Using density functional calculations, we present a comprehensive study of the electronic and magnetic properties of the quantum spin chain materials ${\mathrm{K}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$ and ${\mathrm{K}}_2{\mathrm{CuSO}}_4{\mathrm{Br}}_2$. With the first-principles linear response method, we calculate the magnetic exchange parameters, and the theoretical values are in a quantitatively good agreement with experiments. Depending on the signs and magnitudes of the interchain magnetic exchange interactions, we find that the magnetic order of ${\mathrm{K}}_2{\mathrm{CuSO}}_4{\mathrm{Br}}_2$ along the $b$ axis is antiferromagnetic, while ${\mathrm{K}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$ has strong frustration along the $b$ axis. Based on the obtained magnetic exchange parameters, we successfully reproduce the experimental spin-wave dispersion. We also calculate Dzyaloshinskii-Moriya interactions, which are found to dominate in these compounds compared to the interchain magnetic exchange interactions. Finally, we obtain the phase diagram for these two materials using Monte Carlo simulations. Our results are consistent with previous experiments, giving a complete explanation of the magnetic structure.

中文翻译：

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量子自旋链材料K2CuSO4Cl2和K2CuSO4Br2中计算的磁交换相互作用

使用密度泛函计算，我们对量子自旋链材料的电子和磁性进行了全面的研究 ${\mathrm{ķ}}_2{\mathrm{硫酸铜}}_4{氯}_2$ 和 ${\mathrm{ķ}}_2{\mathrm{硫酸铜}}_4{溴}_2$。使用第一原理线性响应方法，我们可以计算出磁交换参数，并且理论值与实验在数量上很好地吻合。根据链间磁性交换相互作用的符号和强度，我们发现${\mathrm{ķ}}_2{\mathrm{硫酸铜}}_4{溴}_2$ 顺着 $b$ 轴是反铁磁的，而 ${\mathrm{ķ}}_2{\mathrm{硫酸铜}}_4{氯}_2$ 有强烈的挫败感 $b$轴。基于获得的磁交换参数，我们成功地再现了实验自旋波色散。我们还计算了Dzyaloshinskii-Moriya相互作用，发现与链间磁交换相互作用相比，这些化合物占主导地位。最后，我们使用蒙特卡洛模拟获得这两种材料的相图。我们的结果与以前的实验一致，对磁性结构进行了完整的解释。