  A flat band in fermionic system is a dispersionless single-particle state
with a diverging effective mass and nearly zero group velocity. These flat
bands are expected to support exotic properties in the ground state, which
might be important for a wide range of promising physical phenomena. For many
applications it is highly desirable to have such states in Dirac materials, but
so far they have been reported only in non-magnetic Dirac systems. In this work
we propose a realization of topologically protected spin-polarized flat bands
generated by domain walls in planar magnetic topological insulators. Using
first-principles material design we suggest a family of intrinsic
antiferromagnetic topological insulators with an in-plane sublattice
magnetization and a high N\'eel temperature. Such systems can host domain walls
in a natural manner. For these materials, we demonstrate the existence of
spin-polarized flat bands in the vicinity of the Fermi level and discuss their
properties and potential applications.
