Cavity magnonics investigates hybrid systems where magnons interact coherently with photons, providing a platform to harness light-matter interaction in magnetic materials. Progress in this field hinges on achieving stronger and tunable nonlinear effects, which are essential for controlling magnon dynamics and frequency conversion. Here, we demonstrate the magnon Kerr effect in an anisotropic magnonic system comprising a 200~nm-thick yttrium iron garnet film strongly coupled to a three-dimensional microwave resonator. The strong shape anisotropy significantly enhances the magnon Kerr effect compared to a sphere of equivalent volume, while the cavity enables sensitive probing of magnetization dynamics. We demonstrate continuous tunability of the magnitude and sign of the Kerr shift by controlling the static orientation of the magnetization. Input-output modeling of the magnon-photon interaction provides a consistent description of our system and Kerr coefficients matching the experimental results. Our findings demonstrate a scalable approach to enhancing Kerr anharmonicity in hybrid magnon-photon systems while preserving strong coupling.
Petrosyan et al. (Thu,) studied this question.