Magneto-acoustic study near the quantum critical point of the frustrated quantum antiferromagnet Cs₂CuCl₄

Magneto-acoustic investigations of the frustrated triangular-lattice antiferromagnet Cs₂CuCl₄ were performed for the longitudinal modes c₁₁ and c₃₃ in magnetic fields along the a axis. The temperature dependence of the sound velocity at zero field shows a mild softening at low temperature and displays a small kink-like anomaly at T_N. Isothermal measurements at T < T_N of the sound attenuation a reveal two closely spaced features of different characters on approaching the material’s quantum-critical point (QCP) at B_s = 8.5 T for B II a. The peak at slightly lower fields remains sharp down to the lowest temperature and can be attributed to the ordering temperature T_N(B). The second anomaly, which is rounded and which becomes reduced in size upon cooling, is assigned to the material’s spin-liquid properties preceding the long-range antiferromagnetic ordering with decreasing temperature. These two features merge upon cooling suggesting a coincidence at the QCP. The elastic constant at lowest temperatures of our experiment at 32 mK can be well described by a Landau free energy model with a very small magnetoelastic coupling constant G/k_B = 2.8 K. The applicability of this classical model indicates the existence of a small gap in the magnetic excitation spectrum which drives the system away from quantum criticality.