Breakdown of $J_{eff}$ = 0 and $J_{eff}$ = 3/2 states and existence of large magnetic anisotropy energy in vacancy ordered 5$d$ antifluorites: K$_2$ReCl$_6$, K$_2$OsCl$_6$, and K$_2$IrCl$_6$

Abstract

Vacancy-ordered antifluorite materials (A$_2$BX$_6$) are garnering renewed attention as novel magnetic states driven by spin-orbit coupling (SOC) can be realized in them. In this work, by pursuing density functional theory calculations and model studies, we analyze the ground state electronic and magnetic structure of face-centered cubic (fcc) antifluorites K$_2$ReCl$_6$ (KReC, 5$d^3$), K$_2$OsCl$_6$ (KOsC, 5$d^4$), and K$_2$IrCl$_6$ (KIrC, 5$d^5$). We find that KReC stabilizes in the high-spin $S$ = 3/2 state instead of the expected pseudo-spin $J_{eff}$ = 3/2 state. The former occurs due to large exchange-splitting as compared to the SOC strength. On the contrary, the KOsC stabilizes in broken $J_{eff}$ = 0 ($S$ = 1) simple Mott insulating state while KIrC stabilizes in $J_{eff}$ = 1/2 spin-orbit-assisted Mott insulating state. The presence of an isolated metal-chloride octahedron makes these antifluorites weakly coupled magnetic systems with the nearest and next-nearest-neighbor spin-exchange parameters ($J_1$ and $J_2$) are of the order of 1 meV. For KReC and KOsC, the $J_1$ and $J_2$ are estimated to be antiferromagnetic and ferromagnetic, which leads to a Type-I antiferromagnetic ground state, whereas for KIrC, both $J_1$ and $J_2$ are antiferromagnetic, hence, it stabilizes with a Type-III antiferromagnetic state. Interestingly, in their equilibrium structure, these antifluorites possess large magnetic anisotropy energy (0.6-4 meV/transition metal), which is at least one-to-two orders higher than traditional MAE materials like transition metals and multilayers formed out of them. Moreover, with epitaxial tensile/compressive strain, the MAE enhances by one order, becoming giant for KOsC (20-40 meV/Os).