We report on the microscopic magnetic modeling of the spin-1/2 copper mineral malachite at ambient and elevated pressures. Despite the layered crystal structure of this mineral, the ambientpressure susceptibility and magnetization data can be well described by an unfrustrated quasione-dimensional magnetic model. Weakly interacting antiferromagnetic alternating spin chains are responsible for a large spin gap of 120 K. Although the intradimer Cu-O-Cu bridging angles are considerably smaller than the interdimer angles, density functional theory (DFT) calculations revealed that the largest exchange coupling of 190 K operates within the structural dimers. The lack of the inversion symmetry in the exchange pathways gives rise to sizable Dzyaloshinskii-Moriya interactions which were estimated by full-relativistic DFT+U calculations. Based on available high-pressure crystal structures, we investigate the exchange couplings under pressure and make predictions for the evolution of the spin gap. The calculations evidence that intradimer couplings are strongly pressure-dependent and their evolution underlies the decrease of the spin gap under pressure. Finally, we assess the accuracy of hydrogen positions determined by structural relaxation within DFT and put forward this computational method as a viable alternative to elaborate experiments.

Magnetic susceptibility and microscopic magnetic model of the mineral clinoclase Cu3(AsO4)(OH)3 are reported.This material can be well described as a combination of two nonequivalent spin dimers with the sizable magnetic couplings of J 700 K and JD2 300 K. Based on density functional theory calculations, we pinpoint the location of dimers in the crystal structure. Surprisingly, the largest coupling operates between the structural Cu2O6 dimers. We investigate magnetostructural correlations in Cu2O6 structural dimers, by considering the influence of the hydrogen position on the magnetic coupling. Additionally, we establish the hydrogen positions that were not known so far and analyze the pattern of hydrogen bonding.

Periodic and cluster density-functional theory (DFT) calculations, including DFT+U and hybrid functionals, are applied to study magnetostructural correlations in spin-1/2 frustrated chain compounds CuX2: CuCl2, CuBr2, and a fictitious chain structure of CuF2. The nearest-neighbor and second-neighbor exchange integrals, J1 and J2, are evaluated as a function of the Cu-X-Cu bridging angle θ in the physically relevant range 80-110• . In the ionic CuF2, J1 is ferromagnetic for θ ≤ 100• . For larger angles, the antiferromagnetic superexchange contribution becomes dominant, in accord with the Goodenough-Kanamori-Anderson rules. However, both CuCl2 and CuBr2 feature ferromagnetic J1 in the whole angular range studied. This surprising behavior is ascribed to the increased covalency in the Cl and Br compounds, which amplifies the contribution from Hund's exchange on the ligand atoms and renders J1 ferromagnetic. At the same time, the larger spatial extent of X orbitals enhances the antiferromagnetic J2, which is realized via the long-range Cu-X-X-Cu paths. Both, periodic and cluster approaches supply a consistent description of the magnetic behavior which is in good agreement with the experimental data for CuCl2 and CuBr2. Thus, owing to their simplicity, cluster calculations have excellent potential to study magnetic correlations in more involved spin lattices and facilitate application of quantum-chemical methods.

In this joint experimental and theoretical work magnetic properties of the Cu 2+ mineral szenicsite Cu3(MoO4)(OH)4 are investigated. This compound features isolated triple chains in its crystal structure, where the central chain involves an edge-sharing geometry of the CuO4 plaquettes, while the two side chains feature a corner-sharing zig-zag geometry. The magnetism of the side chains can be described in terms of antiferromagnetic dimers with a coupling larger than 200 K. The central chain was found to be a realization of the frustrated antiferromagnetic J1-J2 chain model with J168 K and a sizable second-neighbor coupling J2. The central and side chains are nearly decoupled owing to interchain frustration. Therefore, the low-temperature behavior of szenicsite should be entirely determined by the physics of the central frustrated J1-J2 chain. Our heat-capacity measurements reveal an accumulation of entropy at low temperatures and suggest a proximity of the system to the Majumdar-Ghosh point of the antiferromagnetic J1-J2 spin chain, J2/J1 = 0.5.