  Using density functional theory combined with a Hubbard model (DFT+U ), the
electronic band structure of CrI3 multilayers, both free-standing and enclosed
between graphene contacts, is calculated. We show that the DFT+U approach,
together with the 'around mean field' correction scheme, is able to describe
the vertical magnetotransport in line with the experimental measurements of
magnetoresistance in multi-layered CrI3 enclosed between graphene contacts.
Moreover, by interpolating between different double-counting correction
schemes, namely the 'around mean field' correction and the fully localized
limit, we show their importance for describing both the band structure and the
ground-state total energy consistently. Our description of the magnetic
exchange interaction is compatible with the experimentally observed
antiferromagnetic ground state in the bilayer CrI3 and the transition to a
ferromagnetic arrangement in a small external magnetic field. Thus, using
spin-polarized DFT+U with an 'around mean field' correction, a consistent
overall picture is achieved.
