Anisotropy of rare-earth magnets

Rare-earth intermetallics such as Nd₂Fe₁₄B and Sm-Co are widely used as high-performance permanent magnets, because they combine high magnetocrystalline anisotropy with reasonable magnetization and Curie temperature. The anisotropy is a combined effect of spin-orbit coupling and electrostatic crystal-field interactions. The main contribution comes from the rare-earth 4f electrons, which are well-screened from the crystalline environment but exhibit a strong spin-orbit coupling. In this limit, the magnetocrystalline anisotropy has a very transparent physical interpretation, the anisotropy energy essentially being equal to the energy of Hund's-rules 4f ion in the crystal field. The corresponding expression for the lowest-order uniaxial anisotropy constant K₁ is used to discuss rare-earth substitutions, which have recently attracted renewed interest due to shifts in the rare-earth production and demand. Specific phenomena reviewed in this article are the enhancement of the anisotropy of Sm₂Fe₁₇ due to interstitial nitrogen, the use of Sm-Co magnets for high-temperature applications, and the comparison of rare-earth single-ion anisotropy with other single-ion and two-ion mechanisms.