  In this work, the ultra-strong photon-to-magnon coupling is demonstrated for
on-chip multilayered superconductor/ferromagnet/insulator hybrid thin film
structures reaching the coupling strength above 6 GHz, the coupling ratio about
0.6, the single-spin coupling strength about 350 Hz, and cooperativity about
10^4. High characteristics of coupling are achieved owing to a radical
suppression of the photon phase velocity in electromagnetic resonator. With
achieved coupling the spectrum reveals inapplicability of the Dicke model, and
evidences contribution of the diamagnetic A^2 interaction term in the
Hamiltonian of the system, which satisfies the Thomas-Reiche-Kuhn sum rule. The
contribution of the A^2 term denotes validity of the Hopfield quantum model and
manifests observation of a different hybrid polariton quasi-particle, namely,
the plasmon-magnon polariton.
