Spin fluctuations in the ground state of doped quantum spin system TlCu _1-xMg _xCl ₃ with x = 0:0047 Probed by muon-spin-relaxation technique

Zero-and longitudinal-field muon-spin-relaxation (ZF- and LF-muSR) measurements were carried out down to T - 20 mK on the slightly doped quantum spin system TlCu _1-xMg _xCl ₃ with x mdash0:0047, in which a magnetic phase transition is observed at 0.70 K by specific heat measurement. LF-μ SR measurements above and below the phase transition temperature revealed that the impurity-induced magnetic moments of the Cu-3d spins slowly fluctuate at a frequency of 0.74 MHz at T - 20 mK, far below the magnetic phase transition temperature. It is possible that the impurity-induced magnetic moments are in an exotic state where they fluctuate while preserving their wave vector and relative phase, i.e., a coherently fluctuating state