  The magnetic phase diagram of a ground state is studied theoretically for
graphene nanoflakes of bow-tie shape and various size in external in-plane
magnetic field. The tight-binding Hamiltonian supplemented with Hubbard term is
used to model the electronic structure of the systems in question. The
existence of the antiferromagnetic phase with magnetic moments localized at the
sides of the bow-tie is found for low field and a field-induced spin-flip
transition to ferromagnetic state is predicted to occur in charge-undoped
structures. For small nanoflake doped with a single charge carrier the
low-field phase is ferrimagnetic and a metamagnetic transition to ferromagnetic
ordering can be forced by the field. The critical field is found to decrease
with increasing size of the nanoflake. The influence of diagonal and
off-diagonal disorder on the mentioned magnetic properties is studied. The
effect of off-diagonal disorder is found to be more important than this of
diagonal disorder, leading to significantly widened distribution of critical
fields for disordered population of nanoflakes.
