Magnetic dilution in the geometrically frustrated SrCr${}_{9p}$Ga${}_{12-9p}$O${}_{19}$ and the role of local dynamics: a $\mu$SR study

We investigate the spin dynamics of SrCr${}_{9p}$Ga${}_{12-9p}$O${}_{19}$ for p below and above the percolation threshold p_c using muon spin relaxation. Our major findings are: (I) At T->0 the relaxation rate is T independent and proportional to p^3, (II) the slowing down of spin fluctuation is activated with an energy U which is also a linear function of p^3 and lim_{p-> 0}U = 8 K; this energy scale could stem only from a single ion anisotropy, and (III) the p dependence of the dynamical properties is identical below and above p_c, indicating that they are controlled by local excitation.