Ultrasonic investigation of NiCl₂-4SC(NH₂)₂ in the vicinity of the quantum critical points

We report results of sound-velocity and sound-attenuation measurements in the quantum S = 1 spin-chain magnet NiCl₂-4SC(NH₂)₂ that shows a field-induced antiferromagnetic (AF) ordering and two corresponding quantum critical points at H_c = 2.1 T and H_s = 12.6 T. The longitudinal acoustic c₃₃ mode modulates the in-chain exchange interaction and shows a softening in the vicinity of the quantum critical points, accompanied by energy dissipation in the acoustic wave. We discuss our results with a model where the main contribution to the spin-lattice interaction arises from the exchange-striction coupling within one-dimensional spin-chains.