Vortex Fluctuations in High- ${\mathit{T}}_{\mathit{c}}$ Films: Flux Noise Spectrum and Complex Impedance

The flux noise spectrum and complex impedance for a 500 Å thick YBCO film are measured and compared with predictions for two-dimensional vortex fluctuations. It is verified that the complex impedance and the flux noise spectra are proportional to each other, that the logarithm of the flux noise spectra for different temperatures has a common tangent with slope $\approx -1\mathrm{}$, and that the amplitude of the noise decreases as $d^{-3\mathrm{}}$, where $d$ is the height above the film at which the magnetic flux is measured. A crossover from normal to anomalous vortex diffusion is indicated by the measurements and is discussed in terms of a two-dimensional decoupling.