Low-energy spin dynamics in randomness-introduced spin-gap systems

Zero- and longitudinal-field muon spin-relaxation (ZF- and LF-μSR) measurements were carried out on randomness-introduced quantum spin-gap systems Tl _1-x K _x CuCl ₃ in the wide range of x from 0.40 to 0.65. The temperature changes in the muon spin-relaxation rate λ in longitudinal fields were deduced from LF-μSR measurements. Peak structure in the temperature change in λ in 3950 G, which suggests the soft mode of spin waves, is observed in the region of x>0.53, although a finite frequency of spin fluctuations remains down to T=0, i.e., the ground state is paramagnetic. The temperature giving the peak in λ decreases with decreasing the concentration of x and the peak structure vanishes in x=0.51. In the case of x=0.40, however, λ shows the different behavior and λ in lower fields increases with decreasing temperature down to 0.28 K. The increase in λ is possibly interpreted as a precursor of the transition to the reported Bose-glass phase. These results suggest a possibility of the existence of the quantum critical point from the Bose-glass phase to a paramagnetic phase around x=0.51.