Hole interactions and the spin-spin correlation function in aCuO2plane with completely localized oxygen holes

Abstract

A model of an oxygen-hole-doped ${\mathrm{CuO}}_2$ plane is studied in the low-dopant-concentration limit where the approximation is made that the O holes are completely localized. An effective Hamiltonian is found that represents a nonbipartite lattice where only antiferromagnetic exchange interactions are present, thus leading to geometrical frustration (triangular coordination) that reduces the magnetic order. The diminution of antiferromagnetic order has been studied quantum mechanically for small clusters, and classically for much larger lattices, at zero temperature. The dramatic reduction of 〈Ω^ ${}_{}{}^2{}_{}{}^{}\mathrm{〉}$ with doping found in experiments is mimicked in this model, although the finite-size effects in such cluster studies are demonstrated to be very large. Ground states including quantum fluctuations substantially reduce the order parameter in comparison to systems of classical Heisenberg spins. The obtained ground-state configurations of the clusters composed of classical Heisenberg spins are not planar. When the behavior of the spin-spin correlation function with increasing dopant levels is studied, it is found that for all cluster sizes and dopant concentrations (x≤0.05) the correlation function is extremely well fitted by ${\mathit{C}}_{\mathit{r}}$∼${\mathit{r}}^{\mathrm{-}\nu }$exp(-r/ξ).