Challenges in design of Kitaev materials: Magnetic interactions from competing energy scales

Much interest has emerged in the realization of materials with quantum spin liquid ground states, which would provide fertile ground for realizing exotic excitations. Three “Kitaev” spin liquid candidate materials have been proposed — Na${}_{2}$IrO${}_{3}$, $ensuremath{alpha}$-RuCl${}_{3}$, and $ensuremath{alpha}$-Li${}_{2}$IrO${}_{3}$ — and there has been many diverging proposals for the most relevant interactions. Here, the authors re-evaluate carefully the magnetic interactions in these materials, using nonperturbative exact diagonalization methods. The results clarify misconceptions in the literature and help estimate the potential for realizing the spin liquid state in real materials.