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We performed a Raman scattering study of thin films of LiTi$_2$O$_4$ spineloxide superconductor. We detected four out of five Raman active modes, withfrequencies in good accordance with our first-principles calculations. ThreeT$_{2g}$ modes show a Fano lineshape from 5 K to 295 K, which suggests anelectron-phonon coupling in LiTi$_2$O$_4$. Interestingly, the electron-phononcoupling shows an anomaly across the negative to positive magnetoresistancetransition at 50 K, which may be due to the unset of other competing orders.The strength of the electron-phonon interaction estimated from the Allen'sformula and the observed lineshape parameters suggests that the three T$_{2g}$modes contribute little to superconductivity.

Raman study of electron-phonon coupling in thin films of LiTi$_2$O$_4$ spinel oxide superconductor