Pressure-tuned spin chains in brochantite, Cu$_4$SO$_4$(OH)$_6$

TL;DR

This work determines the microscopic magnetic model of brochantite, Cu$_4$SO$_4$(OH)$_6$, and how it evolves under pressure by integrating high-pressure single-crystal XRD, thermodynamic measurements, and DFT+$U$ exchange-mapping. It identifies dominant zigzag AFM spin chains with $J_1 \approx$ a few $\times 10^2$ K, modulated by ferromagnetic second-neighbor couplings $J_2^A$ and $J_2^B$, as well as longer-range $J_4^A$ and $J_{\perp}$ couplings that induce frustration. Pressure strengthens intrachain couplings (notably via $J_2$) and flips $J_2^A$ from AFM to FM above ~3 GPa, while maintaining nearly isotropic compression; the Néel temperature rises from about 5–6 K to ~7 K at 1.9 GPa, reflecting reduced frustration and enhanced interchain interactions. The results reveal that magnetic couplings in layered Cu$^{2+}$ minerals are governed by lattice translations along structural chains and layer buckling, and they provide a framework to steer quantum magnetism in Cu-based minerals via pressure or strain.

Abstract

Using high-pressure single-crystal x-ray diffraction combined with thermodynamic measurements and density-functional calculations, we uncover the microscopic magnetic model of the mineral brochantite, Cu$_4$SO$_4$(OH)$_6$, and its evolution upon compression. The formation of antiferromagnetic spin chains with the effective intrachain coupling of $J\simeq 100$\,K is attributed to the occurrence of longer Cu--Cu distances and larger Cu--O--Cu bond angles between the structural chains within the layers of the brochantite structure. These zigzag spin chains are additionally stabilized by ferromagnetic couplings $J_2$ between second neighbors and moderately frustrated by several antiferromagnetic couplings that manifest themselves in the reduced Néel temperature of the material. Pressure tuning of the brochantite structure keeps its monoclinic symmetry unchanged and leads to the growth of antiferromagnetic $J$ with the rate of 3.2\,K/GPa, although this trend is primarily caused by the enhanced ferromagnetic couplings $J_2$. Our results show that the nature of magnetic couplings in brochantite and in other layered Cu$^{2+}$ minerals is controlled by the size of the lattice translation along their structural chains and by the extent of the layer buckling.

Figures (6)

• Figure 1: (a) Natural brochantite specimen from Bisbee, Arizona, USA, with flat prismatic plate crystals. (b) Optical and laser image of brochantite crystal aggregates taken using a Keyence VK-X200 microscope. The ambient-pressure crystal structure and the microscopic magnetic model of brochantite along $c$ (c,d) and $a$ (e,f) axes. In panel (f), experimental magnetic structure vilminot2006nikitin2023 is also shown for one of the layers.
• Figure 2: (a) Temperature-dependent magnetic susceptibility of brochantite measured in the applied fields of 0.1 T and 1 T. The inset shows magnetic transition in the low-temperature region. (b) $C_{\rm mag}/T$ of brochantite as a function of temperature at 0 T and the calculated magnetic entropy $S_{\rm mag}$ in zero field.
• Figure 3: (a) The lattice constants $a$/$a_0$, $b$/$b_0$, $c$/$c_0$ as a function of pressure. (b) Pressure dependence of the unit-cell volume. The solid blue line is the fit to the equation of state as described in the text.
• Figure 4: Pressure-dependent evolution of the average values of the Cu–O bond lengths in the crystal structure of brochantite. The insert shows the arrangement of apical and equatorial bonds in the coordination environment of the copper cation.
• Figure 5: Pressure-dependent evolution of the averaged magnetic couplings $J_1$ (a), $J_2^A$ (b), $J_2^B$ (c), $J_3$ (d), $J_4^A$ (e), $J_{\perp}$ (f) and the corresponding structural parameters (bond angles) in brochantite: Cu--O--Cu in the case of $J_1-J_3$ and Cu--O--O in the case of $J_4^A$ and $J_{\perp}$ (see also Table \ref{['tab:exchange']}). Dashed green lines show the trends in the bond angles as a guide for the eye. The inserts show the connectivity pathways of the copper polyhedra for the corresponding magnetic couplings.