Nested Schrieffer-Wolff-type transformations: indirect exchange Hamiltonian for a CuO2 plane

On the basis of the three-band Anderson lattice model for the CuO2 layers in high-Tc superconductors we derive an effective Cu-spin O-hole Hamiltonian which yields simultaneously superexchange and RKKY interaction. By means of two nested canonical transformations of the Schrieffer-Wolff type we perform a perturbative algorithm up to the fourth order in the Cu-O hybridization amplitude. Both O bands are taken into account consequently. The total indirect exchange integral reflects, in dependence on range and O-hole doping, magnetic frustration and the competition between the super and RKKY exchanges of the Cu spins. (orig.)