Spin-orbit excitons and electronic configuration of the $5d^4$ insulator Sr${}_3$Ir${}_2$O${}_7$F${}_2$

Here we report on the low-energy excitations within the paramagnetic spin-orbit insulator Sr${}_3$Ir${}_2$O${}_7$F${}_2$ studied via resonant inelastic X-ray scattering, $\mathit{\text{ab}}\mathit{\text{initio}}$ quantum chemical calculations, and model-Hamiltonian simulations. This material is a unique $d^4$ Ir${}^{5+}$ analog of Sr${}_3$Ir${}_2$O${}_7$ that forms when F ions are intercalated within the SrO layers spacing the square lattice IrO${}_6$ bilayers of Sr${}_3$Ir${}_2$O${}_7$. Due to the large distortions about the Ir${}^{5+}$ ions, our computations demonstrate that a large single-ion anisotropy yields an $S$=1 ($L\approx$1, $J\approx$0) ground state wave function. Weakly coupled, excitonic modes out of the $S_z$=0 ground state are observed and are well-described by a phenomenological spin-orbit exciton model previously developed for $3d$ and $4d$ transition metal ions. The implications of our results regarding the interpretation of previous studies of hole-doped iridates close to $d^4$ fillings are discussed.