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Magnetic properties and underlying magnetic models of the syntheticA$_2$Cu$_3$O(SO$_4)_3$ fedotovite (A = K) and puninite (A = Na) minerals, aswell as the mixed euchlorine-type NaKCu$_3$O(SO$_4)_3$ are reported. We showthat all these compounds contain magnetic Cu$_6$ hexamer units, which attemperatures below about 100 K act as single spin-1 entities. Weak interactionsbetween these magnetic molecules lead to long-range order below $T_N$ = 3.4 K(A = Na), 4.7 K (A = NaK), and about 3.0 K (A = K). The formation of themagnetic order is elucidated by ab initio calculations that revealtwo-dimensional inter-hexamer interactions within crystallographic $bc$ planes.This model indicates the presence of a weakly distorted square lattice of $S=1$magnetic ions and challenges the earlier description of theA$_2$Cu$_3$O(SO$_4)_3$ minerals in terms of Haldane spin chains.

Magnetic hexamers interacting in layers in the (Na,K)$_2$Cu$_3$O(SO$_4)_3$ minerals