Hubbard energy dependence of electronic structures in rare-earth monoxides

To realize the significant potential of optical materials such as strongly electron-correlated open-shell rare-earth monoxides, understanding the electron-localization Hubbard parameters ($U$) is of central importance. The Hubbard energy is believed to be material specific and constant. However, it has recently been pointed out that even subtle structural changes can induce changes in $U$ parameters. For LuO, we theoretically evaluated $U$ energy dependence of the differential transmission and reflectivity spectra to assess the impact of $U$ energy on the optical properties. In addition to the conventional derivative-like contribution, we observed the influence of the Drude tail owing to $U$-induced plasma energy modulation. Given the typical detection sensitivity of differential spectroscopy ($\sim 1 \times 10^{-4}$), even a few meV modulations in $U$ are sufficient for a detectable spectral response.