Model for the high-temperature oxygen-ordering thermodynamics in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$: Inclusion of electron spin and charge degrees of freedom

A lattice-gas model for the high-temperature oxygen-ordering thermodynamics in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$ is presented, which assumes constant effective pair interactions between oxygen atoms and includes in a simple fashion the effect of the electron spin and charge degrees of freedom. This is done using a commonly utilized picture relating the creation of mobile electron holes and unpaired spins to the insertion of oxygen into the basal plane. The model is solved using the nearest-neighbor square approximation of the cluster-variation method. In addition, preliminary Monte Carlo results using next-nearest-neighbor interactions are presented. The model is compared to experimental results for the thermodynamic response function, kT(∂x/∂μ${)}_{\mathit{T}}$ (μ is the chemical potential), the number of monovalent copper atoms, and the fractional site occupancies. The model drastically improves the agreement with measured values of kT(∂x/∂μ${)}_{\mathit{T}}$ as compared to bare lattice-gas models. Additionally, the monovalent copper count, in contrast to the standard lattice-gas models, is determined self-consistently and agrees qualitatively with experiment.