Single-ion magnetic anisotropy of rare-earth–transition-metal compounds and its description by means of analytical expressions

The single-ion magnetic anisotropy energy of 3d-4f compounds is shown to be generally irrepresentable in the form of analytical expressions involving anisotropy constants. Particular cases permitting analytical representation are analyzed and expressions for the anisotropy constants in terms of the crystal field and 3d-4f exchange parameters are derived. In particular, the high-temperature approximation appears useful for analysis of vital properties of hard magnetic materials. Limits of validity of the obtained formulas are established.