Crystal field Hamiltonian in Nd2Fe14B based on Wannier functions

There has been emerging interest in improving the coercivity of Nd-Fe-B permanent magnets, and in revealing its mechanism. It has been widely accepted that the large magnetic anisotropic energy due to the Nd ions is the dominant factor of the coercivity of Nd-Fe-B magnets. For deeper under- standing of the coercivity mechanism, it is necessary to study the crystal field (CF) around the Nd ions which is the origin of the magnetic anisotro- py of Nd ion. Although first-principles calculations can be applied to esti- mate CF parameters, the validity of the results is not evident. Thus in this study, we investigate the CF parameters in Nd2Fe14B by recently developed first-principles approach[1], which is based on Wannier functions and direct- ly construct CF Hamiltonians for the Nd ions. Thus we can determine the most stable direction of the magnetization by using the CF Hamiltonians. It has been known experimentally that Nd2Fe14B undergo the spin-reorienta- tion transition. Therefore, to check the spin-reorientation can be a reasonable criterion for the validity of the first-principles CF parameters estimation. The CF Hamiltonian is expressed by HCF =ΣlmBlmClm, where Blm and Clm are the CF parameters and spherical tensor operators, respectively. At first, we calculate the single particle potential on the Nd site by using the APW+lo method implemented in the WIEN2k code[2]. At this stage, the 4f electrons are treated as core electron. Next, we solve the eigenvalue problem including the shape of the 4f orbitals, the effective potential, and hybridization with ligand states. Finally, we construct the CF Hamiltonian by transforming the Bloch functions to Wannier functions. In this method, it is known that the dependence of the muffin-tin radius is diminished, compared to the conven- tional method[3]. In this paper, we report the CF parameters Blm by using first-principles calculations based on Wannier functions. Table I shows the CF parameters at the Nd sites in Nd2Fe14B. We also discuss the validity of our estimation from the presence or absence of the spin-reorientation.[1] P. Novák, K. Knížek, and J. Kuneš: Phys. Rev. B 87, 205139 (2013). [2] P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka, and J. Luitz, WIEN2k, An Augmented Plane Wave+Local Orbitals Program for Calcu- lating Crystal Properties, edited by Karlheinz Schwarz (Techn. Universitat, Wien, Austria, 2001). [3] H. Moriya, H. Tsuchiura, and A. Sakuma, J. Appl. Phys. 105, 07A740 (2009).