Frequency independence of the vortex-glass transition in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ thin films

The frequency dependence of the vortex-glass phase transition in a ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ thin film was measured at frequencies ranging from ${10}^{\mathrm{-}1}$ to ${10}^5$ Hz in applied fields H ranging from 0 to 50 kOe. The transition temperature ${\mathit{T}}_{\mathit{g}}$ and the critical scaling parameter ν(z-1) were determined from the scaling of both current-voltage characteristics and the resistivity measurements. The critical scaling parameters determined by different methods are found to agree [ν(z-1)=7.2±0.3] and are consistent with the predictions of the continuous vortex-glass phase transition described by Fisher, Fisher, and Huse [Phys. Rev. B 43, 130 (1991)]. No frequency dependence is observed for the vortex-glass transition temperature ${\mathit{T}}_{\mathit{g}}$, for the range of parameters studied here. While the data do provide further support for the existence of a continuous vortex-glass phase transition, no evidence for the divergent time scale is observed, setting an upper limit of ${10}^{\mathrm{-}5}$ sec for this time scale at (T-${\mathit{T}}_{\mathit{g}}$)/${\mathit{T}}_{\mathit{g}}$≊0.02. Since ac-susceptibility data do not actually measure the ‘‘irreversibility line’’ (IRL), these results provide a fundamental measurement of the frequency dependence of the IRL. The observed frequency dependence is inconsistent with the flux-creep-based picture of the IRL.