The minerals $A_2{\mathrm{Cu}}_3\mathrm{O}{\left({\mathrm{SO}}_4\right)}_3(A_2={\mathrm{Na}}_2,\mathrm{NaK},{\mathrm{K}}_2)$ constitute quantum spin systems with copper hexamers as basic structural units. Strong intrahexamer spin couplings give rise to an effective triplet ground state. Weak interhexamer spin couplings are responsible for two-dimensional long-range magnetic order in the ($b,c$) plane below $3.0<T_c<4.7\mathrm{K}$. We investigated the magnetic excitations at $T=1.5$ K by inelastic neutron scattering (INS). The INS technique was based on the observation of wave vector 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 relies on a model in which the interhexamer spin couplings are treated perturbatively on top of the exact $S=1$ ground state. The interhexamer spin couplings turn out to be ferromagnetic.

• Received 28 August 2021
• Revised 30 October 2021
• Accepted 17 November 2021

DOI:https://doi.org/10.1103/PhysRevB.104.L220401