Ce and Dy substitutions in Nd₂Fe₁₄B: Site-specific magnetic anisotropy from first principles

A first-principles approach combining density-functional and dynamical mean-field theories in conjunction with a quasiatomic approximation for the strongly localized 4 f shell is applied to Nd₂Fe₁₄B-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 Nd₂Fe₁₄B, 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 (Nd, R)₂Fe₁₄B-substituted
compounds.