Low-temperature magnetic relaxation in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$: Evidence for quantum tunneling of vortices

Hall-probe measurements of an ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ crystal in the range 0.1–1 K show a temperature-independent time-logarithmic magnetic relaxation. These results rule out conventional thermally activated flux creep, which predicts a ${\mathit{T}}^{2/3}$ dependence at the lowest temperatures if one takes into account the dependence of the barrier on driving force in a simple one-dimensional model. They are consistent with a phenomenological theory assuming a quantum tunneling process for vortex kink motion.