Magnetic properties and spin–orbit coupling-driven Jahn–Teller distortions in K2ReX6 (X = Cl, Br and I) with a half-filled 5d-t 32g shell

Abstract

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 t³_2g 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 S = 3/2 state with a quenched orbital moment, rather than a spin–orbit entangled J_eff = 3/2 state. Theoretically, the presence of the SOC effect can stabilize the spin–orbit-entangled J_eff = 3/2 state and activate the Jahn–Teller effect, leading to lattice distortion in K₂ReX₆ with a half-filled 5d-t³_2g 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 J_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.