Néel and valence-bond crystal order on a distorted kagome lattice: Implications for Zn-paratacamite

Zn-paratacamite is a rare spin-1/2 antiferromagnetic insulator with an ideal kagome lattice structure in part of its phase diagram. As a function of Zn doping, this material undergoes a structural distortion which relieves the frustration and introduces magnetic order in the ground state, though the precise nature of the order is not clear at this point. In this paper, we present strong evidence for Néel ordering in the strongly distorted phase of Zn-paratacamite through the application of quantum Monte Carlo techniques. These numerical results support a recent Schwinger-boson mean-field theory of Zn-paratacamite. For weak distortion, close to the ideal kagome limit, our results indicate a regime with no Néel order but with broken glide-plane symmetry. For this model the glide-plane symmetry is broken by any valence-bond crystal. Hence, our results lend support to recent proposals [P. Nikolic and T. Senthil, Phys. Rev. B 68, 214415 (2003); R. R. P. Singh and D. A. Huse, Phys. Rev. B 76, 180407(R) (2007)] of a valence-bond crystal ground state for the undistorted lattice. The phase transition between the two phases could be in the deconfined universality class if it is not a first-order transition.