We report on the quasi-two-dimensional magnetism of the natural mineral diaboleite Pb${}_2$Cu(OH)${}_4$Cl${}_2$ with a tetragonal crystal structure, which is closely related to that of the frustrated spin-$\frac{1}{2}$ magnet PbVO${}_3$. Magnetic susceptibility of diaboleite is well described by a Heisenberg spin model on a diluted square lattice with the nearest-neighbor exchange of $J\simeq 35$ K and about 5$\%$ of nonmagnetic impurities. The dilution of the spin lattice reflects the formation of Cu vacancies that are tolerated by the crystal structure of diaboleite. The weak coupling between the magnetic planes triggers the long-range antiferromagnetic order below $T_N\simeq 11$ K. No evidence of magnetic frustration is found. We also analyze the signatures of the long-range order in heat-capacity data, and discuss the capability of identifying magnetic transitions with heat-capacity measurements.

• Received 8 December 2012

DOI:https://doi.org/10.1103/PhysRevB.87.064404