Pressure-tuned spin chains in brochantite, Cu4SO4(OH)6

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, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>Cu</a:mi><a:mn>4</a:mn></a:msub><a:msub><a:mi>SO</a:mi><a:mn>4</a:mn></a:msub><a:msub><a:mrow><a:mo>(</a:mo><a:mi>OH</a:mi><a:mo>)</a:mo></a:mrow><a:mn>6</a:mn></a:msub></a:mrow></a:math>, and its evolution upon compression. The formation of antiferromagnetic spin chains with the effective intrachain coupling of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>J</b:mi><b:mo>≃</b:mo><b:mn>100</b:mn><b:mspace width="0.28em"/><b:mi mathvariant="normal">K</b:mi></b:mrow></b:math> 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:msub><e:mi>J</e:mi><e:mn>2</e:mn></e:msub></e:math> 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 <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>J</f:mi></f:math> with the rate of 3.2 K/GPa, although this trend is primarily caused by the enhanced ferromagnetic couplings <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:msub><g:mi>J</g:mi><g:mn>2</g:mn></g:msub></g:math>. Our results show that the nature of magnetic couplings in brochantite and in other layered <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:msup><h:mrow><h:mi>Cu</h:mi></h:mrow><h:mrow><h:mn>2</h:mn><h:mo>+</h:mo></h:mrow></h:msup></h:math> minerals is controlled by the size of the lattice translation along their structural chains and by the extent of the layer buckling.