Local magnetic response of superconducting Sr₂RuO₄ thin films and rings

We conduct local magnetic measurements on superconducting thin-film samples of Sr₂RuO₄ using scanning Superconducting Quantum Interference Device (SQUID) susceptometry. From the diamagnetic response, we extract the magnetic penetration depth, λ, which exhibits a quadratic temperature dependence at low temperatures. Although a quadratic dependence in high-purity bulk samples has been attributed to non-local electrodynamics, our analysis suggests that in our thin-film samples the presence of scattering is the origin of the quadratic dependence. While we observe micron-scale variations in the diamagnetic response and superconducting transition temperature, the form of the temperature dependence of λ is independent of position. Finally, we characterize flux trapping in superconducting rings lithographically fabricated from the thin films, paving the way to systematic device-based tests of the superconducting order parameter in Sr₂RuO₄.