Experimental Study of the Inductance of Pinned Vortices in Superconducting YBa2Cu3O7-d Films

Using a two-coil mutual inductance method, we have measured the complex resistivity, rho_v(T,Be), of pinned vortices in c-axis pulsed laser deposited YBa2Cu3O7-d films with magnetic field Be applied perpendicular to the film. At low frequencies, (<100 kHz), rho_v is inductive and is inversely proportional to the Labusch parameter, the average vortex pinning force constant, kappa_exp. The observed weakening of kappa_exp with Be is consistent with a simple model based on linear pinning defects. Adding classical thermal fluctuations to the model in a simple way describes the observed linear T dependence of rho_v, below ~15 K and provides reasonable values for the effective radius (.3 nm to >.8 nm) of the defects and the depth of the pinning potential. The success of this model implies that thermal supercurrent (phase) fluctuations have their full classical amplitude down to 5 K for frequencies below the characteristic depinning frequency. To date, no sufficient theory exists to explain the data between ~15 K and the vortex glass melting temperature.