SQUID milliattovoltometry of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ thin films: Dissipation in low magnetic fields

The observation of magnetic flux noise in superconducting thin-film flux transformers of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ enables us to measure a very small, frequency-dependent resistance ${\mathit{R}}_{\mathit{v}}$(f) in the films, caused by vortex motion. In static magnetic fields below ${10}^{\mathrm{-}6}$ T and at voltages down to ${10}^{\mathrm{-}20}$ V ${\mathrm{Hz}}^{\mathrm{-}1/2}$,${\mathit{R}}_{\mathit{v}}$ is proportional to the frequency f at which the measurement is made, is approximately independent of temperature, and decreases with increasing static current in the transformer. This behavior cannot be explained by certain currently accepted models of dissipation arising from vortex motion, but is consistent with a model in which independent vortices hop between two potential wells in a confined region.