  The recently discovered natural minerals Cu3Zn(OH)6Cl2 and Cu3Mg(OH)6Cl2 are
spin 1/2 systems with an ideal kagome geometry. Based on electronic structure
calculations, we develop a realistic model which includes couplings across the
kagome hexagons beyond the original kagome model that are intrinsic in real
kagome materials. Exact diagonalization studies for the derived model reveal a
strong impact of these couplings on the magnetic ground state. Our predictions
could be compared to and supplied with neutron scattering, thermodynamic and
NMR data.
