Zero-field muon-spin-relaxation (ZF-μSR) measurements were carried out down to 80 mK on the randomness bond system Tl1-xK xCuCl3 with x = 0.44. Time spectra are well fitted by the stretched exponential function exp(-λt)β. The muon spin relaxation rate λ increases rapidly with decreasing temperature, and β tends to 0.5 at 80 mK. The divergent increase of λ suggests the critical slowing down of the frequency of the Cu-3d spin fluctuations toward a spin frozen state below 80 mK, and the root-exponential-like behavior of the time spectrum indicates that the origin of the relaxation is possibly the spatially-fixed fluctuating dilute moments.
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