Effects of edge cracks on the thermomagnetic instabilities of type-II superconducting thin films

Thermomagnetic instability is a crucial issue for the application of superconductors. Effects of edge cracks on the thermomagnetic instability of superconducting thin films are systematically investigated in this work. Dendritic flux avalanches in thin films are well reproduced through electrodynamics simulations, and relevant physical mechanisms are revealed from dissipative vortex dynamics simulations. It is found that edge cracks sharply decrease the threshold field for the thermomagnetic instability of superconducting films. Spectrum analysis shows that the time series of magnetization jumping displays scale-invariance and follows a power law with an exponent around 1.9. In a cracked film, flux jumps more frequently with lower amplitudes compared with its crack-less counterpart. As the crack extends, the threshold field decreases, the jumping frequency gets lower, while its magnitude gets larger. When the crack has extended long enough, the threshold field increases to even larger than that of the crack-less film. This counterintuitive result originates from the transition of the thermomagnetic instability triggered at the crack tip to the one triggered at the center of the crack edges, which is validated by the multifractal spectrum of magnetization jumping sequences. In addition, with the variation of crack lengths, three different modes of vortex motion are found, which explains the different flux patterns formed in the avalanche process.