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The compounds A$_2$Cu$_3$O(SO$_4$)$_3$ (A=Na, K) are characterized by copperhexamers which are weakly coupled to realize antiferromagnetic order below TN=3K. They constitute novel quantum spin systems with S=1 triplet ground-states.We investigated the energy-level splittings of the copper hexamers by inelasticneutron scattering experiments covering the entire range of the magneticexcitation spectra. The observed transitions are governed by very unusualselection rules which we ascribe to the underlying spin-coupling topology. Thisis rationalized by model calculations which allow an unambiguous interpretationof the magnetic excitations concerning both the peak assignments and the natureof the spin-coupling parameters.

Spin-Coupling Topology in the Copper Hexamer Compounds A$_2$Cu$_3$O(SO$_4$)$_3$ (A=Na, K)