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

TL;DR

This study models the magnetic properties of malachite under pressure, revealing how pressure influences the spin gap and demonstrating the effectiveness of DFT calculations in predicting magnetic interactions and structural details.

Contribution

It provides a detailed microscopic magnetic model of malachite at various pressures, highlighting the pressure dependence of intradimer couplings and the role of DFT in predicting magnetic and structural properties.

Findings

Malachite exhibits a large spin gap of 120K due to weakly interacting antiferromagnetic chains.

Intradimer exchange coupling is the strongest and pressure-dependent, decreasing the spin gap.

DFT calculations effectively predict exchange interactions and hydrogen positions, offering an alternative to experimental methods.

Abstract

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 120K. 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 190K 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.