Iridates supply fertile ground for unconventional phenomena and exotic electronic phases. With respect to well-studied octahedrally coordinated iridates, we focus our attention on a rather unexplored iridate, ${\mathrm{Na}}_4{\mathrm{IrO}}_4$, showing an unusual square planar coordination. The latter is key to rationalizing the electronic structure and magnetic property of ${\mathrm{Na}}_4{\mathrm{IrO}}_4$, which is here explored by first-principles density functional theory calculations and Monte Carlo simulations. Due to the uncommon square planar crystal field, Ir $5d$ states adopt an intermediate-spin state with double occupation of the $d_{z^2}$ orbital, leading to a sizable local spin moment, at variance with many other iridates. The square planar crystal-field splitting is also crucial in opening a robust insulating gap in ${\mathrm{Na}}_4{\mathrm{IrO}}_4$, irrespective of the specific magnetic ordering or treatment of electronic correlations. Spin-orbit coupling plays a minor role in shaping the electronic structure, but leads to strong magnetocrystalline anisotropy. The easy axis perpendicular to the ${\mathrm{IrO}}_4$ plaquette, well explained using perturbation theory, is again closely related to the square planar coordination. Finally, the large single-ion anisotropy suppresses the spin frustration and stabilizes a collinear antiferromagnetic long-range magnetic ordering, as confirmed by Monte Carlo simulations predicting a quite low Néel temperature, expected from almost isolated ${\mathrm{IrO}}_4$ square planar units that act as crystalline building blocks.

• Received 13 July 2017
• Revised 21 September 2017

DOI:https://doi.org/10.1103/PhysRevB.96.205158