  The paper presents a computational study of the ground-state magnetic phases
of a selected bilayer graphene nanoflake in external electric field and
magnetic field. The electric field has parallel and perpendicular component
while the magnetic field is oriented in plane. The system consists of two
rectangular layers having armchair edges and zigzag terminations with Bernal
stacking. The theoretical model is based on a tight binding Hamiltonian with
Hubbard term. The magnetic phase diagram involving the total spin is
constructed, showing the stability areas of phases with total spin values equal
to 0 and 1. A significant stability range of antiferromagnetic, layer-like
arrangements is found and extensively discussed. The possibility of switching
between nonmagnetic, antiferromagnetic and ferrimagnetic phases with both
components of external electric field is demonstrated, being a manifestation of
a magnetoelectric effect. The influence of magnetic field on the phase diagrams
is analysed.
