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.

• Received 10 March 2024
• Revised 21 April 2024
• Accepted 22 April 2024

DOI:https://doi.org/10.1103/PhysRevB.109.184416