There is a great social demand for the development and enhancement of permanent magnet materials that minimize the use of rare elements such as dysprosium. As the first step, our current challenge is to understand the magnetic characteristics of the most powerful permanent magnet, sintered Nd-Fe-B magnet, from the microscopic electronic theory. The sintered Nd-Fe-B magnet comprises the Nd2Fe14B phase and other subphases, but its magnetic properties cannot be understood just from the magnetic state of the Nd2Fe14B monocrystal. This is in contrast with many electronic and optical devices, whose characteristics can be designed from electron structures of their monocrystals. Hence, the effect of the microstructure of sintered magnets must be incorporated. However, first-principles simulation of the entire microstructure is, at least currently, not possible. We therefore aim to understand the nature of the interface between different phases, where events such as magnetization reversal and pinning of domain-wall displacement that dominate magnetic characteristics are predicted to be taking place.
Such a first-principles calculation of the microstructure is performed using OpenMX  by means of a localized basis suitable for massively parallel computing. OpenMX can not only perform the standard first-principles-based calculation, but also support the order-N method, an algorithm suited for large-scale calculations. Order-N calculation, thus, is used to optimize the atomic structure and theoretically analyze the magnetic characteristics using standard algorithms. The scale of calculations depends on the structural model used. As an example, an interfacial structure comprising 2,700 atoms (36,000 electrons) is simulated using K’s HPCI general use category with approximately 20,000 cores to perform the massively parallel computation (Figure).
|Among the various magnetic characteristics, one that is particularly important is anisotropy energy. To theoretically analyze this physical quantity, spatial directional dependency must be investigated in addition to the relative direction of magnetic moments. It is also important to clarify the localized anisotropy energy at the interfacial microstructure. To this end, we have developed a method to decompose the anisotropy energy caused by itinerant electrons into multiple sites . Going forward, we plan to use these methods to understand and optimize the roles that itinerant electrons and localized electrons play in determining the localized anisotropy energy at the interfacial microstructure.|
|Figure: Example interfacial structure between the principal phase (Nd2Fe14B)and sub-phase (dhcp Nd).|
 T. Ozaki, Phys. Rev. B 67, 155108 (2003); www.openmx-square.org/
 Z. Torbatian, T. Ozaki, S. Tsuneyuki, and Y. Gohda, Appl. Phys. Lett. 104, 242403 (2014).