Nonlinear microwave response of Nb3Sn films: a case study of granular superconductors

We have investigated the microwave magnetic field dependent surface resistance, R_s(B_s), of Nb₃Sn films of different film thickness and on different substrates at 19 GHz. The film thickness controls the grain size of the polycrystalline films. It provides a tool to study the role of grain boundaries on the nonlinear microwave response of granular superconductors. We find a non-monotonic dependence of the onset field, B_on, of nonlinear surface resistance on film thickness, with a maximum of 25 mT at 1.2 μm. This behaviour reveals that magnetic losses at grain boundaries dominate in thin films, and microwave heating in thick films. The universal scaling behaviour of B_on with temperature, its dependence on the thermal conductivity of the substrate, and the good agreement between the quadratic field dependence of R_s and a weakly-coupled grain model indicate heating at grain boundaries as a possible mechanism. The correlation between the nonlinear microwave response and microstructure of the granular films indicates possible improvements and intrinsic limitations