Evolution of crystal field and intraionic interactions in the ilmenite $A$IrO$_3$ ($A$ = Mg, Zn, Cd) and hyperhoneycomb $β$-ZnIrO$_3$
Spin-orbit Mott insulators with the $t_{2g}^5$ electron configuration are promising platforms for the Kitaev spin liquid, yet fine-tuning of their crystal structures is essential to suppress non-Kitaev interactions. Here, we investigate the local electronic structures of the ilmenite iridates $A\mathrm{IrO}_3$ ($A = \mathrm{Mg}, \mathrm{Zn}, \mathrm{Cd}$) and the hyperhoneycomb $β\text{-}\mathrm{ZnIrO}_3$ using Ir $L_3$-edge resonant inelastic x-ray scattering (RIXS). Multiplet analysis of the RIXS spectra reveals a systematic evolution of the crystal field and intraionic interaction parameters upon chemical substitution at the $A$-site. We observe an enhancement of the trigonal distortion with increasing $A$-site ionic radius. This provides a microscopic explanation for the deviation from the ideal $J=1/2$ state and the antiferromagnetic interactions identified in $\mathrm{CdIrO}_3$. Furthermore, the local multiplet parameters of ilmenite $\mathrm{ZnIrO}_3$ and hyperhoneycomb $β\text{-}\mathrm{ZnIrO}_3$ are found to be nearly identical, demonstrating that their different magnetic ground states are primarily governed by their distinct lattice structures rather than the single-ion properties. These findings establish a solid foundation for understanding how local crystal-field distortions control the magnetic Hamiltonian in Kitaev candidate materials.