Theoretical study of effective magnetic interactions in high-${\mathit{T}}_{\mathit{c}}$ Cu oxides

Starting from a two-band Hubbard model for cupric oxides and using perturbation theory, we study the effect of a small O-O hopping term ${\mathit{t}}_{\mathit{p}}$ on the parameters of the single-band t-J model. It is found that as long as the wave function on the oxygen site is extended and Bloch-like, the antiferromagnetic coupling between the nearest-neighbor copper spins decreases rapidly with increasing hole doping. This behavior seems to be insensitive to the value of ${\mathit{t}}_{\mathit{p}}$ and dispersion of the oxygen band, and is consistent with the results of recent experiments. We also show that between next-nearest-neighbor copper spins, there exists a non-negligible antiferromagnetic coupling even in the zero-doping limit.