Spin dynamics of the S=1/2 kagom\'e lattice antiferromagnet ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$

An important challenge in condensed matter physics is the search for quantum spin liquid states in two dimensional frustrated systems. We have performed thermodynamic and neutron scattering measurements on the $S=1/2$ kagom\'e lattice antiferromagnet ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$. The susceptibility indicates a Curie-Weiss temperature of $\theta_{CW} \simeq -300$~K; however, no magnetic order is observed down to 50~mK. Inelastic neutron scattering reveals a spectrum of low energy spin excitations with no observable gap down to 0.1~meV. The specific heat at low-$T$ follows a power law with exponent $\alpha \leq 1$. These results suggest that an unusual spin-liquid state with essentially gapless excitations is realized in this kagom\'e lattice system.