Imbalanced spin couplings in the copper hexameter compounds A2Cu3O(SO4)3 (A2=Na2, NaK, K2)

Abstract

The minerals A2Cu3O(SO4)3 (A2=Na2, NaK, K2) constitute quantum spin systems with copper hexamers as basic structural units. Strong intra-hexamer spin couplings give rise to an effective triplet ground-state. Weak inter-hexamer spin couplings are responsible for two-dimensional long-range magnetic order in the (b,c)-plane below 3.0<Tc<4.7 K. We investigated the magnetic excitations at T=1.5 K by inelastic neutron scattering (INS). The INS technique was based on the observation of wavevector-dependent slices in reciprocal space in order to selectively probe the magnetic signals in different Brillouin zones with different weight. Due to the imbalance of the spin couplings, the data analysis relied on a model in which the inter-hexamer spin couplings are treated perturbatively on top of the exact S=1 ground state. The inter-hexamer spin couplings turn out to be ferromagnetic.