Evolution of orbital excitations from insulating to superconducting MgTi$_2$O$_4$ films

Spinel oxides are well-known functional materials but rarely show superconductivity. Recently, emergent superconductivity was discovered in MgTi$_2$O$_4$, which is attributed to the increase of electron doping and the suppression of orbital order. Here, we utilized Ti $L$-edge resonant inelastic X-ray scattering to study the orbital excitations in superconducting (SC) and insulating MgTi$_2$O$_4$ films. We find that the spectral weight of orbital excitations is enhanced and the energy of $t_{2g}$ intra-band excitation is softened in the SC film compared to the insulating one, suggesting higher electron doping and suppressed orbital order gap in the SC sample. These observations were further supported by our multiplet calculations using minimal two-site model. Our results provide spectroscopic evidence for the competition between orbital order and superconductivity in MgTi$_2$O$_4$ and shed light on searching for novel superconductors in spinel oxides.