Coupling microwave photons to topological spin-textures in Cu$_2$OSeO$_3$

Topologically protected nanoscale spin textures, known as magnetic skyrmions, possess particle-like properties and feature emergent magnetism effects. In bulk cubic heli-magnets, distinct skyrmion resonant modes are already identified using a technique like ferromagnetic resonance in spintronics. However, direct light-matter coupling between microwave photons and skyrmion resonance modes has not been demonstrated yet. Utilising two distinct cavity systems, we realise to observe a direct interaction between the cavity resonant mode and two resonant skyrmion modes, the counter-clockwise gyration and breathing modes, in bulk Cu$_2$OSeO$_3$. For both resonant modes, we find the largest coupling strength at 57 K indicated by an enhancement of the cavity linewidth at the degeneracy point. We study the effective coupling strength as a function of temperature within the expected skyrmion phase. We attribute the maximum in effective coupling strength to the presence of a large number of skyrmions, and correspondingly to a completely stable skyrmion lattice. Our experimental findings indicate that the coupling between photons and resonant modes of magnetic skyrmions depends on the relative density of these topological particles instead of the pure spin number in the system.