Crystal field parameters for rare-earth permanent magnets: wannier function approach

Crystal electric fields (CEF) acting on the 4f electrons of rare-earth (RE) ions in RE permanent magnets play a dominant role in determining their magnetic anisotropy. The interaction between the anisotropic 4f electronic clouds of RE ions and the CEF of surrounding charges control the magnetic moments along a specific crystalline direction. The large magnetic anisotropy energy of RE magnets produced by the CEF is strongly believed to mainly dominate their coercivity. Thus, precise information of CEF is needed to study and to improve the magnetic anisotropy and coercivity of RE magnets.Theoretically, there still remain problems to treat the 4f electrons of RE ions. The open-core method may give good results when 4f electrons are well-localized. Unfortunately, however, some RE magnets have been known to be not the case. Quite recently, a new method has been developed to carry out an accurate calculation of CFPs by using Wannier functions.[1] Now it is interesting to estimate the CFPs of RE magnets by using this method.The CFPs for crystalline R₂Fe₁₄B have been obtained by the Wannier function approach, which enables us to visualize the 4f electron clouds. By diagonalizing CEF Hamiltonian based on the Wannier functions, we have confirmed that the low energy wave functions for R=Nd and Dy are expanded to the a-b plane, which result in the single-ion anisotropy along the c-axis. The 4f electron clouds in Nd ions are more expanded to radial direction than that in Dy ions reflected by the lanthanide contraction. On the other hand, we also calculate the CFPs of Nd ions around the surface of the crystalline Nd₂Fe₁₄B and have found that the Nd ions exposed on the (001) surface have 4f electron clouds extended to the c-axis accompanying the c-plane magnetic anisotropy. The results for CFPs are consistent with previous theoretical study. [2]References:[1] P. Novák, K. Knížek, and J. Kuneš, Phys. Rev. B Vol. 87 (2013) 205139[2] H. Moriya, H. Tsuchiura, and A. Sakuma, J. Appl. Phys. 105 (2009) 07A740