Effects of the structural distortion on the electronic band structure of {\boldmath $\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{s}{\mathrm{O}}_3$} studied within density functional theory and a three-orbital model

Effects of the structural distortion associated with the $\mathrm{O}\mathrm{s}{\mathrm{O}}_6$ octahedral rotation and tilting on the electronic band structure and magnetic anisotropy energy for the $5d^3$ compound NaOsO${}_3$ are investigated using the density functional theory (DFT) and within a three-orbital model. Comparison of the essential features of the DFT band structures with the three-orbital model for both the undistorted and distorted structures provides insight into the orbital and directional asymmetry in the electron hopping terms resulting from the structural distortion. The orbital mixing terms obtained in the transformed hopping Hamiltonian resulting from the octahedral rotations are shown to account for the fine features in the DFT band structure. Staggered magnetization and the magnetic character of states near the Fermi energy indicate weak coupling behavior.