  Different from previous scenarios that topological magnons emerge in local
spin models, we propose an alternative that itinerant electron magnets can host
topological magnons. A one-dimensional Tasaki model with a flat band is
considered as the prototype. This model can be viewed as a quarter filled
periodic Anderson model with impurities located in between and hybridizing with
the nearest-neighbor conducting electrons, together with a Hubbard repulsion
for these electrons. By increasing the Hubbard interaction, the gap between the
acoustic and optical magnons closes and reopens while the Berry phase of the
acoustic band changes from 0 to $\pi$, leading to the occurrence of a
topological transition. After this transition, there always exist in-gap edge
magnonic modes which is consistent with the bulk-edge correspondence. The
Hubbard interaction driven transition reveals a new mechanism to realize
non-trivial magnon bands.
