Starting from the two-band Hubbard Hamiltonian a systematic derivation of the spin-dependent interactions within the ${\mathrm{CuO}}_2$ planes of the perovskite high-${\mathit{T}}_{\mathit{c}}$ superconductors is presented, taking the remarkably strong Cu-O hybridization of these materials into account. We show that in the case of hole doping the kinetic energy of the holes plays a dominant role leading to a ferromagnetic ordering in the surrounding of an additional hole (ferron state). In addition we show that any reduction of the two-band model to a one-band model clearly underestimates the influence of the kinetic energy of the holes.

• Received 24 September 1990

DOI:https://doi.org/10.1103/PhysRevB.44.795