A $j_{\mathrm{e}\mathrm{f}\mathrm{f}}=1\mathrm{/}2$ Kitaev material on the triangular lattice: The case of NaRuO${}_2$

Motivated by recent reports of a quantum disordered ground state in the triangular lattice compound NaRuO${}_2$, we derive a $j_{\mathrm{e}\mathrm{f}\mathrm{f}}=1\mathrm{/}2$ magnetic model for this system by means of first-principles calculations. The pseudospin Hamiltonian is dominated by bond-dependent off-diagonal $\mathrm{\Gamma }$ interactions, complemented by a ferromagnetic Heisenberg exchange and a notably antiferromagnetic Kitaev term. In addition to bilinear interactions, we find a sizable four-spin ring exchange contribution with a strongly anisotropic character, which has been so far overlooked when modeling Kitaev materials. The analysis of the magnetic model, based on the minimization of the classical energy and exact diagonalization of the quantum Hamiltonian, points toward the existence of a rather robust easy-plane ferromagnetic order, which cannot be easily destabilized by physically relevant perturbations.