Nature of the low energy excitations in the spin liquid state of Cs$_2$CuCl$_4$

We have performed detailed measurements as a function of temperature and applied magnetic field of the NMR rate in the spin liquid phase of the spin-1/2 frustrated antiferromagnet Cs$_2$CuCl$_4$. Comparison of the magnetization and relaxation rate to the spin-1/2 antiferromagnetic chain $\alpha$-CuNSal and to variational calculations using Gutzwiller-projected mean-field theory implies that the low energy excitations in Cs$_2$CuCl$_4$ are characterized by gapless fermionic excitations in the spin liquid phase at non-zero temperature and applied field. To investigate the ability of one dimensional versus two dimensional models to reproduce the low energy properties of Cs$_2$CuCl$_4$ \footnote{M.-A. Vachon {\it et al.}, New J. Phys. {\bf 13} 093029 (2011)} we compare the measured T$^{-1}$ NMR rate to a field theoretical description of a Luttinger liquid\footnote{H. K{\"u}hne {\it et al.}, Phys. Rev. B {\bf 83} 100407(R) (2011)}.