Incommensurate quantum magnetism and multiple-q magnetic order in synthetic antlerite, Cu3SO4(OH)4

In frustrated magnetic systems, geometric constraints or the competition amongst interactions introduce extremely high degeneracy and prevent the system from readily selecting a low-temperature ground state. In the mineral antlerite, Cu$_3$SO$_4$(OH)$_4$, Cu$^{2+}$ ($S$=1/2) quantum spins populate triangular-lattice three-leg ladders in a novel highly-frustrated quasi-one-dimensional structural motif. We demonstrate that this mineral hosts several exotic magnetic phases, including a candidate multiple-{\bfseries q} phase, and that the magnetic ground state is not idle-spin as previously proposed. Multiple-{\bfseries q} phases are extremely uncommon in centrosymmetric compounds of 3d and lighter elements, and the discovery of such a phase in antlerite is likely to open a new route to finding new materials platforms for novel magnetic order.