Positive muon spin-relaxation (μ+SR) measurements on a spin-ladder material Na2Co2(C2O 4)3(H2O)2 are reported. We find that the relaxation rate, λ, under a longitudinal field of 3950 Oe increases with decreasing temperature, T, and is a maximum at Tpeak ≃ 18 K. Below Tpeak, λ decreases with decreasing T. This finding implies the observation of a spin gap formation by μ+SR technique. The approach of the exponent β in the relaxation function to 0.5 with decreasing T suggests a freezing of dilute moments. Below about 5K, we observe a sinusoidal oscillation in the time spectrum in zero applied field, which indicates an onset of long-range magnetic order. All these observations give microscopic evidence that the spin-ladder material is close to a quantum critical point.
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