Exchange interaction betweenJmultiplets

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 ∝J₁·J₂ (or ∝J₁·S₂ 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.