  Temperature- and fluence-dependent carrier dynamics of the magnetic Kagome
metal Fe$_3$Sn$_2$ were studied using the ultrafast optical pump-probe
technique. Two carrier relaxation processes ($\tau_1$ and $\tau_2$) and a laser
induced coherent optical phonon were observed. By using the two-temperature
model for metals, we ascribe the shorter relaxation $\tau_1$ (~1 ps) to hot
electrons transferring their energy to the crystal lattice via electron-phonon
scattering. $\tau_2$ (~25 ps), on the other hand, cannot be explained as a
conventional process and is attributed to the unconventional (localized)
carriers in the material. The observed coherent oscillation is assigned to be a
totally symmetric A$_{1g}$ optical phonon dominated by Sn displacements out of
the Kagome planes, and possesses a prominently large amplitude, on the order of
10$^{-3}$, comparable to the maximum of the reflectivity change ($\Delta$R/R).
This amplitude is equivalent to charge-density-wave (CDW) systems, although no
signs of such an instability were hitherto reported in Fe$_3$Sn$_2$. Our
results set an unexpected connection between Fe$_3$Sn$_2$ and kagome metals
with CDW instabilities, and suggest a unique interplay between phonon and
electron dynamics in this compound.
