Theory of Neel and valence-bond solid phases on the kagome lattice of Zn paratacamite

Recently, neutron scattering data on powder samples of Zn paratacamite, ZnxCu4-x(OH)(6)Cl-2, with small Zn concentration has been interpreted as evidence for valence-bond solid and Neel ordering [S.-H. Lee , 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.