Strong Coupling of an Fe-Co Alloy with Ultralow Damping to Superconducting Co-planar Waveguide Resonators

We report on the strong coupling between a metallic ferromagnetic ${\mathrm{Fe}}_{75}{\mathrm{Co}}_{25}$ thin-film patterned element and a range of superconducting $\mathrm{Nb}$ half-wavelength co-planar waveguide (CPW) resonators. By varying the volume of the ferromagnet we demonstrate that the coupling rate scales linearly with the square root of the number of spins and achieve a coupling rate over 700 MHz, approaching the ultrastrong coupling regime. Experiments varying the center conductor width while maintaining constant magnetic volume verify that decreasing the center conductor width increases coupling and cooperativity. Our results show that the frequency dependence of the coupling rate is linear with the fundamental and higher-order odd harmonics of the CPW, but with differing efficiencies. The results show promise for scaling planar superconducting resonator-magnetic hybrid systems to smaller dimensions.