$\mu$SR study of the quantum dynamics in the frustrated $S=3/2$ kagome bilayers

We present $\mu$SR experiments in the $S=3/2$ kagome bilayer compound Ba$_{2}$Sn$_{2}$ZnGa$_{10-7p}$Cr$_{7p}$O$_{22}$ (BSZCGO$(p)$) and compare it to the isostructural SrCr$_{9p}$Ga$_{12-9p}$O$_{19}$ (SCGO$(p)$), including for the latter new results for $p\geq0.89$. Quantum-dynamical low energy magnetic excitations are evidenced in this novel compound. We study the evolution of the muon relaxation rate with $p$, $T$ and field. A phenomenological model for the muon relaxation based on sporadic dynamics due to spin excitations in a singlet sea proposed by Uemura \emph{et al.} [Phys. Rev. Lett. \textbf{73}, 3306 (1994)]. is extended to all fields and $T$-range. Its connexion to the RVB picture is discussed, and we argue that such coherent states might mediate the interactions between "impurities" which induce the spin glass freezing.