Exact Diagonalization Study of the Quantum Antiferromagnet Cs$_2$CuCl$_4$

We exactly diagonalize a model of the quantum antiferromagnet Cs$_2$CuCl$_4$. The quasi two-dimensional material is one of only two strong candidate systems that may exhibit a spin-liquid phase\footnote{R. Coldea, D. A. Tennant, A. M. Tsvelik and Z. Tylczynski, Phys. Rev. Lett. {\bf 86}, 1335 (2001).}. To compare with NMR experiments we calculate the total magnetization for clusters of up to 24 sites as a function of temperature and the applied magnetic field. The spin-1/2 degrees of freedom reside on an anisotropic triangular lattice; in addition to the usual nearest-neighbor Heisenberg exchange, interactions of the Dzyaloshinskii-Moriya type must also be included\footnote{K. Kodama, S. Miyahara, M. Takigawa, M. Horvatic, C. Berthier, F. Mila, H. Kageyama and Y. Ueda, J. Phys.: Condens. Matter {\bf 17} L61 (2005).}. We investigate the potential importance of additional higher-order terms\footnote{T. Yildirim, A. B. Harris, Amnon Aharony and O. Entin-Wohlman, Phys. Rev. B {\bf 52}, 10239 (1995).}.