$\alpha {\text{-RuCl}}_3$ has been proposed recently as an excellent playground for exploring Kitaev physics on a two-dimensional (2D) honeycomb lattice. However, structural clarification of the compound has not been completed, which is crucial in understanding the physics of this system. Here, using ab initio electronic structure calculations, we study a full three-dimensional (3D) structure of $\alpha {\text{-RuCl}}_3$, including the effects of spin-orbit coupling (SOC) and electronic correlations. The three major results are as follows: (i) SOC suppresses dimerization of Ru atoms, which exists in other Ru compounds such as isostructural ${\mathrm{Li}}_2{\text{RuO}}_3$, and makes the honeycomb closer to an ideal one. (ii) The nearest-neighbor Kitaev exchange interaction between the $j_{\mathrm{eff}}=1/2$ pseudospin strongly depends on the Ru-Ru distance and the Cl position, originating from the nature of the edge-sharing geometry. (iii) The optimized 3D structure without electronic correlations has $P\overline{3}1m$ space-group symmetry independent of SOC, but including electronic correlation changes the optimized 3D structure to either $C2/m$ or $Cmc{2}_1$ within 0.1 meV per formula unit (f.u.) energy difference. The reported $P{3}_{1}12$ structure is also close in energy. The interlayer spin-exchange coupling is a few percent of the in-plane spin-exchange terms, confirming that $\alpha {\text{-RuCl}}_3$ is close to a 2D system. We further suggest how to increase the Kitaev term via tensile strain, which sheds light in realizing the Kitaev spin-liquid phase in this system.

• Received 22 September 2015
• Revised 8 March 2016

DOI:https://doi.org/10.1103/PhysRevB.93.155143