Effect of Crystalline Electric Fields on Ferromagnetic Anisotropy

The effect of the electrostatic crystalline field has been considered for a magnetic crystal in which the ions are strongly coupled by ferromagnetic exchange. On the basis of the one-ion approximation that the exchange can be represented by a Weiss molecular field, it is possible to derive expressions for the anisotropy constants, K₈ (T), in terms of the parameters occurring in the spin Hamiltonian of the isolated ions, and the magnetization of the lattice at the temperature, T. The treatment assumes that the magnetic electrons can be considered as localized on the individual ions, and thus applies primarily to nonmetallic substances such as ferrites. The presence of more than one aligned sublattice is easily taken into account if the magnetization of each sublattice can be calculated from the N\'eel equations.