  We report on the strong coupling between a metallic ferromagnetic Fe75Co25
thin film patterned element and a range of superconducting 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.
