First-Principles Study of the Role of Cu in Improving the Coercivity of Nd-Fe-B Permanent Magnets Y. Tatetsu, 1,* S. Tsuneyuki, 1,2 and Y. Gohda 1,3,4,† 1 Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan 2 Institute for Solid State Physics, The University of Tokyo, Kashiwa 277-8581, Japan 3 Department of Materials Science and Engineering, Tokyo Institute of Technology, Yokohama 226-8502, Japan 4 ESICMM, RCMSM, National Institute for Materials Science, Tsukuba 305-0047, Japan (Received 19 July 2016; revised manuscript received 25 October 2016; published 30 December 2016) We study the magnetic and electronic properties of Cu-doped Nd 2 Fe 14 B=NdO x systems with first- principles calculations in order to understand the roles of Cu in improving the coercivity of Nd-Fe-B permanent magnets. By analyzing the formation energies of several model systems, we find that Cu prefers to be at the interface. We conclude that the Cu addition to Nd-Fe-B magnets is a practical way of not only increasing the anisotropy of Nd atoms at the interface but also of lessening the magnetic coupling between the Nd and Fe atoms. Particularly, substituting Fe at the interface of the main phase with Cu works effectively in terms of improving the magnetic anisotropy in Nd atoms. This may explain the coercivity improvements reported recently. DOI: 10.1103/PhysRevApplied.6.064029 I. INTRODUCTION Strong magnets are demanded not only for the develop- ment of technologies but also for energy saving. Among permanent magnets, Nd-Fe-B magnets are known as the strongest permanent magnets with a high-energy product ðBHÞ max and are widely used in various kinds of applica- tions, for example, high-performance computers, hybrid vehicles, and wind turbines, as well as premium-efficiency motors [1–6]. However, the thermal stability of Nd-Fe-B magnets, especially their coercivity at high temperatures, is a well-known issue, and the mechanism of this low coercivity is an unsolved problem. Recent experimental studies on the microstructures of Nd-Fe-B magnets show that controlling the structural and magnetic properties around the interfaces between main phases and subphases is important for improving the coercivity [7,8]. Wettability around the grain boundaries in Nd-Fe-B magnets is improved by the Nd-Cu grain-boundary diffusion process. In addition, several experimental annealing processes have succeeded in improving the coercivity, which indicates the importance of Cu around the interface [9–19]. Considering these experimental results, the existence of Cu around the interface can be expected to influence the coercivity improvement directly. As reported in several studies [9,11,12,18,19], Cu is thought to be located around the main-phase (Nd 2 Fe 14 B) grains. The total amount of Cu atoms is quite small, about 2 at. %. However, the roles of Cu in Nd-Fe-B magnets are still unclear since it is difficult to identify the exact position of the Cu atoms by experi- ment. Hence, first-principles calculations are an alternative and powerful tool for finding where Cu prefers to be around the interfaces in Nd-Fe-B magnets. In the present study, we simulate Cu-doped Nd 2 Fe 14 B= NdO x systems as the first step toward understanding the role of Cu in the coercivity improvement and the magnetic and electronic structures around the interfaces. These systems are discovered around triple junctions in annealed Nd-Fe-B magnets [10,11,20,21]. We study how the mag- netic anisotropy in Nd is affected by Cu because this is directly related to the coercivity. We find that Fe at the interface can be replaced by Cu due to having a lower formation energy than the non-Cu-doped system, and this replacement improves the magnetic anisotropy of Nd atoms at the interface. In particular, the anisotropy improvement in Nd near Cu is about 40%. This is one of the reasons for the coercivity improvement. II. COMPUTATIONAL METHOD We calculate the formation energies and the magnetic anisotropy of Cu-doped Nd 2 Fe 14 B=NdO x model systems by using the computational code OpenMX [22], which is based on optimized pseudopotentials and pseudo- atomic-orbital basis functions within density-functional theory (DFT). As basis sets, s2p2 configurations are adopted for B and O atoms and s2p2d2 for Nd, Fe, and Cu atoms with cutoff radii of 7.0, 7.0, 8.0, 6.0, and 6.0 a.u., respectively. Semicore orbitals of 3s and 3p in Fe and Cu as well as 5s and 5p in Nd are treated as valence electrons. In order to reduce computational costs as much as possible, we use an open-core pseudopotential for Nd * tatetsu@cms.phys.s.u‑tokyo.ac.jp † gohda.y.ab@m.titech.ac.jp PHYSICAL REVIEW APPLIED 6, 064029 (2016) 2331-7019=16=6(6)=064029(6) 064029-1 © 2016 American Physical Society