Effects of trace elements on the crystal field parameters of Nd ions at the surface of Nd₂Fe₁₄B grains

Using first-principles calculations, we investigate the positional dependence of trace elements such as O and Cu on the crystal field parameter A20, proportional to the magnetic anisotropy constant K_u of Nd ions placed at the surface of Nd₂Fe₁₄B grains. The results suggest the possibility that the A20 parameter of Nd ions at the (001) surface of Nd₂Fe₁₄B grains exhibits a negative value when the O or Cu atom is located near the surface, closer than its equilibrium position. At the (110) surface, however, O atoms located at the equilibrium position provide a negative A20, while for Cu additions A20 remains positive regardless of Cu's position. Thus, Cu atoms are expected to maintain a positive local K_u of surface Nd ions more frequently than O atoms when they approach the grain surfaces in the Nd-Fe-B grains.