On superchange in magnetic insulators

The problem of superexchange interaction between orbitally degenerate ions is considered in the case of ground state resulting from different configurations. A new kind of exchange contributions due to the configurational mixing is found. The general effective Hamiltonian is given, using the tensor operator formalism. The concept of general channels is used to describe the microscopic theory of its parameters. It is shown that in the case of orbitally nondegenerate ground state for the strong crystal field, the Heisenberg from of the exchange Hamiltonian can be expressed as a sum of simple channels (pairs of interacting half-filled orbitals). In the other cases (orbital degeneracy or mixing of configurations) we can decompose the exchange Hamiltonian into the sum of collective channels (pairs of interacting subconfigurations or configurations). The second order correlations are taken into account. (author)