Frequency dependence of the surface impedance of YBa2Cu3O7- delta thin films in a dc magnetic field: Investigation of vortex dynamics.

Abstract

We report measurements of the surface impedance ${\mathit{Z}}_{\mathit{s}}$=${\mathit{R}}_{\mathit{s}}$+i\ensuremath{\omega}\ensuremath{\lambda}' of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ thin films in an externally applied dc magnetic field B (parallel to the c axis) using a stripline resonator. At T=4.3 K we obtain the surface resistance ${\mathit{R}}_{\mathit{s}}$ and the microwave penetration depth \ensuremath{\lambda}' as a function of applied dc field up to 5 T and as a function of microwave frequency f from 1.2 to 20 GHz. While \ensuremath{\lambda}' increases linearly with B for Bg1 T at all frequencies, ${\mathit{R}}_{\mathit{s}}$ is found to be roughly \ensuremath{\propto}${\mathit{B}}^{\mathrm{\ensuremath{\alpha}}(\mathit{f})}$, where \ensuremath{\alpha}(f)1 for f\ensuremath{\le}10 GHz and \ensuremath{\alpha}(f)\ensuremath{\approxeq}1 for f\ensuremath{\ge}10 GHz. In zero dc field, ${\mathit{R}}_{\mathit{s}}$\ensuremath{\propto}${\mathit{f}}^{2}$. For Bg1 T, ${\mathit{R}}_{\mathit{s}}$ shows a much weaker dependence on f. The results for ${\mathit{Z}}_{\mathit{s}}$(f,T,B) have been quantitatively explained using a model developed by Coffey and Clem, based on a self-consistent treatment of vortex dynamics that includes the influence of vortex pinning, viscous drag, and flux creep. The pinning force constant ${\mathrm{\ensuremath{\alpha}}}_{\mathit{p}}$, the pinning frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$, and the pinning activation energy ${\mathit{U}}_{0}$(T,B) are obtained through the fitting procedure. We find that the effects of thermally activated flux creep at 4.3 K upon the surface resistance are significant. The low ${\mathit{U}}_{0}$\ensuremath{\approxeq}35 K that we determine is interpreted as arising from the interaction of the vortex lattice with a dense random pinning potential as described in the collective-pinning theory.