Herbertsmithite: a slightly less than ideal kagom\'e antiferromagnet

Herbertsmithite, one of the best realizations of the Heisenberg antiferromagnet on kagom\'e, shows no signs of magnetic order down to the lowest accessible temperatures and likely possesses a quantum-disordered ground state. A recent site-specific X-ray diffraction experiment [1] shows deviations from the ideal model, most notably in the form of excess copper spins residing outside of kagom\'e planes. We study the influence of these impurities on the magnetic properties of herbertsmithite, focusing on locally induced Jahn-Teller distortions in kagom\'e planes and on exchange interactions between the excess spins.\\[4pt][1] Danna E. Freedman \textit{et al}, J. Am. Chem. Soc. {\bf132}, 16185 (2010).