Effect of structural distortion on the electronic band structure of NaOsO3 studied within density functional theory and a three-orbital model

Abstract

Effects of the structural distortion associated with the OsO 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.

Spin-orbit coupling induced magnetic anisotropy and large spin wave gap in NaOsO3

“…Strong SOC significantly reduces the indirect band gap (conduction band minimum at T), yielding a marginally insulating AFM state. The electronic band structure for the minimal three-orbital model is broadly consistent with the realistic three-orbital model calculation and DFT result [12]. Henceforth, the values of t 1 , t 4 (both negative) will refer to their magnitudes, and values of t 2 , ò xy will be as given above, unless specifically mentioned.…”

“…Similar magnitude of the MAE was obtained within the three orbital model with realistic hopping parameters obtained by comparing the electronic band structure with DFT results [12]. This calculation included the orbital mixing hopping terms (t m1 , t m2 ) given in equation (5).…”

“…Combining the SOC, band, and staggered field terms, the Hamiltonian in the composite three-orbital yz xz xy , , s s s (¯), two-sublattice (s=±1) basis is obtained as [12]:…”

“…Furthermore, the t 2g sector orbitals (xz, yz, xy) and spin space directions are defined with respect to coordinate axes along the Os-O-Os directions. Specifically, the x-y axes of the orbital-spin coordinate system (same as the crystal a-c plane) are rotated by angle π/4 with respect to the a-c axes, while the z axis is same as the crystal b axis [12].…”

“…In the simplified model (equation (5)), several hopping terms which account for the fine features of the electronic band structure have been neglected from the realistic model. These include first-neighbor δ overlaps and third-neighbor terms as well as the orbital and directional asymmetry associated with the cubic symmetry breaking resulting from structural distortion [12].…”