Magnetic properties and spin–orbit coupling-driven Jahn–Teller distortions in K ₂ ReX ₆ (X = Cl, Br and I) with a half-filled 5d-t32g shell

Vacancy-ordered antifluorite halides hosting 5d transition metals have garnered increased attention in recent years due to the interplay between crystal field splitting, electronic correlations, and spin-orbit coupling (SOC), which collectively promote the emergence of novel quantum phenomena. In this work, we performed first-principles density functional theory calculations to comprehensively investigate the structural, electronic and magnetic properties of cubic K₂ReX₆ (X = Cl, Br, and I) with a t32g electronic configuration. Our results, in excellent agreement with the experimental findings, revealed that all three compounds adopted a type-I antiferromagnetic ordering, resulting from moderate nearest-neighbor antiferromagnetic interactions and weaker next-nearest-neighbor ferromagnetic couplings, despite the presence of geometric frustration in the face-centered cubic (fcc) framework. Furthermore, the systems are well described as insulators in the high-spin <i>S</i> = 3/2 state with a quenched orbital moment, rather than a spin-orbit entangled <i>J</i>_eff = 3/2 state. Theoretically, the presence of the SOC effect can stabilize the spin-orbit-entangled <i>J</i>_eff = 3/2 state and activate the Jahn-Teller effect, leading to lattice distortion in K₂ReX₆ with a half-filled 5d-t32g shell. However, even when the SOC strength is artificially increased to 2.5 times its self-consistent value-bringing the system closer to the ideal spin-orbit entangled <i>J</i>_eff = 3/2 state-the resulting SOC-driven Jahn-Teller distortion within the ReX₆ octahedron remains subtle. While the magnitude (∼0.01 Å) is significantly smaller than that observed in typical Jahn-Teller systems, the trend (both in magnitude and mode) of SOC-driven Jahn-Teller distortion across the halide series provides a crucial insight into the paradoxical distortion within the ReX₆ octahedron observed experimentally in low-temperature phases. These findings contribute to a broader understanding of intrinsic SOC-induced Jahn-Teller distortions in spin-orbit-entangled systems while revealing the experimental challenges associated with detecting such subtle lattice displacements.