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

(a) Schematic picture of the Cu2+ hexamers in the compounds A2Cu3O(SO4)3 (A = Na, K). The parameters Jij denote the exchange coupling scheme adopted to describe the observed spin excitations. (b) Energies of the spin excitations observed for A2Cu3O(SO4)3 (A = Na, K) denoted by Si , Ti, and Qi for the singlet, triplet, and quintet states, respectively. from Fig. 1

The compounds A2Cu3O(SO4)3(A=Na,K) are characterized by copper hexamers which are weakly coupled along the b axis to realize one-dimensional antiferromagnetic chains below TN≈3K, 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 TN. 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 A2Cu3O(SO4)3 serve as cluster-based spin-1 antiferromagnets to support Haldane's conjecture that a gap appears in the excitation spectrum below TN, which was verified by inelastic neutron scattering.