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We report the realization of a strong coupling between a Gd$^{3+}$ spinensemble hosted in a scheelite (CaWO$_4$) single crystal and the resonant modeof a coplanar stripline superconducting cavity leading to a large separation ofspin-photon states of 146 MHz. The interaction is well described by the Dickemodel and the crystal-field Hamiltonian of the multilevel spin system. Weobserve a change of the crystal-field parameters due to the presence of photonsin the cavity that generates a significant perturbation of the crystal groundstate. Using finite-element calculations, we numerically estimate the cavitysensing volume as well as the average spin-photon coupling strength of$g_0\approx$ 620 Hz. Lastly, the dynamics of the spin-cavity states areexplored via pulsed measurements by recording the cavity ring-down signal as afunction of pulse length and amplitude. The results indicate a potential methodto initialize this multilevel system in its ground state via an active coolingprocess.

Strong coupling of a Gd$^{3+}$ multilevel spin system to an on-chip superconducting resonator