Dzyaloshinskii-Moriya interactions and non-magnetic impurities in the s=1/2 kagome antiferromagnet*

Motivated by recent NMR experiments[1] on ZnCu$_3$(OH)$_6$Cl$_2$, we present an exact diagonalization study of the combined effect of non-magnetic impurities and Dzyaloshinskii-Moriya (DM) interactions in the $s=1/2$ Kagom\'e antiferromagnet. The magnetization response and the correlation matrix data reveal that the dimer freezing which occurs around the vacancy for $D=0$ [2,3] ($D$ is the magnitude of the DM vectors) persists up to $D/J \simeq 0.07$, above which a phase transition to the $Q=0$ semiclassical 120$^{\circ}$ state[4] takes place. Surprisingly however, the dimers next to the vacancy remain strong up to $D/J \sim 2-3$, i.e. well above the critical point. Implications for ZnCu$_3$(OH)$_6$Cl$_2$ will be discussed. 1. A. Olariu, {\it et al.}, Phys. Rev. Lett. {\bf 100}, 087202 (2008). 2. S. Dommange, {\it et al.}, Phys. Rev. B {\bf 68}, 224416 (2003). 3. A. L\"auchli, {\it et al.}, Phys. Rev. B {\bf 76}, 144113 (2007). 4. O. C\'epas, {\it et al.}, Phys. Rev. B {\bf 78}, 140405 (2008).