Crystal structure and magnetism in $\alpha$-RuCl3: an ab-initio study

$\alpha$-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 {\it ab-initio} electronic structure calculations, we study a full three dimensional (3D) structure of $\alpha$-RuCl$_3$ including the effects of spin-orbit coupling (SOC) and electronic correlations. Three major results are as follows; i) SOC suppresses dimerization of Ru atoms, which exists in other Ru compounds such as isostructural Li$_2$RuO$_3$, and making the honeycomb closer to an ideal one. ii) The nearest-neighbor Kitaev exchange interaction between the $j_{\rm eff}$=1/2 pseudospin depends strongly 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 $P{\bar 3}1m$ space group symmetry independent of SOC, but including electronic correlation changes the optimized 3D structure to either $C2/m$ or $Cmc2_1$ within 0.1 meV per formula unit (f.u.) energy difference. The reported $P3_112$ structure is also close in energy. The interlayer spin exchange coupling is a few percent of in-plane spin exchange terms, confirming $\alpha$-RuCl$_3$ is close to a 2D system. We further suggest how to increase the Kitaev term via tensile strain, which sheds new light in realizing Kitaev spin liquid phase in this system.