Apical Oxygen and Frustration Effects in CuO2 Lattice

A microscopic model for the CuO2 lattice which takes into account two orbitals of copper (3d x 2−y 2, 3d 3z 2−r 2 and three orbitals of oxygen (2px, y, z) is considered. Applying the canonical transformation to eliminate the d–p hybridizations, the effective spin‐dependent Hamiltonian is derived describing superexchange interaction (SX) and Ruderman‐Kittel‐Kasuya‐Yosida (RKKY)‐type interaction. The possible role of apical oxygen degrees of freedom (β (2pz − 2px(y) hopping integral), Δ (2pz − 3d 3z 2−r 2 hybridization), and ε pz (apical oxygen energy)) for antiferromagnetic frustration effects in the CuO2 plane due to SX is investigated. The presence of an apical orbital coupled to the in‐plane copper and oxygen orbitals can effectively enhance these effects. Therefore, both these interactions (SX and RKKY) can cooperate in destroying the antiferromagnetic order in the sublattice of copper spins upon doping. It is shown that the increase of the frustration due to doping favours the formation of the superconducting state. The RKKY interaction is of ferromagnetic character. For small hole concentrations SX and RKKY integrals are of the same order of magnitude but different in sign.