Frequency dependence of the vortex-state resistivity in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$

Swept-frequency measurements (1–600 MHz) of the vortex resistivity in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ were performed in fields from 0.5 to 8 T. At all fields studied, both the real and imaginary parts of the resistivity display a power-law frequency dependence with exponents ${\mathrm{\alpha }}_1$ and ${\mathrm{\alpha }}_2$ that depend only on the reduced field h=H/${\mathit{H}}^{\mathrm{*}}$(T). The scaling field ${\mathit{H}}^{\mathrm{*}}$(T) is identified with the critical field for the solid-to-liquid transition. The power-law dependence and the frequency variation of the phase angle are consistent with the model of Fisher, Fisher, and Huse. In particular, we confirm that the frequency dependence of the phase angle is qualitatively distinct on boths sides of the transition. The field dependence of ${\mathrm{\alpha }}_1$ and ${\mathrm{\alpha }}_2$ provides an improved determination of the critical phase angle (65.7°) and the dynamic exponent z (3.7).