Testing the Validity of the Strong Spin-Orbit-Coupling Limit for Octahedrally Coordinated Iridate Compounds in a Model System ${\mathrm{Sr}}_3{\mathrm{CuIrO}}_6$

The electronic structure of ${\mathrm{Sr}}_3{\mathrm{CuIrO}}_6$, a model system for the $5d$ Ir ion in an octahedral environment, is studied through a combination of resonant inelastic x-ray scattering and theoretical calculations. Resonant inelastic x-ray scattering spectra at the Ir $L_3$ edge reveal an Ir $t_{2g}$ manifold that is split into three levels, in contrast to the expectations of the strong spin-orbit-coupling limit. Effective Hamiltonian and ab inito quantum chemistry calculations find a strikingly large noncubic crystal field splitting comparable to the spin-orbit coupling, which results in a strong mixing of the $j_{\mathsf{e}\mathsf{f}\mathsf{f}}=\frac{1}{2}$ and $j_{\mathsf{e}\mathsf{f}\mathsf{f}}=\frac{3}{2}$ states and modifies the isotropic wave functions on which many theoretical models are based.

Figure 1

The $\mathrm{Cu}\mathrm{\text{−}}{\mathrm{IrO}}_6\mathrm{\text{−}}\mathrm{Cu}\mathrm{\text{−}}{\mathrm{IrO}}_6$ chain of ${\mathrm{Sr}}_3{\mathrm{CuIrO}}_6$. The local coordinates for the ${\mathrm{IrO}}_6$ octahedra and the ${\mathrm{CuO}}_6$ prism are labeled with ($x$, $y$, $z$) and ($x^{\prime }$, $y^{\prime }$), respectively.

Figure 2

Incident x-ray energy dependence of the RIXS spectra from ${\mathrm{Sr}}_3{\mathrm{CuIrO}}_6$ at the Ir $L_3$ edge. Three low energy features at 0.28, 0.58, and 0.81 eV are observed. These show similar resonant behavior, each peaking at 11.216 keV.

Figure 3

RIXS spectra at different $Q=\zeta \left(\begin{array}{ccc}1.98& 0& 1\end{array}\right)+\left(\begin{array}{ccc}0& 13& 0\end{array}\right)$ points along the chain direction. The data at $\zeta =-0.3$ are fit with multiple Gaussian peaks. The black solid line shows the total fitting result. Individual Gaussian peaks are shown with red dashed lines, which are centered at 0.28, 0.58, 0.81, 3.14, 3.90, 4.72, and 6.20 eV, respectively. The vertical and horizontal bars indicate the excitations listed in Table  from the $\mathrm{MRCI}+\mathrm{SOC}$ calculations.

Figure 4

Density profile of the $t_{2g}$ hole. Left: $j_{\mathsf{e}\mathsf{f}\mathsf{f}}=\frac{1}{2}$ state for perfect ${\mathrm{IrO}}_6$ octahedra. Right: the modified wave function $|{\varphi }_0⟩$ [Eq. (3)] due to the noncubic crystal field arising from distortions of the octahedra.