$\alpha \text{−}{\mathrm{RuCl}}_3$ is a candidate Kitaev material that exhibits zigzag antiferromagnetic ordering below 7 K. One contentious issue regarding this material is its bulk structure in the low-temperature phase. Recently, it has become generally accepted from experiments that the low- and high-temperature structures belong to the $R\overline{3}$ and $C2/m$ space groups, respectively. However, there was no theoretical study supporting the $R\overline{3}$-type structure as the low-temperature structure. In this study, we use constrained density functional theory to show that the $R\overline{3}$ structure is lower in energy than the $C2/m$ structure, in agreement with experimental observations. Then, we show that the conduction band minimum states are almost of the $J_{\mathrm{eff}}=1/2$ and $m_{\mathrm{eff}}=-1/2$ character, if we set the angular momentum quantization axis to be parallel to the Néel vector; this is the first analysis of the $J_{\mathrm{eff}}$ picture for $\alpha \text{−}{\mathrm{RuCl}}_3$ from this perspective. In addition, we compute the anisotropic magnetic exchange parameters and $g$ factors of monolayer $\alpha \text{−}{\mathrm{RuCl}}_3$, thereby providing a comprehensive understanding of its magnetism. Our results demonstrate that both second-nearest-neighbor exchange interactions and magnetic moments not captured by the conventional atomic orbital projection method are necessary for accurate description of the magnetism in $\alpha \text{−}{\mathrm{RuCl}}_3$. Moreover, the calculated $g$ factors are in fairly good agreement with experimental measurements, especially the small anisotropy between their in-plane and out-of-plane components. Finally, we examine the effects of structural distortions from a perfect ${\mathrm{RuCl}}_6$ octahedron, already present in bulk $\alpha \text{−}{\mathrm{RuCl}}_3$ without any external perturbation, on the magnetic properties. Our results indicate that relative twist of the upper and lower Cl triangles in the ${\mathrm{RuCl}}_6$ octahedron significantly influences the magnetic anisotropy, suggesting a novel way of engineering the magnetism in this class of materials.

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• Crystal structure
• Exchange interaction
• First-principles calculations
• Magnetic order
• Density functional calculations