coercivity at high temperatures, the Nd component is substituted with dysprosium (Dy) in the commercial products of the magnet. Surface Dy-rich shells are considered important for enhancing coercivity. However, the underlying microscopic mechanism has not been studied based on atomistic theories. In this study, first, the features and mechanisms of the enhancement were studied using an atomistic model of the Nd magnet. Subsequently, the threshold field (coercive force) for magnetization reversal and the dynamical features at absolute zero and finite temperatures were investigated. The results show that a change from surface to bulk nucleation occurs when the number of substituted layers increases and the anisotropy energy of Dy is resistant to temperature increase, which significantly enhances coercivity, especially at high temperatures.