Ground-state properties of a single oxygen hole in aCuO2plane

The properties of a single O hole, either localized or mobile, in a ${\mathrm{CuO}}_2$ plane are studied for an effective Hamiltonian derived from the extended Hubbard model in the strong-coupling limit. The ground-state wave function for a 16-Cu-site cluster is found exactly and compared with a semiclassical variational treatment of the same problem. In the ground state, whether localized or mobile, there is a long-range dipolar distortion of the Cu spin background around the O hole, as well as a strong antiferromagnetic correlation between the spin of the O hole and the two adjacent Cu spins (corresponding to the ‘‘3-spin polaron’’). These correlations are forced by hopping and/or direct Cu-O exchange and can be saturated by either one of them, suggesting that the two processes have similar effects on the spin configuration and do not significantly interfere. The minimum of the mobile hole band lies at k=(±π/2,±π/2) (at least in the presence of the small oxygen-oxygen hopping). The bandwidth scales with the Cu-Cu exchange and not the bare hopping, when the former is smaller. The ground state has spin (1/2 with the z magnetization residing in the canting of the Cu spins, and the expectation value of the O spin vector being very nearly zero. Thus, both the quantum numbers of the mobile vacancy ground state, as well as the far-field structure of the Cu spin configuration, are the same as those found for the vacancy in the single-band t-J model.