  We implement a self-consistent Hartree-Fock approximation based on a
microscopic model in real space, which allows us to consider the interplay
between the Hubbard and the extended Coulomb interaction in twisted bilayer
graphene at the magic angle. These two interactions tend to favor different
symmetry breaking patterns, having therefore complementary roles in the regimes
where one or the other dominates. We show that, for sufficiently large values
of the on-site Hubbard repulsion, magic angle graphene has an antiferromagnetic
ground state at the charge neutrality point, while at half-filling of the
lowest valence band the state becomes fully spin-polarized. In general, a
suitable screening of the extended Coulomb interaction is required to observe
the magnetic state in either case, as otherwise the instabilities take place in
the charge sector, preferentially in the form of time-reversal, chiral or
valley symmetry breaking.
