Spectroscopic signature of trimer Mott insulator and charge disproportionation in ${\mathrm{BaIrO}}_3$

We have measured the reflectivity spectra of the barium iridate $9R{\mathrm{BaIrO}}_3$, the crystal structure of which consists of characteristic ${\mathrm{Ir}}_3{\mathrm{O}}_{12}$ trimers. In the high-temperature phase above the transition temperature $T_c\simeq 180$ K, we find that the optical conductivity involves two temperature-dependent optical transitions with an ill-defined Drude response. These features are reminiscent of the optical spectra in the organic dimer Mott insulators, implying a possible emergence of an unusual electronic state named trimer Mott insulator in ${\mathrm{BaIrO}}_3$, where the carrier is localized on the trimer owing to the strong Coulomb repulsion. Along with a pronounced splitting of the phonon peak observed below $T_c$, which is a hallmark of charge disproportionation, we discuss a possible phase transition from the trimer Mott insulator to a charge-ordered insulating phase in ${\mathrm{BaIrO}}_3$.

Figure 1

(a) Reflectivity spectra measured at several temperatures with polarization parallel to the $c$ axis (solid curves) and the $a$ axis (dotted curves). The inset depicts the crystal structure of $9R{\mathrm{BaIrO}}_3$. Light- and dark-blue colors show the inequivalent ${\mathrm{Ir}}_3{\mathrm{O}}_{12}$ trimers. (b) Optical conductivity spectra measured with polarization parallel to the $c$ axis. The inset shows the temperature dependence of the dc conductivity along the $c$ axis taken from Ref. [17].

Figure 2

(a) Temperature dependence of the low-energy optical conductivity at $\hslash \omega =0.1$ eV. The dashed line represents the transition temperature $T_c\simeq 180$ K. (b) Temperature variations of the optical conductivity at the $\beta$ peak (open squares) and the $\gamma$ peak (filled circles).

Figure 3

Schematic energy diagrams for the electronic state of ${\mathrm{BaIrO}}_3$ constructed from a localized picture [24]. The red arrows labeled as $\alpha$, $\beta$, $\gamma$ correspond to the optical transitions shown in Fig. 1. Energy diagrams for Ir $5d$ electrons in (a) ${\mathrm{IrO}}_6$ octahedron, (b) trigonally distorted octahedron, (c) ${\mathrm{Ir}}_3{\mathrm{O}}_{12}$ trimer. (d) In the trimer, three $a_{1g}$ orbitals form the bonding (B), nonbonding (NB), and antibonding (AB) orbitals. (e) Under strong correlation effect, the half-filled NB orbitals split into lower-Hubbard (LH) and upper-Hubbard (UH) bands. (f) Energy levels for ${\mathrm{Ir}}^{4+}$ under spin-orbit and crystal-field interactions [26]. (g) Trimer Mott insulating state realized above $T_c\simeq 180$ K. The energy difference of NB orbitals $\mathrm{\Delta }{\varepsilon }_{\mathrm{NB}}$ between two inequivalent trimers is relatively small. (h) Charge disproportionation below $T_c$.

Figure 4

(a) Optical phonon spectra measured at several temperatures with polarization parallel to the $c$ axis. The experimental data are fitted using two Lorentz oscillators shown as the dashed curves for each temperature. The sum of two oscillators is represented as the solid curves. (b)–(e) Temperature variations of the fitting parameters: (b) the resonance energies at around $\hslash {\omega }_1\simeq 79$ meV (solid squares, left axis) and $\hslash {\omega }_2\simeq 81$ meV (open squares, right axis), (c) the difference of the resonance energies $\mathrm{\Delta }{\varepsilon }_{\mathrm{ph}}=\hslash {\omega }_2-\hslash {\omega }_1$, (d) the plasma frequencies, and (e) the damping factors. The vertical dashed line represents the transition temperature $T_c\simeq 180$ K.