$\mathbf{^{17}O}$ Single Crystal NMR Evidence for a Gapped Spin-liquid Ground State in the S=1/2 Kagome Lattice $\mathbf{ZnCu_{3}(OH)_{6}Cl_{2}}$

The two-dimensional S=1/2 Kagome lattice in Herbersmithite $\rm{ZnCu_{3}(OH)_{6}Cl_{2}}$ is the best candidate for experimental realization of a quantum spin liquid ground state known to date. The recent discovery of a continuum of spinon excitations using inelastic neutron scattering\footnote{T. Han et al., Nature \textbf{492}(2012) 406} has drawn strong attention to its exotic magnetic properties. Understanding the nature of the paramagnetic ground state of $\rm{ZnCu_{3}(OH)_{6}Cl_{2}}$, however, remains a challenge, due to excess magnetic Cu defects occupying the interlayer Zn sites. We conducted single crystal NMR measurements of the $\rm{^{17}O}$ Knight shift, and succeeded in measuring the intrinsic spin susceptibility of the Kagome layer down to $\rm{T\sim0.01J(J\sim17 meV)}$ for the first time. We demonstrate that the intrinsic spin susceptibility decays exponentially at low temperatures, revealing the presence of a spin gap $\rm{\Delta \sim 0.1J}$. Moreover, we show that application of a high magnetic field suppresses the gap. These results provide direct evidence for a gapped spin-liquid ground state realized in $\rm{ZnCu_{3}(OH)_{6}Cl_{2}}$.\footnote{M. Fu et al., preprint.}