Effect of the multiorbital structure of Cu2+ ions on the model Hamiltonian for superconducting cuprate oxides

We propose a microscopic model of a CuO2 plane which includes the essential features of the multiorbital structure of Cu2+ ions and preserves the translational invariance of the lattice. We perform the second-order perturbation theory in the hybridization parameter by writing it in terms of a generalized Schrieffer-Wolf canonical transformation and derive the effective Hamiltonian for a p-d spin-spin interaction. The form of this effective Hamiltonian is shown to be modified by the complex structure of Cu2+ ions and is directly compared with simpler commonly used models. We emphasize inconsistencies of these models and raise questions on their applicability