Covalency-driven collapse of strong spin-orbit coupling in face-sharing iridium octahedra

We report ab initio density functional theory calculation and Raman scattering results to explore the electronic structure of ${\mathrm{Ba}}_5{\mathrm{CuIr}}_3{\mathrm{O}}_{12}$ single crystals. This insulating iridate, consisting of face-sharing ${\mathrm{IrO}}_6$ octahedra forming quasi-one-dimensional chains, cannot be described by the local $j_{\mathrm{eff}}=1/2$ moment picture commonly adopted for discussing the electronic and magnetic properties of iridate compounds with ${\mathrm{IrO}}_6$ octahedra. The shorter Ir-Ir distance in the face-sharing geometry, compared to corner- or edge-sharing structures, leads to strong covalency between neighboring Ir. Then, this strong covalency results in the formation of molecular orbitals (MOs) at each Ir trimer as the low-energy electronic degree of freedom. The theoretically predicted three-peak structure in the joint density of states, a distinct indication of deviation from the $j_{\mathrm{eff}}=1/2$ picture, is verified by observing the three-peak structure in the electronic excitation spectrum by Raman scattering.

Figure 1

Three representative local geometries consisting of ${\mathrm{IrO}}_6$ octahedra and their schematic energy-level diagrams. (a) depicts corner- and edge-sharing geometries where the size of spin-orbit coupling (SOC) ${\lambda }_{\mathrm{SO}}$ is larger than the covalency between neighboring Ir $5d$ orbitals. (b) shows a face-sharing local geometry, where the Ir-O bond length is shorter compared to the other two cases so that the strength of $d\text{−}d$ covalency $t_{dd}$ can overcome SOC. Schematic energy-level diagrams for each case, the conventional atomic $j_{\mathrm{eff}}$ picture and a trimer molecular-orbital (MO) picture for (a) and (b), respectively, are represented.

Figure 2

${\mathrm{Ba}}_5{\mathrm{CuIr}}_3{\mathrm{O}}_{12}$ crystal structure employed for the ab initio calculations. Copper atoms are at the center of the prism face.

Figure 3

(a) Energy-level diagram showing the splitting of the Ir $t_{2g}$ states in an Ir trimer into MO states. Here, $\sigma /\pi /\delta$, $\overline{\sigma }/\overline{\pi }/\overline{\delta }$, and ${\sigma }^{*}/{\pi }^{*}/{\delta }^{*}$ denote bonding, nonbonding, and antibonding states, respectively. Electrons in fully filled states are represented by circles, while magnetically active electrons are represented by arrows. (b), (c) Projected DOS from the simple tight-bonding model for Ir trimers (b), and from ab initio calculations without SOC and magnetism (c). The color scheme for the orbital character is the same in (a)–(c).

Figure 4

(a)–(c) Schematic diagram showing the MO levels (a) with both SOC and $U_{\mathrm{Ir}}$ not included, (b) with SOC included but with no $U_{\mathrm{Ir}}$, and (c) both SOC and $U_{\mathrm{Ir}}$ included ($U_{\mathrm{Ir}}$ denoting $U$ at Ir sites). The $l_{\mathrm{eff}}^z$ and $j_{\mathrm{eff}}^z$ eigenvalues are given. (d), (e) Projected DOS from $\mathrm{DFT}+\mathrm{SOC}+U$ calculations for the $a_{1g}$ and $e_g^{\prime }$ states at Ir sites, where the $U$ values employed are $(U_{\mathrm{Ir}},U_{\mathrm{Cu}})=(0,6)$ eV and (2.8, 6) eV for (d) and (e), respectively ($U_{\mathrm{Cu}}$ denoting $U$ at Cu sites). The blue and red curves in (a)–(e) depict the $a_{1g}$ and $e_g^{\prime }$ characters, respectively. (f) The joint DOS (JDOS) with $(U_{\mathrm{Ir}},U_{\mathrm{Cu}})=(2.8,6)$ eV, showing a three-peak structure ($\alpha$, $\beta$, and $\gamma$).

Figure 5

Raman spectrum ${\chi }^{″}\left(\omega \right)$ at 25 K. Sharp features below 0.1 eV are phonon modes; the two peaks at 0.13 and 0.17 eV result from second-order phonon scattering while the broad feature at 0.24 meV originates from third-order phonon scattering. The three high-energy electronic excitations at 0.58, 0.66, and 0.74 eV are labeled by $\alpha$, $\beta$, and $\gamma$, respectively, corresponding to the labeling in Fig. 4.