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High-field electrical transport and point-contact tunneling spectroscopy wereused to investigate superconducting properties of the unique spinel oxide,LiTi$_2$O$_{4-\delta}$ films with various oxygen content. We find that theupper critical field $B_\mathrm{c2}$ gradually increases as more oxygenimpurities are brought into the samples by carefully tuning the depositionatmosphere. It is striking that although the superconducting transitiontemperature and energy gap are almost unchanged, an astonishing isotropic$B_\mathrm{c2}$ up to $\sim$ 26 Tesla is observed in oxygen-rich sample, whichis doubled compared to the anoxic sample and breaks the Pauli limit. Suchanomalies of $B_\mathrm{c2}$ were rarely reported in other three dimensionalsuperconductors. Combined with all the anomalies, three dimensional spin-orbitinteraction induced by tiny oxygen impurities is naturally proposed to accountfor the remarkable enhancement of $B_\mathrm{c2}$ in oxygen-richLiTi$_2$O$_{4-\delta}$ films. Such mechanism could be general and thereforeprovides ideas for optimizing practical superconductors with higher$B_\mathrm{c2}$.

Anomalies of upper critical field in the spinel superconductor LiTi$_2$O$_{4-\delta}$