  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 TN. Isothermal measurements at T < TN of the sound
attenuation reveal two closely-spaced features of different character on
approaching the materials quantum-critical point (QCP) around Bs = 8.5 T for B
// a. The peak at slightly lower fields remains sharp down to the lowest
temperature and can be attributed to the ordering temperature TN(B). The second
anomaly which is rounded and which becomes reduced in size upon cooling is
assigned to the materials spin-liquid properties preceding the long-range
antiferromagnetic ordering. 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/kB = 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.
