Universal critical scaling of dc and ac complex resistivities in an indium film near the vortex-glass transition

We have made ac complex resistivity measurements from 100 Hz to 5 MHz in the linear regime, as well as dc resistivity measurements, for a thick indium film in constant magnetic fields $B.\mathrm{}$ At $B=0.1\mathrm{}\mathrm{T},$ the vortex-glass transition temperature $T_g$ can be defined from the frequency-independent phase of the ac resistivity, which is in good accordance with the value determined independently from dc measurements. Critical exponents ($\nu \sim 1.4$, $z\sim 8$) extracted from both dc and ac measurements are consistent. In addition to the vortex-correlation length ${\xi }_g\mathrm{}\left(T\right),$ the vortex-relaxation time ${\tau }_g\mathrm{}\left(T\right)\mathrm{}$ is directly obtained from the frequency dependence of the ac resistivity. Within a limited critical regime $\left(|T-T_g|\sim 0.1\mathrm{K}\right)$ about the phase transition, the amplitude and phase of the ac resistivity as well as the dc resistivity follow the universal scaling functions, which resemble those found in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7.$ In $B=1\mathrm{}\mathrm{T},$ we have observed the similar scaling behavior for the dc resistivity to that in $B=0.1\mathrm{}\mathrm{T},$ whereas degradation of the scaled isotherms is visible for the ac resistivity. Although this problem still awaits further studies, all of these findings offer strong experimental evidence for the second-order transition in indium films.