  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.
