Coupled antiferromagnetic spin-12chains in green dioptaseCu6[Si6O18]·6H2O

In this paper, we report inelastic neutron scattering measurements of the magnetic excitations of green dioptase ${\mathrm{Cu}}_{6}[{\mathrm{Si}}_{6}{\mathrm{O}}_{18}]\ifmmode\cdot\else\textperiodcentered\fi{}6{\mathrm{H}}_{2}\mathrm{O}$. The observed spectrum contains two magnetic modes and a prominent spin gap that is consistent with the ordered ground state of Cu moments coupled antiferromagnetically in spiral chains along the $c$ axis and ferromagnetically in $ab$ planes on the hexagonal cell. The data are in excellent agreement with a spin-$\frac{1}{2}$ Hamiltonian that includes antiferromagnetic nearest-neighbor intrachain coupling ${J}_{c}=10.6(1)$ meV, ferromagnetic interchain coupling ${J}_{ab}=\ensuremath{-}1.2(1)$ meV, and exchange anisotropy $\mathrm{\ensuremath{\Delta}}{J}_{c}=0.14(1)$ meV. We calculated the sublattice magnetization to be strongly reduced, $\ensuremath{\sim}0.39{\ensuremath{\mu}}_{\mathrm{B}}$. This appears compatible with a reduced N\'eel temperature, ${T}_{\mathrm{N}}=14.5\phantom{\rule{0.28em}{0ex}}\text{K}\ensuremath{\ll}{J}_{c}$, and can be explained by a presence of quantum spin fluctuations.