  Three dimensional materials with strong spin-orbit coupling and magnetic
interactions represent an opportunity to realize a variety of rare and
potentially useful topological phases. In this work, we use first principles
calculations to show that the recently synthesized material Bi2MnSe4 displays a
combination of band inversion and magnetic interactions, leading to several
topological phases. Bi2PbSe4, also studied, also displays band inversion and is
a topological insulator. In bulk form, the ferromagnetic phase of Bi2MnSe4 is
either a nodal line or Weyl semimetal, depending on the direction of the spins.
When the spins are arranged in a layered antiferromagnetic configuration, the
combination of time reversal plus a partial translation is a new symmetry, and
the material instead becomes an antiferromagnetic topological insulator.
However, the intrinsic TRS breaking at the surface of Bi2MnSe4 removes the
typical Dirac cone feature, allowing the observation of the half-integer
quantum anomalous Hall effect (AHC). Furthermore, we show that in thin film
form, for some thicknesses, Bi2MnSe4 becomes a Chern insulator with a band gap
of up to 58 meV. This combination of properties in a stoichiometric magnetic
material makes Bi2MnSe4 an excellent candidate for displaying robust
topological behavior.
