Non-linear vortex dynamics in the mixed state of superconducting a-MoGe and NbN thin films using low-frequency two-coil mutual inductance technique

We use a two-coil mutual inductance technique to investigate the non-linear response of the vortex lattice of two type-II superconducting thin films, namely a very weakly pinned amorphous Molybdenum Germanium (a-MoGe) and a moderate-to-strongly pinned Niobium Nitride (NbN). We observe a strong dependence of the magnetic shielding response of the superconductors on the ac excitation amplitude in the primary coil of the two-coil setup. The sample response is studied through the evolution of the radial profile of the induced current density with increasing drive amplitude, which gets significantly modified by the effect of flux creep. We develop a computation scheme where we iteratively combine the coupled Maxwell-London equations for the geometry of the two coils and the sample involved, with a model developed by Coffey and Clem, to analyze the non-linear ac response. The central result of this analysis is that the effect of flux creep gives rise to a strong nonlinearity in the electrodynamic response in the vortex state of the superconducting thin films, that extends down to very low amplitudes of ac excitation. Our results also show that at subcritical low frequency ac drives, the vortex viscosity is exponentially larger than the Bardeen-Stephen estimate. We present a simple scheme to obtain the intrinsic value of the pinning force constant, which otherwise gets affected due to flux creep even at very low ac drives and point out some outstanding issues that need to be addressed in future theoretical and experimental studies.