Role of Square Planar Coordination in the Magnetic Properties of Na4IrO4

Iridates supply fertile grounds for unconventional phenomena and exotic electronic phases. With respect to well-studied octahedrally-coordinated iridates, we pay our attention to a rather unexplored iridate, Na4IrO4, showing an unusual square-planar coordination. The latter is key to rationalize the electronic structure and magnetic property of Na4IrO4, which is here explored by first-principles density functional theory and Monte Carlo simulations. Due to the uncommon square-planar crystal field, Ir 5d states adopt intermediate-spin state with double occupation of dz2 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 Na4IrO4, 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 a strong magnetocrystalline anisotropy. The easy axis perpendicular to the IrO4 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 N\'eel temperature, expected from almost isolated IrO4 square-planar units as crystalline building blocks.