Monte Carlo study of oxygen-vacancy ordering inYBa2Cu3−xMxO6+2c(M=Co,Fe,Al,Ga)

The effect of impurities at the Cu(1) site in the basal plane of the high-temperature superconductor ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+2\mathit{c}}$ on the oxygen-vacancy phase diagram is investigated by Monte Carlo simulation of an asymmetric next-nearest-neighbor lattice-gas model, in which the impurities are assumed to act as traps for oxygen atoms. First the phase diagram of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+2\mathit{c}}$ is determined, which shows the high-temperature orthorhombic and tetragonal phases, as well as the low-temperature double-cell orthorhombic and antiorthorhombic phases. Next the high-temperature orthorhombic-to-tetragonal transition of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_{3\mathrm{-}\mathit{x}}$ ${\mathit{M}}_{\mathit{x}}$ ${\mathrm{O}}_{6+2\mathit{c}}$ is studied within a single orthorhombic domain. This orthorhombic-to-tetragonal transition is a true phase transition, with a peak in the specific heat, in contrast with the orthorhombic-to-pseudotetragonal transition studied in previous theoretical studies. The orthorhombic-to-tetragonal phase boundary is found to shift to higher oxygen concentrations with increasing impurity concentration. A first-order approximation for the shift of the phase boundary is derived, which agrees with the Monte Carlo results.