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We present an anti-ferromagnetically ordered ground state of  Na$_{2}$IrO$_{3}$ based on density-functional-theory calculations includingboth spin-orbit coupling and on-site Coulomb interaction $U$. We show that thesplitting of $e_{g}'$ doublet states by the strong spin-orbit coupling ismainly responsible for the intriguing nature of its insulating gap and magneticground state. Due to its proximity to the spin-orbit insulator phase, themagnetic ordering as obtained with finite $U$ is found to exhibit a strongin-plane anisotropy. The phase diagram of Na$_{2}$IrO$_{3}$ suggests a possibleinterplay between spin-orbit insulator and Mott anti-ferromagnetic insulatorphases.

Mott Insulating Ground State and its Proximity to Spin-Orbit Insulators in Na$_{2}$IrO$_{3}$