标题： 硫酸铜矿中的压力调制自旋链，Cu$_4$SO$_4$(OH)$_6$ 显示英文标题

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

摘要： 使用高压单晶X射线衍射结合热力学测量和密度泛函计算，我们揭示了矿物brochantite，Cu$_4$SO$_4$(OH)$_6$的微观磁性模型及其在压缩下的演化。 由于brochantite结构层内结构链之间的Cu-Cu距离更长以及Cu-O-Cu键角更大，导致形成了具有有效链内耦合的反铁磁自旋链，其值为$J\simeq 100$K。 这些锯齿形自旋链还通过第二近邻之间的铁磁耦合$J_2$得到额外稳定，并且由于几种反铁磁耦合而受到中等程度的挫折，这体现在材料的奈尔温度降低上。 对brochantite结构的压力调节保持其单斜对称性不变，并导致反铁磁$J$的增长，其速率为3.2 K/GPa，尽管这一趋势主要由增强的铁磁耦合$J_2$引起。 我们的结果表明，蓝铜矿和其他层状 Cu$^{2+}$矿物中的磁耦合性质是由其结构链上的晶格平移大小以及层弯曲的程度所控制的。 显示英文摘要

摘要： 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 N\'eel 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.