Spin triplet ground-state in the copper hexamer compounds A 2 C u 3 O ( S O 4 ) 3 ( A = Na , K )
The compounds ${A}_{2}\mathrm{C}{\mathrm{u}}_{3}\mathrm{O}{(\mathrm{S}{\mathrm{O}}_{4})}_{3}(A=\mathrm{Na},\mathrm{K})$ are characterized by copper hexamers which are weakly coupled along the $b$ axis to realize one-dimensional antiferromagnetic chains below ${T}_{\mathrm{N}}{\approx}3\mathrm{K}$, whereas the interchain interactions along the $a$ and $c$ axes are negligible. Here 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.