Ultrastrong Magnon-Photon Coupling Achieved by Magnetic Films in Contact with Superconducting Resonators

Coherent coupling between spin-wave excitations (magnons) and microwave photons in a cavity may disclose new paths to unconventional phenomena as well as novel applications. Here, we present a systematic investigation of yttrium iron garnets (YIG) films on top of coplanar waveguide resonators made of superconducting YBa2Cu3O7 (YBCO). We first show that spin-wave excitations with frequency higher than the Kittel mode can be excited by putting in direct contact a 5-?m-thick YIG film with the YBCO coplanar resonator (cavity frequency ?c/2?=8.65 GHz). With this configuration, we obtain very large values of the collective coupling strength ?/2??2 GHz and cooperativity C=5×104. Transmission spectra are analyzed by a modified Hopfield model for which we provide an exact solution that allows us to well reproduce spectra by introducing a limited number of free parameters. It turns out that the coupling of the dominant magnon mode with photons exceeds 0.2 times the cavity frequency, thus demonstrating the achievement of the ultrastrong-coupling regime with this architecture. Our analysis also shows a vanishing contribution of the diamagnetic term, which is a peculiarity of pure spin systems.