  Magnon polarons are novel elementary excitations possessing hybrid magnonic
and phononic signatures, and are responsible for many exotic spintronic and
magnonic phenomena. Despite long-term sustained experimental efforts in chasing
for magnon polarons, direct spectroscopic evidence of their existence is hardly
observed. Here, we report the direct observation of magnon polarons using
neutron spectroscopy on a multiferroic Fe$_{2}$Mo$_{3}$O$_{8}$ possessing
strong magnon-phonon coupling. Specifically, below the magnetic ordering
temperature, a gap opens at the nominal intersection of the original magnon and
phonon bands, leading to two separated magnon-polaron bands. Each of the bands
undergoes mixing, interconverting and reversing between its magnonic and
phononic components. We attribute the formation of magnon polarons to the
strong magnon-phonon coupling induced by Dzyaloshinskii-Moriya interaction.
Intriguingly, we find that the band-inverted magnon polarons are topologically
nontrivial. These results uncover exotic elementary excitations arising from
the magnon-phonon coupling, and offer a new route to topological states by
considering hybridizations between different types of fundamental excitations.
