Tunable Cooperativity in Coupled Spin--Cavity Systems

We experimentally study the tunability of the cooperativity in coupled spin--cavity systems by changing the magnetic state of the spin system via an external control parameter. As model system, we use the skyrmion host material Cu$_2$OSeO$_3$ coupled to a microwave cavity resonator. In the different magnetic phases we measure a dispersive coupling between the resonator and the magnon modes and model our results by using the input--output formalism. Our results show a strong tunability of the normalized coupling rate by magnetic field, allowing us to change the magnon--photon cooperativity from 1 to 60 at the phase boundaries of the skyrmion lattice state.