Quantum Magnetism in the Paratacamite Family: Towards an Ideal Kagomé Lattice

We report muon spin rotation measurements on the $S=1/2$ (Cu²⁺) paratacamite ZnₓCu_4-x(OH)₆Cl₂ family. Despite a Weiss temperature of ~-300 K, the $x=1$ compound is found to have no transition to a magnetic frozen state down to 50 mK as theoretically expected for the kagom\'e Heisenberg antiferromagnet. We find that the limit between a dynamical and a partly frozen ground state occurs around $x=0.5$. For $x=1$, we discuss the relevance to a singlet picture.