Longitudinal-field muon spin relaxation (LF-μSR) measurements were performed on the spin-1=2 kagome lattice compound (Rb0.47Cs0.53)2Cu3SnF12 down to 26 mK. It is reported that the spin-1/2 kagome lattice antiferromagnet system (Rb1-xCsx)2Cu3SnF12 has the quantum critical point at x = 0.53 between the antiferromagnetically ordered phase and the valence-bond-glass phase observed by macroscopic measurements. Recently, we have reported that LF-μSR measurement results show no evidence of a magnetic order, and that the muon-spin-relaxation rate increases monotonically at least at temperatures down to 0.3K [J. Phys. Soc. Jpn. 87, 074708 (2018).]. Our new results below 0.3K in this study show muon-spin-relaxation rates in LFs have an almost constant temperature dependence, and the LF dependence of the muon-spin-relaxation rate reveals that muon spins experience fluctuating internal fields with lower frequencies at temperatures down to 26 mK. These results suggest that the ground state of (Rb1-xCsx)2Cu3SnF12 with x = 0.53 is a spin fluctuating state with no magnetic order.
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