  In this paper, the effects of the external transverse magnetic field $B$
(perpendicular to the surface of the layers) on the electronic and excitonic
properties are studied in the AA-stacked bilayer graphene (BLG). The effects of
the Coulomb interactions and excitonic pairing have been taken into account and
analyzed in detail within the bilayer Hubbard model. Both half-filling and
partial filling regimes have been taken into account and the magnetic field
dependence of a series of physical parameters was found. It is shown that the
difference between the average electron concentrations in the layers vanishes
at some critical value of magnetic field $B_{c}$ and the chemical potential is
calculated numerically above and below that value. The role of the Coulomb
interactions on the average carrier concentrations in the layers has been
analyzed, and the excitonic order parameters have been calculated for different
spin orientations. We found a possibility for the particle population inversion
between the layers when varying the external magnetic field. The calculated
electronic band structure in the AA-BLG shows the presence of
metal-semiconductor transition, governed by the strength of the applied
magnetic field or the interlayer interaction potential. We show that for high
magnetic fields the band-gap is approaching the typical values of the gaps in
the usual semiconductors. It is demonstrated that, at some parameter regimes,
the AA-BLG behaves like a spin-valve device, by permitting the electron
transport with only one spin direction. All calculations have been performed at
the zero-temperature limit.
