$^{63}$Cu and $^{35}$Cl NMR Investigation of the $S=1/2$ Kagomé Lattice System ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$

The possible realization of a spin-liquid state in ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$ (herbertsmithite) has attracted much recent attention. We report a $^{63}$Cu and $^{35}$Cl NMR investigation of the Kagom\'e lattice formed by Cu$^{2+}$ ions ($S=1/2$). From the measurements of $^{35}$Cl NMR Knight shifts, we demonstrate that the local spin susceptibility develops a large distribution below $\sim 125$ K. Low frequency spin fluctuations grow toward T=0 without the signature of a critical slowing down.