  We establish that the interplay of itinerant fermions with localized magnetic
moments on a checkerboard lattice leads to magnetic flux-phases. For weak
itineracy the flux-phase is coplanar and the electronic dispersion takes the
shape of graphene-like Dirac fermions. Stronger itineracy drives the formation
of a non-coplanar, chiral flux-phase, in which the Dirac fermions acquire a
topological mass that is proportional to a ferromagnetic spin polarization.
Consequently the system self-organizes into a ferromagnetic Quantum Anomalous
Hall state in which the direction of its dissipationless edge-currents can be
switched by an applied magnetic field.
