Quantum Theory of Rare-Earth Magnets

Strong permanent magnets mainly consist of rare earths ($R$) and transition metals ($T$). The main phase of the neodymium magnet, which is the strongest magnet, is Nd$_2$Fe$_{14}$B. Sm$_{2}$Fe$_{17}$N$_{3}$ is another magnet compound having excellent magnetic properties comparable to those of Nd$_{2}$Fe$_{14}$B. Their large saturation magnetization, strong magnetocrystalline anisotropy, and high Curie temperature originate from the interaction between the $T$-3d electrons and $R$-4f electrons. This article discusses the magnetism of rare-earth magnet compounds. The basic theory and first-principles calculation approaches for quantitative description of the magnetic properties are presented, together with applications to typical compounds such as Nd$_2$Fe$_{14}$B, Sm$_{2}$Fe$_{17}$N$_{3}$, and the recently synthesized NdFe$_{12}$N.