Ligand-SOC enhanced $4f^5$ Kitaev antiferromagnet: Application to $\mathrm{SmI}_3$

The search for Kitaev quantum spin liquids (Kitaev-QSLs) in real materials has mainly focused on $4d$- and $5d$-electron honeycomb systems. A recent experimental study on the $4f^5$ honeycomb iodide $\mathrm{SmI}_3$ reported the absence of long-range magnetic order down to $0.1\ \text{K}$, suggesting a possible Kitaev-QSL phase. Motivated by the interplay between the complex exchange processes inherent to the $4f^5$ multi-electron configuration and the strong spin-orbit coupling (SOC) of the iodine ligands, we systematically investigate the effective exchange interactions in $\mathrm{SmI}_3$ using the strong coupling expansion method. Our findings reveal that bond-dependent SOCs (bond-SOCs), extracted from relativistic density functional theory (DFT) calculations, significantly enhance the antiferromagnetic (AFM) Kitaev interaction, driving the system close to the AFM Kitaev point. A microscopic analysis based on the Slater-Koster approach further indicates that the strong SOC of the iodine ligands (ligand-SOC) is the origin of bond-SOCs and plays a pivotal role in mediating the superexchange processes. Additionally, we identify a spin-flop transition induced by the bond-SOCs, where the enhanced AFM Kitaev interactions shift the AFM order from the out-of-plane $[1, 1, 1]$-direction to an in-plane orientation, breaking the $C_3$ rotational symmetry. Linear spin-wave theory (LSWT) further predicts the emergence of gapless modes following the spin-flop transition, indicating enhanced fluctuations and increased instability near the AFM Kitaev point. Our results highlight the crucial role of strong ligand-SOC in stabilizing the dominant AFM Kitaev interactions in $\mathrm{SmI}_3$ and provide valuable insights for discovering new $f$-electron Kitaev-QSL candidates.