Universality of frequency and field scaling of the conductivity measured by ac susceptibility of a ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ film

Utilizing an exact inversion scheme, we determine the complex linear conductivity σ(ω) of a ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ film from the linear magnetic ac susceptibility which has been measured from 3 mHz to 50 MHz in fields between 0.4 and 4 T applied parallel to the c axis of a 250-nm thin disk. The frequency derivative of the phase σ’ ’/σ’ and the dynamical scaling of σ(ω) above and below ${\mathit{T}}_{\mathit{g}}$(B) provide clear evidence for a continuous phase transition at ${\mathit{T}}_{\mathit{g}}$ to a generic superconducting state. Based on the vortex-glass scaling model, the resulting critical exponents ν and z are close to those frequently obtained on films by other means and associated with an isotropic vortex glass. The field effect on σ(ω) can be related to the increase of the glass coherence length, ${\xi }_{\mathit{g}}$∼B.