# Coercivity reduction in Nd-Fe-B particles due to local anomalous magnetic anistropy around their interfaces.

INTERMAG Europe 2017

Hiroki Tsuchiura(Tohoku University), Takuya Yoshioka(Tohoku University)

## Abstract

Understanding coercivity mechanisms in rare-earth based permanent magnets such as Nd-Fe-B is crucially important from the aspect of renewable and sustainable development in engineering. Recently, several experimental studies have shown that atomic scale structures and elemental distributions around the grain boundaries of sintered Nd-Fe-B magnets significantly affect their coercivity [1]. This observation is quite intriguing, as it implies that atomic scale perturbations less than magnetic coherence length have an influence on macroscopic coercivity.

One of the authors and his coworkers have found based on first-principles calculations that the Nd ions exposed on the (001) surface not only lose their uniaxial local magnetic anisotropy but also exhibit in-plane anisotropy. Here we call such Nd ions as anomalous Nd. It has been also confirmed that this is the case even for Dy ions on the surface when Dy are substituted into the Nd2Fe14B particle. It is quite plausible that anomalous Nd/Dy ions exist even around the interfaces of Nd2Fe14B particles in sintered Nd-Fe-B magnets. Thus these anomalous Nd/Dy can be a physical origin of the experimental observations mentioned above. To investigate if this is the case theoretically, it is preferable to use a Heisenberg-type effective spin model than to use continuous micromagnetic model.

Here we construct an effective spin model for a Nd2Fe14B particle based on the microscopic information obtained by first-principle electronic state calculation. Each spin in this model represents the magnetic moments of Fe or Nd, and there are 64 spins per the unit cell of this model. The magnetic moments and the magnetic anisotropy energies of these spins, and the exchange interactions between them are determined by using first principles calculations. In particular, the magnetic anisotropy of the Nd ions is described by the crystal field Hamiltonian determined by first-principle calculations to study finite-temperature effects. We have confirmed that the magnetization curves are satisfactory reproduced by this model even at and above room temperature when we carry out equilibrium calculations. It is worth noting here that anomalous Nd/Dy can be easily incorporated in the effective spin model.

In this work, we analyze the magnetization reversal processes of a Nd2Fe14B particle by solving the atomistic LLG equation for the effective spin model with anomalous Ndions, and study the effects of the anomalous Nd on the coercivity of the particle. We assume that the shape of the particle is almost cubic for simplicity (with 16x16x12 unit cells), and also that anomalous Nd ions are randomly distributed on the (001) surface of the particle. We note here that there are four Nd sites on the (001) surface of each unit cell of 2-14-1 structure, thus there are Nd 1024 sites on this particle. We find that the magnetization reversal processes in the particle always begin at the anomalous Nd. Thus the anomalous Nd ions can be a nucleation sites for magnetization reversal. Figure 1 shows the coercivity of the particle for several temperatures as functions of the density of the anomalous Nd on the (001) surface. We can see that the coercivity monotonically decreases with increasing the density of the anomalous Nd ions, and almost vanishes when the density is around 60% for T=300K. Thus the coercivity of the particle is strongly affected by the anomalous Nd existing just on the (001) surface, which is consistent with the experimental observations.