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

We report the results of a study of the complex microwave surface impedance Z(S) resulting from vortex motion in YBa2Cu3O7-delta thin films in a dc magnetic field applied parallel to the film c axis. Using the technique of stripline resonators we have measured Z(S) at frequencies from 1.2 to 22 GHz and at temperatures from 5 to 65 K in magnetic fields from 0 to 4 T. We find that both the surface resistance Rs and the surface reactance X(S) increase almost linearly with the magnetic field. In zero applied magnetic field we find the frequency dependence of the surface resistance to be f(2). In the mixed state, however, there is a significant increase in R(S), particularly at lower frequencies, causing R(S) to be approximately proportional to f(1.2) at all measured temperatures. We show that fits of these data to models which include only a single pinning energy and a single characteristic pinning frequency are not able to explain our results. We propose that these data indicate the existence of a large number of metastable bound vortex states separated by energy barriers U-b whose magnitudes extend from U-b similar to 0 K to several hundred K, and that the dominant part of R(S) arises from vortex transitions between these states.