Spin triplet ground-state in the copper hexamer compounds A2Cu3O(SO4)3(A=Na,K)

The compounds ${A}_{2}\mathrm{C}{\mathrm{u}}_{3}\mathrm{O}{(\mathrm{S}{\mathrm{O}}_{4})}_{3}\phantom{\rule{0.28em}{0ex}}(A=\mathrm{Na},\phantom{\rule{0.16em}{0ex}}\mathrm{K})$ are characterized by copper hexamers which are weakly coupled along the $b$ axis to realize one-dimensional antiferromagnetic chains below ${T}_{\mathrm{N}}\ensuremath{\approx}3\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, whereas the interchain interactions along the $a$ and $c$ axes are negligible. We investigated the energy-level splittings of the copper hexamers by inelastic neutron scattering below and above ${T}_{\mathrm{N}}$. The eight lowest-lying hexamer states could be unambiguously assigned and parametrized in terms of a Heisenberg exchange Hamiltonian, providing direct experimental evidence for an $S=1$ triplet ground-state associated with the copper hexamers. Therefore, the compounds ${A}_{2}\mathrm{C}{\mathrm{u}}_{3}\mathrm{O}{(\mathrm{S}{\mathrm{O}}_{4})}_{3}$ serve as cluster-based spin-1 antiferromagnets to support Haldane's conjecture that a gap appears in the excitation spectrum below ${T}_{\mathrm{N}}$, which was verified by inelastic neutron scattering.