The orthorhombic perovskite NaOsO${}_3$ undergoes a continuous metal-insulator transition (MIT), accompanied by antiferromagnetic (AFM) order at $T_N=410$ K, suggested to be an example of the rare Slater (itinerant) MIT. We study this system using ab initio and related methods, focusing on the origin and nature of magnetic ordering and the MIT. The rotation and tilting of OsO${}_6$ octahedra in the GdFeO${}_3$ structure result in moderate narrowing of the bandwidth of the $t_{2g}$ manifold but sufficient to induce flattening of bands and AFM order within the local spin density approximation, where it remains metallic but with a deep pseudogap. Including on-site Coulomb repulsion $U$, at $U_c\approx 2$ eV a MIT occurs only in the AFM state. Effects of spin-orbit coupling (SOC) on the band structure seem minor, as expected for a half-filled $t_{2g}^3$ shell, but SOC doubles the critical value $U_c$ necessary to open a gap and also leads to large magnetocrystalline energy differences in spite of normal orbital moments no greater than 0.1 ${\mu }_B$. Our results are consistent with a Slater MIT driven by magnetic order, induced by a combination of structurally induced band narrowing and moderate Coulomb repulsion, with SOC necessary for a full picture. Strong $p$-$d$ hybridization reduces the moment, and when bootstrapped by the reduced Hund's rule coupling (proportional to the moment) gives a calculated moment of $\sim$1 ${\mu }_B$, consistent with the observed moment and only a third of the formal $d^3$ value. We raise and discuss one important question: Since this AFM ordering is at $q=0$ (in the 20 atom cell) where nesting is a moot issue, what is the microscopic driving force for ordering and the accompanying MIT?

• Received 3 October 2012

DOI:https://doi.org/10.1103/PhysRevB.87.115119