Abstract
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.
Highlights
Modern permanent magnets are the consequences of the fine combination of various magnetic and nonmagnetic materials, as well as micro, macro, and metallographic structures.1) quantum theory tells only part of the story of rare-earth magnets
The majority component is 3d transition metals, which are essential for a large saturation magnetization and high Curie temperature, while R elements are responsible for strong magnetocrystalline anisotropy
The above consideration indicates that the strength of the crystal field at the rare-earth site is a good measure of the magnetocrystalline anisotropy of a rare-earth magnet compound
Summary
Modern permanent magnets are the consequences of the fine combination of various magnetic and nonmagnetic materials, as well as micro-, macro-, and metallographic structures.1) quantum theory tells only part of the story of rare-earth magnets. We will concentrate mostly on the electronic and magnetic properties of single crystals of rare-earth magnet materials, discussing some selected topics that may be essential in terms of developing permanent magnets. The magnetic anisotropy originates from either crystalline or shape anisotropy; the latter can never be strong enough for modern magnets The former is the result of spinorbit coupling (SOC) which eventually sticks spins to a crystal structure. As is widely recognized, there is no established way to treat the electronic and magnetic properties of 4f electron systems from first principles. This makes the theoretical treatment of rare-earth magnets rather difficult. We will review the recent development of quantum mechanical approaches to the problem of rare-earth magnets,
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