Superexchange Interaction in the d-p model

An analytic form of superexchange interaction in the metallic phase of the d-p model simulating 2D electronic systems on CuO2 planes of high-T-c superconducting materials is obtained by using the slave-boson technique together with Feynman's diagrammatical expansion and the expansion from the limit of the large spin-orbital degeneracy N (1/N-expansion). The result recovers the well-known form obtained in the insulating phase and shows strong dependence on density of doped-carriers in metallic phases, which is compared with experiments.