Spin gap in malachite Cu2(OH)2CO3 and its evolution under pressure

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 ambient-pressure susceptibility and magnetization data can be well described by an unfrustrated quasi-one-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.