Multiple Spin-Orbit Excitons and the Electronic Structure of \(\alpha\)-RuCl\(_3\)

The honeycomb compound \(\alpha\)-RuCl\(_3\) is widely discussed as a proximate Kitaev spin-liquid material. This scenario builds on spin-orbit entangled \(j = 1/2\) moments arising for a \(t_{2g}^5\) electron configuration with strong spin-orbit coupling \(\lambda\) and a large cubic crystal field. The low-energy electronic structure of \(\alpha\)-RuCl\(_3\), however, is still puzzling. In particular infrared absorption features at 0.30 eV, 0.53 eV, and 0.75 eV seem to be at odds with theory. Also the energy of the spin-orbit exciton, the excitation from \(j = 1/2\) to 3/2, and thus the value of \(\lambda\) are controversial. Combining infrared and Raman data, we show that the infrared features can be attributed to single, double, and triple spin-orbit excitons. We find \(\lambda\) = 0.16 eV and \(\Delta\) =42(4) meV for the observed non-cubic crystal-field splitting, supporting the validity of the \(j= 1/2\) picture for \(\alpha\)-RuCl\(_3\). The unusual strength of the double excitation is related to the underlying hopping interactions which form the basis for dominant Kitaev exchange.