Crystal field splitting and optical band gap of hexagonal LuFeO$_3$ films

In order to study the electronic structures, we have characterized the hexagonal LuFeO$_3$ films (grown by pulsed laser deposition) using x-ray absorption and optical spectroscopy. The crystal splitting of Fe$^{3+}$ is extracted as $E_{e'}-E_{e''}$=0.7 eV and $E_{a_1'}-E_{e'}$=0.9 eV and a 2.0 eV optical band gap is determined assuming a direct gap. First-principles calculations confirm the experiments that the relative energies of crystal field splitting states do follow $E_{a_1'}>E_{e'}>E_{e''}$ with slightly underestimated values and a band gap of 1.35 eV.