Challenges in Design of Kitaev Materials: Magnetic Interactions from Competing Energy Scales

In this study, we reanalyze the magnetic interactions in the Kitaev spin liquid candidate materials Na${}_2$IrO${}_3$, $\alpha$-RuCl${}_3$, and $\alpha$-Li${}_2$IrO${}_3$ using nonperturbative exact diagonalization methods. These methods are more appropriate given the relatively itinerant nature of the systems suggested in previous works. We treat all interactions up to third neighbours on equal footing. The computed terms reveal significant long range coupling, bond-anisotropy, and/or off-diagonal couplings which we argue naturally explain the observed ordered phases in these systems. Given these observations, the potential for realizing the spin-liquid state in real materials is analyzed, and synthetic challenges are defined and explained.