Macroscopic effects of local oxygen fluctuations inYBa2Cu3O6+x

Recent experimental studies of the high-temperature superconductor ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$ at high temperatures (above 700 K) detect a maximum in the derivative with respect to oxygen chemical potential of the stoichiometric factor x, located within the disordered tetragonal-phase region. Here we present approximate numerical calculations by a new mean-field technique, which explain this macroscopic effect in terms of local, essentially one-dimensional, fluctuations in the distribution of oxygen atoms in a lattice-gas model for the Cu-O basal planes of this material. Such fluctuations are characteristic of a system near a disorder line in its phase diagram, and are associated with the formation of finite fragments of positionally and orientationally disordered oxygen chains. Our calculations agree with the positions and widths of the experimentally observed maxima, and also predict corresponding peaks in the specific heat. The mean-field results are complemented with large-scale Monte Carlo and numerical transfer-matrix calculations for the same model. The finite-size scaling behavior of the local-fluctuation peaks in the Monte Carlo data is distinctly different from that of the peaks which correspond to phase transitions. The physical picture developed in this study also provides an alternative to the low-density, low-temperature orthorhombic phase that has been proposed by other authors.