Ce and Dy substitutions inNd2Fe14B: Site-specific magnetic anisotropy from first principles

Abstract

A first-principles approach combining density-functional and dynamical mean-field theories in conjunction with a quasiatomic approximation for the strongly localized $4f$ shell is applied to ${\mathrm{Nd}}_{2}{\mathrm{Fe}}_{14}\mathrm{B}$-based hard magnets to evaluate crystal-field and exchange-field parameters at rare-earth sites and their corresponding single-ion contribution to the magnetic anisotropy. In pure ${\mathrm{Nd}}_{2}{\mathrm{Fe}}_{14}\mathrm{B}$, our calculations reproduce the easy-cone to easy-axis transition; theoretical magnetization curves agree quantitatively with experiment. Our study reveals that the rare-earth single-ion anisotropy in the 2-14-1 structure is strongly site dependent, with the $g$ rare-earth site exhibiting a larger value. In particular, we predict that increased $f$- and $g$-site occupancy of $R=$ Ce and Dy, respectively, leads to an increase of the magnetic anisotropy of the corresponding (${\mathrm{Nd},R)}_{2}{\mathrm{Fe}}_{14}\mathrm{B}$-substituted compounds.