Theory of Néel and Valence-Bond Solid Phases on the Kagome Lattice of Zn Paratacamite

Recently, neutron scattering data on powder samples of Zn paratacamite, Zn_xCu_4-x(OH)₆Cl₂, with small Zn concentration has been interpreted as evidence for valence-bond solid and Néel ordering [ S.-H. Lee et al. Nat. Mater. 6 853 (2007)]. We study the classical and quantum Heisenberg models on the distorted kagome lattice appropriate for Zn paratacamite at low Zn doping. Our theory naturally leads to the emergence of the valence-bond solid and collinear magnetic order at zero temperature. Implications of our results to the existing experiments are discussed. We also suggest future inelastic neutron and x-ray scattering experiments that can test our predictions.