First detection of CF$^{+}$ in the Large Magellanic Cloud
CF$^{+}$ has been established as a valuable diagnostic tool for investigating photo-dissociation regions (PDRs) and fluorine abundances in the Milky Way. However, its role in extragalactic environments remains largely uncharted. Our objective is to explore the significance of CF$^{+}$ in the Large Magellanic Cloud (LMC) and assess its utility as a valuable probe for examining C$^{+}$ and fluorine abundances in external galaxies. We performed pointed CF$^{+}$ observations toward an active star-forming region, N113 in the LMC, using the Atacama Pathfinder EXperiment 12~m sub-millimeter telescope. We report the first discovery of CF$^{+}$ in the LMC through the successful detection of the CF$^{+}$ (2$\to$1) and (3$\to$2) lines. The excitation models indicate that CF$^{+}$ emission originates from dense PDRs characterized by an H$_{2}$ number density of $(0.5-7.9)\times 10^{4}$~cm$^{-3}$ in N113. Our observations provide the first constraint on the fluorine abundance in molecular clouds in the LMC, disclosing a value of $\lesssim 1.7\times 10^{-9}$. This value is about an order of magnitude lower than those previously measured toward red giants in the LMC, indicative of fluorine deficiency in the molecular gas. The estimated column density ratio between C$^{+}$ and CF$^{+}$ appears to be lower than the anticipated equilibrium ratio derived from the fluorine abundance in red giants. Both phenomena can be explained by the deficiency of CF$^{+}$ caused by the freeze-out of its primary chemical precursor, HF, onto dust grains. The deficiency of CF$^{+}$ within molecular clouds suggests that the measurements presented in this work serve exclusively as conservative estimates, establishing lower bounds for both the fluorine abundance and C$^{+}$ column densities in external galaxies.