Nature of Excitons and Their Ligand-Mediated Delocalization in Nickel Dihalide Charge-Transfer Insulators

The fundamental optical excitations of correlated transition-metal compounds are typically identified with multielectronic transitions localized at the transition-metal site, such as $dd$ transitions. In this vein, intense interest has surrounded the appearance of sharp, below-band-gap optical transitions, i.e., excitons, within the magnetic phase of correlated ${\mathrm{Ni}}^{2+}$ van der Waals magnets. The interplay of magnetic and charge-transfer insulating ground states in ${\mathrm{Ni}}^{2+}$ systems raises intriguing questions on the roles of long-range magnetic order and of metal-ligand charge transfer in the exciton nature, which inspired microscopic descriptions beyond typical $dd$ excitations. Here we study the impact of charge transfer and magnetic order on the excitation spectrum of the nickel dihalides ($\mathrm{Ni}{X}_2$, $X=\mathrm{Cl}$, Br, and I) using Ni-$L_3$ edge resonant inelastic x-ray scattering (RIXS). In all compounds, we detect sharp excitations, analogous to the recently reported excitons, and assign them to spin-singlet multiplets of octahedrally coordinated ${\mathrm{Ni}}^{2+}$ stabilized by intra-atomic Hund’s exchange. Additionally, we demonstrate that these excitons are dispersive using momentum-resolved RIXS. Our data evidence a ligand-mediated multiplet dispersion, which is tuned by the charge-transfer gap and independent of the presence of long-range magnetic order. This reveals the mechanisms governing nonlocal interactions of on-site $dd$ excitations with the surrounding crystal or magnetic structure, in analogy to ground-state superexchange. These measurements thus establish the roles of magnetic order, self-doped ligand holes, and intersite-coupling mechanisms for the properties of $dd$ excitations in charge-transfer insulators.