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 ${mathrm{Zn}}_{x}{mathrm{Cu}}_{4ensuremath{-}x}(mathrm{OH}{)}_{6}{mathrm{Cl}}_{2}$ family. Despite a Weiss temperature of $ensuremath{sim}ensuremath{-}300text{ }text{ }mathrm{K}$, the $x=1$ compound is found to have no transition to a magnetic frozen state down to 50 mK as theoretically expected for the 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.