Magnetic flux noise in copper oxide superconductors

We report on the magnetic flux noise in thin films of YBa₂Cu₃O_7-x (YBCO), Tl₂Ca₂Ba₂Cu₃O_x, and TlCa₂Ba₂Cu₃O_x and in crystals of YBCO and Bi₂Sr₂CaCu₂O_8+x, measured with a Superconducting QUantum Interference Device (SQUID). We ascribe the noise to the motion of flux vortices. In the low magnetic fields in which the experiments are performed the average vortex spacing always exceeds the superconducting penetration depth. The spectral density of the noise usually scales as 1/f (f is frequency) from 1 Hz to 1 kHz and increases with temperature to a peak which is of the same magnitude in all samples, at the transition temperature. Furthermore, the noise power increases with the magnitude of the magnetic field in which the sample is cooled, with a power-law dependence over several decades, whereas a supercurrent well below the critical current density applied to YBCO films suppresses the noise power by an order of magnitude. Most of the measurements were made on YBCO films, and for this set of samples the noise decreases dramatically as the crystalline quality is improved. A model of thermally activated vortex motion is developed which explains the dependence of the noise on frequency, temperature, magnetic field, and current. The pinning potential is idealized as an ensemble of symmetrical double wells, each with a different activation energy separating the two states. From the noise measurements, this model yields the distribution of pinning energies, the vortex hopping distance, the number density of mobile vortices, and the restoring force on a vortex at a typical pinning site. The distribution of pinning energies in YBa₂Cu₃O_7-x shows a broad peak below 0.1 eV. Over narrow temperature intervals, most samples exhibit random telegraph signals in which the flux switches between two discrete levels, with activation energies and hopping distances much greater than those deduced from the 1/f noise measurements.