Electronic structure of hyper-kagome ${\text{Na}}_4{\text{Ir}}_3{\text{O}}_8$

We investigate the electronic structure of the frustrated magnet ${\text{Na}}_4{\text{Ir}}_3{\text{O}}_8$ using density-functional theory. Due to strong spin-orbit coupling, the hyper-kagome lattice is characterized by a half-filled complex of $d$ states, making it a cubic iridium analog of the high-temperature superconducting cuprates. The implications of our results for this unique material are discussed.

Figure 1

(Color online) DOS in states/Ryd for the scalar relativistic calculation of ${\text{Na}}_4{\text{Ir}}_3{\text{O}}_8$. The Fermi energy, $E_F$, is at zero.

Figure 2

Energy bands of the $t_{2g}$ complex for the scalar relativistic calculation of ${\text{Na}}_4{\text{Ir}}_3{\text{O}}_8$. $\Gamma =\left(0,0,0\right)$, $X=\left(1,0,0\right)$, $M=\left(1,1,0\right)$, and $R=\left(1,1,1\right)$ in units of $\pi /a$. The horizontal line marks $E_F$.

Figure 3

(Color online) Decomposition of the (a) $t_{2g}$ states and (b) $e_g$ states, averaged over each band, into their individual components relative to the $C_2$ axis of the distorted ${\text{IrO}}_6$ octahedra (scalar relativistic calculation).

Figure 4

(Color online) DOS in states/Ryd for the full relativistic calculation of ${\text{Na}}_4{\text{Ir}}_3{\text{O}}_8$.

Figure 5

Energy bands of the $t_{2g}$ complex for the full relativistic calculation of ${\text{Na}}_4{\text{Ir}}_3{\text{O}}_8$. The horizontal line marks $E_F$.

Figure 6

(Color online) Decomposition of the states of the upper $t_{2g}$ “doublet” complex, averaged over each band, into their atomic spin-orbit components, $j,\pm m_j$ (full relativistic calculation). The weights are normalized to the total $d$ weight.

Figure 7

Fermi surface for the full relativistic calculation of ${\text{Na}}_4{\text{Ir}}_3{\text{O}}_8$ in the symmetry planes of the zone.

Figure 8

Energy bands for the upper $t_{2g}$ doublet complex from the tight-binding fit to the full relativistic calculation of ${\text{Na}}_4{\text{Ir}}_3{\text{O}}_8$. The horizontal line marks $E_F$.

Figure 9

Fermi surface from the tight-binding fit to the full relativistic calculation of ${\text{Na}}_4{\text{Ir}}_3{\text{O}}_8$.

Figure 10

(Color online) Superexchange pathway between two Ir ions as marked by the arrows. The Ir ions are the large (red) spheres and the oxygen ions the small ones. The lower left (green) pathway is via an O2 (blue) ion and the upper right (purple) pathway via an O1 (brown) ion.