Search for spontaneous nucleation of magnetic flux during rapid cooling of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ films through $T_c$

We describe an experimental search for spontaneous formation of flux lines during a rapid quench of thin ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ films through $T_c.$ This effect is expected according to the Kibble-Zurek mechanism of a creation of topological defects of the order parameter during a symmetry-breaking phase transition. Spontaneously formed vortices were previously observed in superfluid ${}^3\mathrm{He},$ while a similar experiment in superfluid ${}^4\mathrm{He}$ gave negative results. Using a high-$T_c$ superconducting quantum interference device, we measured both the magnetic flux in the sample during a quench with a sensitivity of 20 ${\phi }_0/{\mathrm{cm}}^2,$ and the field noise which one would expect from flux lines pinned in the film. The sensitivity was sufficient to detect spontaneous flux at a level corresponding to ${10}^{-3}$ of the prediction. Within our resolution, we saw no evidence for this effect.