Spin-strain coupling in NiCl₂-4SC(NH₂)₂

We report results of sound-velocity and sound-attenuation measurements in the quantum S = 1 spin-chain magnet NiCl₂-4SC(NH₂)₂, in magnetic fields up to 18 T. This material is discussed in the context of Bose-Einstein condensation of magnons. The longitudinal c33 acoustic mode, which has a propagation direction along the spin chains, shows pronounced spin-lattice effects. This mode demonstrates a softening in the vicinity of the field-induced antiferromagnetic ordering (below T = 1.2 K), accompanied by an energy dissipation in the acoustic wave. A broad maximum has been observed in the temperature dependence of the sound velocity at 44 K. The low-temperature sound-velocity and sound-attenuation behavior is subject to fluctuations of Ni spin degrees of freedom resulting in frequency-dependent effects. The B − T phase diagram obtained from the ultrasonic measurements is compared with results extracted from other experimental investigations. The ultrasonic results are analyzed with a theory based on exchange-striction spin-phonon coupling.