Nb$_3$Sn Thin Films Using a Cu-Sn Route for Dark Matter Detection

Axion dark matter searches require superconducting radio-frequency (SRF) cavities on copper (Cu) substrates with quality factors Q > 10^5 in multi-tesla magnetic fields. Copper reduces thermal noise and allows complex geometries. Nb3Sn is a strong candidate due to its superior superconducting properties. However, uniform high-Tc Nb3Sn thin films on Cu are challenging due to Sn loss and substrate strain. This work uses solid-state diffusion of Sn from high-Sn Cu-Sn alloys into Nb layers to form Nb3Sn at Cu-compatible temperatures (650-750{\deg}C), avoiding the traditional ~1100{\deg}C vapor method. Varying Cu-Sn composition yielded an optimal alloy that maintains high Sn activity. Compositional and thermal expansion analyses showed Tc is suppressed below 18 K by Cu substrate strain. Experiments on Nb and sapphire substrates isolated the strain effects. Two routes were developed: (1) Cu-Sn on Ta-coated Cu with hot Nb sputtering (Tc = 16 K), and (2) Nb on Ta/Cu with Cu-Sn evaporation and ex-situ reaction. Route 2 gave uniform Nb3Sn and was chosen for cavity coating. A hexagonal cavity combining designs from the University of Washington and Center for Axion and Precision Physics was coated using Route 2 and tested to 50 mK and 9 T. At zero field it reached Q = 77,000 (40% above bare Cu's Q = 55,000), but Q dropped sharply in field. Nb3Sn coatings on Cu cavities outperform bare Cu at zero field and provide practical routes for improved axion detectors.