Nature of the Insulating Ground State of the $5d$ Postperovskite ${\mathrm{CaIrO}}_3$

The insulating ground state of the $5d$ transition metal oxide ${\mathrm{CaIrO}}_3$ has been classified as a Mott-type insulator. Based on a systematic density functional theory (DFT) study with local, semilocal, and hybrid exchange-correlation functionals, we reveal that the Ir $t_{2g}$ states exhibit large splittings and one-dimensional electronic states along the $c$ axis due to a tetragonal crystal field. Our hybrid DFT calculation adequately describes the antiferromagnetic (AFM) order along the $c$ direction via a superexchange interaction between ${\mathrm{Ir}}^{4+}$ spins. Furthermore, the spin-orbit coupling (SOC) hybridizes the $t_{2g}$ states to open an insulating gap. These results indicate that ${\mathrm{CaIrO}}_3$ can be represented as a spin-orbit Slater insulator, driven by the interplay between a long-range AFM order and the SOC. Such a Slater mechanism for the gap formation is also demonstrated by the DFT $+$ dynamical mean field theory calculation, where the metal-insulator transition and the paramagnetic to AFM phase transition are concomitant with each other.

Figure 1

Crystal structure of ${\mathrm{CaIrO}}_3$ projected on the $bc$ plane (left side) and the $ab$ plane (right side). $a$, $b$, and $c$ denote unit vectors of the conventional unit cell. The primitive unit cell is indicated by the dashed lines. The large, medium, and small circles represent Ca, Ir, and O atoms, respectively. The bond lengths ($d_1$ and $d_2$) and the tilt angle (${\theta }_t$) are indicated for Table IS [19]. The reference frame $xyz$ is drawn in an ${\mathrm{IrO}}_6$ octahedron.

Figure 2

Band structures of (a) the NM structure obtained using LDA, (b) the AFM structure obtained using PBE, and (c) the AFM structure obtained using HSE. The band dispersions are plotted along the path $\mathrm{\Gamma }(0,0,0)\to Y(0,0.5,0)\to T(0,0.5,0.5)\to \mathrm{\Gamma }(0,0,0)\to S(0.25,0.25,0)\to R(0.25,0.25,0.5)\to \mathrm{\Gamma }(0,0,0)\to Z(0,0,0.5)$ in the Brillouin zone of the unit cell [see the inset in (b)]. The energy zero represents the Fermi level. The bands projected onto $d_{xy}$, $d_{yz}$, and $d_{zx}$ orbitals are also displayed. Here, the radii of circle and semicircles are proportional to the weights of corresponding orbitals. In (a), the charge characters of $t_{2g}^{S1}$ and $t_{2g}^{D2}$ states at the $T$ point are shown with an isosurface of $0.02e/{\AA }^3$.

Figure 3

Band structure of the AFM structure, obtained using the (a) $\mathrm{PBE}+\mathrm{SOC}$ and (b) $\mathrm{HSE}+\mathrm{SOC}$ calculations. The DOS obtained using HSE+SOC is also given in (b). The theoretical estimation of the $B$ and $C$ features observed from RIXS experiment [13] is drawn in DOS. In (c), the sum of the spin and orbital magnetic moments obtained using the $\mathrm{HSE}+\mathrm{SOC}$ calculation is drawn with three components ($m_a$, $m_b$, $m_c$) along the $a$, $b$, and $c$ axes. Here, $m_i$ is calculated by integrating the corresponding component of the magnetic moment inside the PAW sphere with a radius of 1.4 (0.8) Å for Ir (O).

Figure 4

(a) Density of states with respect to temperature, obtained using the $\mathrm{DFT}+\mathrm{DMFT}$ calculation. The calculated magnetic moment ($\mu$) of Ir atom as a function of temperature is plotted in (b), together with spin (${\mu }_S$) and orbital (${\mu }_L$) components.