Magnetic measurements of the upper and lower critical fields of oxygen-deficient ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ single crystals

We present dc-magnetization measurements in fields up to 5 T on oxygen-deficient (${\mathit{T}}_{\mathit{c}}$≃60 K) ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ single crystals. The upper-critical-field slopes are -2.0 and -8.7 T/K and the lower critical fields at 5 K are 83 and 25 Oe for fields perpendicular and parallel to the Cu-O planes, respectively. The upper-critical-field slope anisotropy is not substantially different from the anisot- ropy found for the 90-K crystals. The ${\mathit{H}}_{\mathit{c}1}$ values are, however, much smaller for the 60-K crystals. We explain these results through a model in which the chains do not contribute significantly to the coupling between the Cu-O planes but rather serve as a charge reservoir for the superconductivity that occurs in the planes.