Role of Quantum Fluctuations in the triangular antiferromagnet Cs$_2$CuCl$_4$

We have performed a detailed comparison of static properties of the anisotropic triangular antiferromagnet Cs$_2$CuCl$_4$ with a calculation taking into account the leading order of the zero point fluctuations at zero temperature. The Hamiltonian of the Cs$_2$CuCl$_4$ compound is known to a high degree of accuracy and allows for a parameter-free calculation. A distinction must be made between transverse and longitudinal field due to a weak Dzyaloshinkii-Moriya interaction that introduce an easy-plane anisotropy in the Hamiltonian. The phase diagram is determined in a classical approximation along the two field directions. Building on these results, we calculate the contribution of quantized spin-waves in a large S expansion to themagnetization, ordering wavevector, sublattice magnetization and transverse spin component. The results are shown to depend sensitively on the weak anisotropy. In high field, we find the zero-point fluctuations to be quenched and use a mapping to a dilute Bose gas to determine the exact quantum contribution near the critical field. The results of the linear spin wave analysis are found to be in excellent agreement with the experimental data.