Muon spin relaxation measurements on a spin-ladder material Na ₂Co₂(C₂O₄)₃(H ₂O)₂

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 T_peak ≃ 18 K. Below T_peak, 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.