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Magnetic and crystallographic properties of the mineral langiteCu$_4$(OH)$_6$SO$_4\cdot 2$H$_2$O are reported. Its layered crystal structurefeatures a peculiar spatial arrangement of spin-$\frac12$ Cu$^{2+}$ ions thatarises from a combination of corner- and edge-sharing chains. Experimentally,langite orders antiferromagnetically at $T_N\simeq 5.7$ K as revealed bymagnetization and specific heat measurements. Despite this very low energyscale of the magnetic transition, langite features significantly strongercouplings on the order of 50-70 K. Half of the Cu$^{2+}$ spins are weaklycoupled and saturate around 12T, where the magnetization reaches 0.5$\mu_B$/Cu.These findings are rationalized by density-functional band-structurecalculations suggesting a complex interplay of frustrated exchange couplings inthe magnetic planes. A simplified model of coupled magnetic sublatticesexplains the experimental features qualitatively. To start from reliablestructural data, the crystal structure of langite in the 100-280 K temperaturerange has been determined by single-crystal x-ray diffraction, and the hydrogenpositions were refined computationally.

Frustrated magnetic planes with intricate interaction pathways in the mineral langite Cu$_4$(OH)$_6$SO$_4\cdot 2$H$_2$O