Percolation effects and oxygen inhomogeneities in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ crystals

The magnetization curves of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ crystals are widely observed to exhibit a pronounced low-field minimum in the temperature range 30 K<T<${\mathit{T}}_{\mathit{c}}$. We demonstrate that these magnetization anomalies correlate with the c-axis lattice parameter, and hence with the specific oxygen deficiency δ. We interpret this low-field feature in terms of a field-induced decoupling of regions of oxygen-rich material by boundaries of oxygen-poor material, a phenomenon reminiscent of the behavior in granular superconductors. A ‘‘phase diagram’’ that demarcates the multigrain onset as a function of temperature and δ is then constructed. The shape of the ‘‘phase boundaries’’ is described using a percolation model. This analysis demonstrates that magnetization is a very sensitive measure of crystal quality.