  In the weak ferromagnetic MnCO$_3$ system, a low-frequency collective spin
excitation (magnon) is the hybridized oscillation of nuclear and electron spins
coupled through the hyperfine interaction. By using a split-ring resonator, we
performed transmission spectroscopy measurements of MnCO$_3$ system and
observed, for the first time, avoiding crossing between the hybridized
nuclear-electron magnon mode and the resonator mode in the NMR-frequency range.
The splitting strength is quite large due to the large spin density of
$^{55}$Mn, and the cooperativity value $C=0.2$ (magnon-photon coupling
parameter) is close to the conditions of strong coupling. The results reveal a
new class of spin systems, in which the coupling between nuclear spins and
photons is mediated by electron spins via the hyperfine interaction, and in
which the similar normal-mode splitting of the hybridized nuclear magnon mode
and the resonator mode can be observed.
