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

We report muon spin rotation measurements on the $S=1/2$ (${\mathrm{Cu}}^{2+}$) paratacamite ${\mathrm{Zn}}_x{\mathrm{Cu}}_{4-x}(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$ family. Despite a Weiss temperature of $\sim -300\mathrm{K}$, the $x=1$ compound is found to have no transition to a magnetic frozen state down to 50 mK as theoretically expected for the kagomé 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.