Vacancy-ordered halide double perovskites hosting $4d/5d$ transition metals have emerged as a distinct platform for investigating unconventional magnetism arising out of the interplay of strong atomic spin-orbit coupling (SOC) and Coulomb interactions. Focusing on the $d^2$ system ${\mathrm{Cs}}_2{\mathrm{WCl}}_6$, our ab initio electronic structure calculation reveals very narrow electronic bands, fulfilling the necessary condition to realize exotic orders. Using this input, we solve the many-body spin-orbit coupled single-site problem by exact diagonalization and show that the multiplet structure of ${\mathrm{Cs}}_2{\mathrm{WCl}}_6$ hosts ground non-Kramers doublets on W, with vanishing dipole moment and a small gap to an excited magnetic triplet. Our work provides the rationale for the observed strong deviation from the classic Kotani behavior in ${\mathrm{Cs}}_2{\mathrm{WCl}}_6$ for the measured temperature dependence of the magnetic moment. The non-Kramers doublets on W exhibit nonzero quadrupolar and octupolar moments, and our calculated two-site exchange supports the dominance of intersite octupolar exchange over quadrupolar interactions. We predict ferro-octupolar order with $T_c\sim 5\mathrm{K}$, which may get somewhat suppressed by quantum fluctuations and disorder; this could be tested in future low-temperature experiments.

中文翻译：

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5d2空位有序卤化物双钙钛矿中的多极磁性

空位有序卤化物双钙钛矿托管$4d/5d$过渡金属已成为研究强原子自旋轨道耦合（SOC）和库仑相互作用相互作用产生的非常规磁性的独特平台。专注于$d^2$系统${\mathrm{CS}}_2{\mathrm{氯化钨}}_6$，我们的从头算电子结构计算揭示了非常窄的电子能带，满足实现奇异订单的必要条件。使用该输入，我们通过精确对角化解决了多体自旋轨道耦合单点问题，并表明${\mathrm{CS}}_2{\mathrm{氯化钨}}_6$W 上存在接地非克莱默双峰，其偶极矩消失且与受激磁三重态之间存在小间隙。我们的工作为观察到的与经典小谷行为的强烈偏差提供了理论依据${\mathrm{CS}}_2{\mathrm{氯化钨}}_6$用于测量磁矩的温度依赖性。 W 上的非克莱默双峰表现出非零四极和八极矩，我们计算的双位点交换支持位点间八极交换相对于四极相互作用的主导地位。我们预测铁八极序${\mathrm{时间}}_C～5\mathrm{K}$，这可能会受到量子涨落和无序的一定程度的抑制；这可以在未来的低温实验中进行测试。