FREQUENCY-DEPENDENCE OF THE SURFACE IMPEDANCE OF YBA2CU3O7-DELTA THIN-FILMS IN A DC MAGNETIC-FIELD - INVESTIGATION OF VORTEX DYNAMICS

We report measurements of the surface impedance Z(s) = R(s) + iomegalambda' of YBa2Cu3O7-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 R(s) and the microwave penetration depth 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 lambda' increases linearly with B for B > 1 T at all frequencies, R(s) is found to be roughly is-proportional-to B(alpha)(f), where alpha(f) < 1 for f less-than-or-equal-to 10 GHz and alpha(f) almost-equal-to 1 for f greater-than-or-equal-to 10 GHz. In zero dc field, R(s) is-proportional-to f2. For B > 1 T, R(s) shows a much weaker dependence on f. The results for Z(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 alpha(p), the pinning frequency omega(p), and the pinning activation energy U0(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 U0 almost-equal-to 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.