Long-term nonlogarithmic magnetic relaxation in single-crystal ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ superconductors

The time dependence of the irreversible superconductive magnetization (flux creep) has been studied in a high-${\mathit{J}}_{\mathit{c}}$, proton-irradiated ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ single crystal for long periods, up to 3.5×${10}^5$ s. A nonlogarithmic decay of the magnetization M with time was observed. This deviation from the conventional logarithmic time dependence was not an approach of the system to the equilibrium state. The decay fits extremely well to the relation M(t)=${\mathit{M}}_0$/[1+(μkT/${\mathit{U}}_0$)ln(t/${\mathit{t}}_{\mathrm{eff}}$)${]}^{1/\mathrm{\mu }}$ from vortex-glass theory or to the empirical expression M(t)=${\mathit{M}}_0$+a(T)ln[ln(t/${\mathit{t}}_{\mathrm{eff}}$)]. Another possible explanation is based on the theory of thermally activated flux creep, wherein the magnitude of the pinning-energy barrier ${\mathit{U}}_0$ is a function of current density. From the latter we obtain an exponential dependence of ${\mathit{U}}_0$ on current density for J near its critical value.