Influence of local structural distortion on the magnetism of Na2IrO3 compounds

First-principles calculations are conducted to investigate the magnetic properties of the ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ compounds. We reveal that the ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$'s local structural distortions are essential for an accurate description of the magnetism of such systems. They provide a feasible explanation for the experimentally observed antiferromagnetic zigzag magnetic ground state. We demonstrate that the underlying competition between the spin-orbit coupling and the crystal-field splitting rules the crystal structure and profoundly influences the strength of the magnetic exchange interactions. We unambiguously identify that the ${D}_{4h}$-type distortions, due to the Jahn-Teller effect, are disclosed in an elongation along the ${\mathrm{IrO}}_{6}$ polyhedra's apical axis in the $ac$ plane. On the other hand, the Ir atoms off-centering in the basal plane (perpendicular to the local ${D}_{4h}$ elongation axis) arises owing to an inhomogeneous cationic charge distribution of ${\mathrm{Ir}}^{4+}/{\mathrm{Na}}^{+}$ in the transition-metal layer resulting in both effects being decisive in controlling the magnetism of ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ together with the spin-orbit interactions.