Exchange interaction between J multiplets

Analytical expressions for the exchange interaction between J multiplets of interacting metallic centers are derived on the basis of a complete electronic model which includes the intrasite relativistic effects. A common belief that this interaction can be approximated by an isotropic form alpha J(1) (.) J(2) (or alpha J(1) (.) S-2 in the case of interaction with an isotropic spin) is found to be ungrounded. It is also shown that the often used 1/U approximation for the description of the kinetic contribution of the exchange interaction is not valid in the case of J multiplets. The developed theory can be used for microscopic description of exchange interaction in materials containing lanthanides, actinides, and some transition-metal ions.