Oxygen configurations and their effect on charge transfer in off-stoichiometric ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{\mathit{z}}$

The relationship between oxygen structure, charge transfer (hole count), and oxygen content in the ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{\mathit{z}}$ superconductor is studied by combining Monte Carlo simulation with existing electronic-structure calculations. The present model proposes an expansion of the hole count in terms of oxygen configuration variables for states of an arbitrary degree of order. Configurations are obtained by Monte Carlo simulation on a two-dimensional asymmetric next-nearest-neighbor Ising model. Calculations of hole count as a function of oxygen content suggest that oxygen ordering is, at least in part, responsible for the observed plateau structure of ${\mathit{T}}_{\mathit{c}}$ versus the oxygen content z. The fact that, in the present model, the hole count does not exhibit two well-defined plateaus indicates that the value of ${\mathit{T}}_{\mathit{c}}$ is not simply related to the amount of charge transfer. Previous models, which claim to predict the 90- and 60-K plateaus on the basis of either electronic-structure or oxygen order considerations, are shown to agree with experimental findings for (partially) fortuitous reasons.