THE EXCHANGE CONSTANT FOR SYSTEMS WITH INFINITE COULOMB INTERACTIONS

In this paper we discuss the exchange interaction between two magnetic ions in the limit of very large on-site Coulomb interactions. We find that in this limit the exchange interaction is due to fundamental principles of quantum mechanics: the difference in permutation symmetry of the orbital part of the singlet and triplet states and the Pauli principle. We call this the permutation mechanism; it is also known as ring mechanism. The order of the lowest-order contribution to this exchange mechanism depends on the atomic configuration. It is of fourth-order in the atomic orbital basis in the case there is a double anion bridge between the two magnetic ions. It is of fifth-order in the case of a single bridge between the two magnetic ions. The double bridge can be either two ions or two orbitals at the same bridging ion. We show that this contribution is already contained in the second-order perturbation expansion based on molecular orbitals reported by the author (1990). We conclude that the original theory of Anderson for superexchange only needs to be reinterpreted to incorporate this mechanism. Finally, we calculate all contributions to the nearest-neighbor superexchange interaction in La cuprates, in order to discuss the importance of the permutation mechanism.