Finite-Temperature Dynamical and Static Properties of the Nd Magnet Studied by an Atomistic Modeling INVITED

Abstract

Nd–Fe–B permanent magnets are indispensable materials for high-technology commercial products such as motors, electronic devices, etc., because of their high coercive force. However, the mechanism of the coercive force has not been well understood [1]. For the understanding of the microscopic mechanisms, atomistic modeling, which is a new trend of permanent-magnet modeling, is important. We have studied dynamical and static properties of the Nd magnet, Nd2Fe14B, by applying the stochastic LLG equation [2] and Monte Carlo methods to an atomistic model, in which microscopic parameters were introduced by first-principles calculations [2-7]. We have shown the temperature dependencies of the magnetization, domain-wall profiles, dipolar-interaction effect, ferromagnetic resonance, inhomogeneity effect, surface Nd anisotropy effect, etc. [2-7] In this presentation, we mainly show dynamical aspects of the magnet, focusing on the effect of the interface between grains and grain boundaries. There exist difficulties to estimate long relaxation times of barrier-crossing magnetization reversal quantitatively due to the limitation of simulation time and the dependence on the damping factor. Here we propose a statistical method to estimate precisely long relaxation times in the stochastic region, by which one can identify an initial transient process and a long-time regularly relaxation process. We show an estimation of the coercive force of a single grain using this method [6]. Local environments around rare-earth ions at the interfaces of rare-earth magnets may be different from those in the bulk. First-principles studies have suggested that the magnetocrystalline anisotropies of the Nd atoms at the (001) surface of grains in the Nd magnet have in-plane (c-plane) anisotropy, while those in the bulk have out-of-plane anisotropy. Thus, we investigated the effect of the surface magnetic anisotropy of the Nd atoms on the coercivity in the Nd magnet (Fig. 1). We analyzed the coercive force in three cases, in which the Nd atoms in surface layers have (I) no anisotropy, (II) in-plane anisotropy, and (III) doubly reinforced anisotropy for not only the (001) surface but also (100) surface, with the layer-depth dependence [6]. We find that at zero temperature the modification of the anisotropy of the Nd atoms at the first-surface layer reduces the coercive force in cases I and II and enhances the force in case III, but at room temperature, this modification does not affect the coercive force, and the modification at several surface layers is necessary to reduce or enhance the coercivity at room temperature. We also present the nucleation and pinning fields of the Nd magnet as a function of the strength of the anisotropy energy of the soft magnet and also as a function of the thickness of the soft magnet (Fig. 2) [7]. In the Nd magnet, reflecting the lattice structure, the properties of domain walls (DWs) depend on their moving directions. Bloch and Néel DWs move along the a (or b) and c axes, respectively. We show the difference in the nucleation and pinning fields between the Bloch and Néel DWs. We find that the thermal fluctuation effect affects the threshold fields in the Nd magnet significantly. We also find that the strength of the anisotropy energies of the soft magnet phase is not so important for the pinning field, while it is essential for the nucleation field, etc.