Theory of superexchange in antiferromagnetic insulators

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Abstract
An extended Hubbard Hamiltonian, which models Mott insulating transition-metal compounds, is shown to have a ground manifold described by the usual superexchange effective Hamiltonian but with an enhanced exchange constant due to virtual transitions onto the non-magnetic ions. These are fourth-order processes in the Rayleigh-Schrodinger perturbation expansion of the effective Hamiltonian and are considered explicitly since the linked-cluster theorem is not applicable in its usual form. The enhancement is large when the virtual transition energy is comparable with the intra-ionic Coulomb repulsion and may be significant in the new high-temperature superconducting oxides.