Evidence for a time-dependent crossover from surfacelike to bulklike flux relaxation in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$

Dc flux-relaxation experiments were performed on single crystals of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ at low magnetic fields. A sharp, time-dependent crossover in the logarithmic magnetization decay rate was observed in two different crystals. Consideration of the size dependence of the relaxation rate in one of the ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ crystals suggests that the crossover in the relaxation rate is due to a transition from surface-controlled to bulk-controlled relaxation behavior. Our observations seem to indicate that, over a certain range of temperatures and magnetic fields, surface pinning may play a significant role in the flux-relaxation behavior of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$.