### Theoretical study of the crystal and electronic properties of $α−RuI3$

Ling-Fang Lin, Adriana Moreo, Elbio Dagotto
Published: 4 February 2022

Abstract: The material $\alpha \text{−}{\mathrm{RuCl}}_{3}$, with a two-dimensional Ru honeycomb sublattice, has attracted considerable attention because it may be a realization of the Kitaev quantum spin liquid. Recently, a new honeycomb material, $\alpha \text{−}{\mathrm{RuI}}_{3}$, was prepared under moderately high pressure, and it is stable under ambient conditions. However, different from was reported to be a paramagnetic metal without long-range magnetic order down to 0.35 K. Here, the structural and electronic properties of the quasi-two-dimensional $\alpha \text{−}{\mathrm{RuI}}_{3}$ are theoretically studied. First, based on first-principles density functional theory calculations, the ABC stacking honeycomb-layer $R\overline{3}$ (No. 148) structure is found to be the most likely stacking order for $\alpha \text{−}{\mathrm{RuI}}_{3}$ along the $c$ axis. Furthermore, both $R\overline{3}$ and $P\overline{3}1c$ are dynamically stable because no imaginary frequency modes were obtained in the phononic dispersion spectrum without Hubbard $U$. Moreover, the different physical behavior of $\alpha \text{−}{\mathrm{RuI}}_{3}$ compared to $\alpha \text{−}{\mathrm{RuCl}}_{3}$ can be understood naturally. The strong hybridization between Ru $4d$ and I $5p$ orbitals decreases the “effective” atomic Hubbard repulsion, leading the electrons of ${\mathrm{RuI}}_{3}$ to be less localized than in ${\mathrm{RuCl}}_{3}$. As a consequence, the effective electronic correlation is reduced from Cl to I, leading to the metallic nature of $\alpha \text{−}{\mathrm{RuI}}_{3}$. Based on the $\mathrm{DFT}+U$ (${U}_{\mathrm{eff}}=2$ eV) plus spin-orbital coupling, we obtained a spin-orbit Mott insulating behavior for $\alpha \text{−}{\mathrm{RuCl}}_{3}$ and, with the same procedure, a metallic behavior for $\alpha \text{−}{\mathrm{RuI}}_{3}$, in good agreement with experimental results. Furthermore, when introducing large (unrealistic) ${U}_{\mathrm{eff}}=6$ eV, the spin-orbit Mott gap opens in $\alpha \text{−}{\mathrm{RuI}}_{3}$ as well, supporting the physical picture we are proposing. Our results provide guidance to experimentalists and theorists working on two-dimensional transition metal tri-iodide layered materials.
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