  We report the results of a Hartree-Fock study applied to interacting
electrons moving in two different bipartite lattices: the dice and the Lieb
lattices, at half-filling. Both lattices develop ferrimagnetic order in the
phase diagram $U$-$\lambda$, where $U$ is the Hubbard onsite repulsion and
$\lambda$ the Rashba spin-orbit coupling strength. Our main result is the
observation of an unexpected multitude of topological phases for both lattices.
All these phases are ferrimagnetic, but they differ among themselves in their
set of six Chern numbers (six numbers because the unit cells have three atoms).
The Chern numbers $|C|$ observed in our study range from 0 to 3, showing that
large Chern numbers can be obtained by the effect of electronic correlations,
adding to the recently discussed methodologies to increase $|C|$ based on
extending the hopping range in tight-binding models, using sudden quenches, or
photonic crystals, all without including electronic interactions.
