Calculations of relativistic crystal-field contributions to the zero-field splittings in 4f and 3d ion complexes

The equivalent operator method has been extended and applied to anisotropic intersite electron-electron interactions between a central paramagnetic ion and its ligand neighbours. The relativistic character of both the interaction operator, in Breit-Pauli form, as well as the electronic wave-function has been fully incorporated. The tensorial form of the resultant effective Hamiltonian has been analysed and selection rules for its matrix elements have been determined. The importance of relativistic crystal-field effects is illustrated by examples in which the zero-field splitting is calculated for both S-state ions (e.g. Mn2+, Gd3+) and non-S-state ions (e.g. Eu3+, Sm3+, Er3+) in various host lattices. In the former group, particularly the 4f S-state ion, a much more pronounced relativistic effect on the zero-field splitting is exhibited.