Theory of Collinear ordering on the Kagome Lattice of Zn-paratacamite*

We present a theory of the collinearly ordered phase discovered in a recent neutron scattering experiment [1] on Zn-paratacamite, Zn$_x$Cu$_ {4-x}$(OH)$_6$Cl$_2$, at small $x$. Zn-paratacamite has been considered as an excellent model system for the kagome lattice of spin-1/2 moments with antiferromagnetic exchange interactions. We studied both the classical and quantum Heisenberg models on the distorted kagome lattice appropriate for Zn-paratacamite with small x. Our theory naturally explains the emergence of a N\'eel phase. A theory for the Valence-Bond Solid phase also discovered in this experiment is presented in a related contributed talk.\newline \newline [1] S.-H. Lee et al., Nature Materials, 6, 853