Ultrasonic Investigation of NiCl₂-4SC(NH₂)₂

We report results of ultrasonic investigations of the quantum S = 1 spin-chain magnet NiCl₂-4SC(NH₂)₂ (DTN), in magnetic fields up to 18 T and temperatures down to 0.3 K. A field H along the c axis induces a transition into an antiferromagnetic phase with Tmax N ≈ 1:2 K. Accordingly, at T = 0 there are two quantum critical points at ~ 2:1 T and at ~ 12:6 T. The acoustic c33 mode, propagating along the spin chains, shows a pronounced softening close to the phase transition, accompanied by energy dissipation of the sound-wave. The H - T phase diagram obtained from our measurements is compared with results from other experimental investigations, and the low temperature acoustic anomalies are traced up to T > TN. We suggest a model where the main contribution to the spin-lattice interactions arises from the exchange- striction coupling within one-dimensional spin chains, and find a good qualitative agreement with the experimental data from the disordered phase.