Observation of Magnetic Flux Generated Spontaneously During a Rapid Quench of Superconducting Films

We report observations of spontaneous formation of magnetic flux lines during a rapid quench of ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{7-\delta }$ films through $T_c$. This effect is predicted according to the Kibble-Zurek mechanism of creation of topological defects of the order parameter during a symmetry-breaking phase transition. Our previous experiment, at a quench rate of $20\mathrm{K}/\mathrm{s}$, gave null results. In the present experiment, the quench rate was increased to $>{10}^8\mathrm{K}/\mathrm{s}$. The amount of spontaneous flux increases weakly with the cooling rate.

Figure 1

Temperature cycle of the film after a laser pulse. The energy of the pulse is 7.1 mJ (solid symbols) and 3.1 mJ (open symbols). The horizontal line is $T_c$ for our sample. Note that the cooling rate through $T_c$ is slower for the high energy pulse.

Figure 2

Typical sequence of 100 raw data readings of the magnetometer, each following a separate quench at a rate of ${10}^8\mathrm{K}/\mathrm{s}$. Open symbols: control sample (“noise”); solid symbols: superconducting film. The conversion into flux units is $4\mathrm{m}\mathrm{V}/{\varphi }_0$ for the noise and $1\mathrm{m}\mathrm{V}/{\varphi }_0$ for the signal from the superconducting film. The lines connect successive data points.

Figure 3

Typical histogram of spontaneous flux from several hundred quenches. The dashed line is a Gaussian fit. The solid line is a fit to the noise measurements taken at the same conditions. The inset shows that the distribution width does not depend on the external field. The error bars in the inset are the uncertainty of the fits. The cooling rate for all the data in the figure (including the inset) is $\simeq {10}^8\mathrm{K}/\mathrm{s}$.

Figure 4

Dependence of the distribution of spontaneous flux versus the cooling rate. The vertical error bars are those of the fit to a Gaussian distribution. The solid line is the prediction of Refs. 2, 17 scaled to fit the data.