First-principles calculations of magnetic properties for analysis of magnetization processes in rare-earth permanent magnets

It has been empirically known that the coercivity of rare-earth permanent magnets depends on the size and shape of fine particles of the main phase in the system. Also, recent experimental observations have suggested that the atomic-scale structures around the grain-boundaries of the fine particles play a crucial role to determine their switching fields. In this article, we review a theoretical attempt to describe the finite temperature magnetic properties and to evaluate the reduction of the switching fields of fine particles of several rare-earth permanent magnetic materials based on an atomistic spin model that is constructed using first-principles calculations. It is shown that, over a wide temperature range, the spin model gives a good description of the magnetization curves of rare-earth intermetallic compounds such as R ₂Fe₁₄B (R= Dy, Ho, Pr, Nd, Sm) and SmFe₁₂. The atomistic spin model approach is also used to describe the local magnetic anisotropy around the surfaces of the fine particles, and predicts that the rare-earth ions may exhibit planar magnetic anisotropy when they are on the crystalline-structure surfaces of the particles. The dynamical simulation of the atomistic spin model and the corresponding micromagnetic simulation show that the planar surface magnetic anisotropy causes a reduction in the switching field of fine particles by approximately 20-30%, which may be relevant to the atomic-scale surface effects found in the experimental studies.