Spin-coupling topology in the copper hexamer compounds A2Cu3O(SO4)3 (A=Na, K)

The compounds ${A}_{2}\mathrm{C}{\mathrm{u}}_{3}\mathrm{O}{(\mathrm{S}{\mathrm{O}}_{4})}_{3}$ $(A=\mathrm{Na},\phantom{\rule{0.16em}{0ex}}\mathrm{K})$ are characterized by copper hexamers that are weakly coupled to realize antiferromagnetic order below ${T}_{N}\ensuremath{\approx}3\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. They constitute quantum spin systems with $S=1$ triplet ground states. We investigated the energy-level splittings of the copper hexamers by inelastic neutron scattering experiments covering the entire range of the magnetic excitation spectra. The observed transitions are governed by very unusual selection rules that we ascribe to the underlying spin-coupling topology. This…