Character of magnetic excitations in a quasi-one-dimensional antiferromagnet near the quantum critical points: Impact on magneto-acoustic properties

We report results of magneto-acoustic studies in the quantum spin-chain magnet NiCl$_2$-4SC(NH$_2$)$_2$ (DTN) having a field-induced ordered antiferromagnetic (AF) phase. In the vicinity of the quantum critical points (QCPs) the acoustic $c_{33}$ mode manifests a pronounced softening accompanied by energy dissipation of the sound wave. The acoustic anomalies are traced up to $T > T_N$, where the thermodynamic properties are determined by fermionic magnetic excitations, the "hallmark" of one-dimensional (1D) spin chains. On the other hand, as established in earlier studies, the AF phase in DTN is governed by bosonic magnetic excitations. Our results suggest the presence of a crossover from a 1D fermionic to a 3D bosonic character of the magnetic excitations in DTN in the vicinity of the QCPs.