μSRStudy of the Quantum Dynamics in the FrustratedS=32Kagomé Bilayers

We present $\mu \mathrm{S}\mathrm{R}$ experiments in the $S=\frac{3}{2}$ kagomé bilayer compound ${\mathrm{B}\mathrm{a}}_2{\mathrm{S}\mathrm{n}}_2{\mathrm{Z}\mathrm{n}\mathrm{G}\mathrm{a}}_{10-7p}{\mathrm{C}\mathrm{r}}_{7p}{\mathrm{O}}_{22}$ [BSZCGO$(p)$] and compare it to the isostructural ${\mathrm{S}\mathrm{r}\mathrm{C}\mathrm{r}}_{9p}{\mathrm{G}\mathrm{a}}_{12-9p}{\mathrm{O}}_{19}$ [SCGO$(p)$], including for the latter new results for $p\ge 0.89$. 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 et al. is extended to all fields and $T$ range. Its connection 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.