Predominance of the Kitaev interaction in a three-dimensional honeycomb iridate: from ab-initio to spin model

The recently discovered three-dimensional hyperhoneycomb iridate, $\beta$-Li${}_2$IrO${}_3$, has raised hopes for the realization of dominant Kitaev interaction between spin-orbit entangled local moments due to its near-ideal lattice structure. If true, this material may lie close to the sought-after quantum spin liquid phase in three dimensions. Utilizing ab-initio electronic structure calculations, we first show that the spin-orbit entangled basis, $j_{\mathrm{e}\mathrm{f}\mathrm{f}}$=1/2, correctly captures the low energy electronic structure. The effective spin model derived in the strong coupling limit supplemented by the ab-initio results is shown to be dominated by the Kitaev interaction. We demonstrated that the possible range of parameters is consistent with a non-coplanar spiral magnetic order found in a recent experiment. All of these analyses suggest that $\beta$-Li${}_2$IrO${}_3$ may be the closest among known materials to the Kitaev spin liquid regime.