  Manipulation of intrinsic magnetic and electronic structures of graphene
nanoflakes is of technological importance. Here we carry out systematic study
of the magnetic and electronic phases, and its manipulation in graphene
nanoflakes employing first-principles calculation. We illustrate the intricate
shape and size dependence on the magnetic and electronic properties, and
further investigate the effects of carrier doping, which could be tuned by gate
voltage. A transition from nonmagnetic to magnetic phase is observed at a
critical flake size for the flakes without sublattice imbalance, which we
identify to be originated from the armchair defect at the junctions of two
sublattices on the edge. Electron, or hole doping simultaneously influences the
magnetic and electronic structures, and triggers phase changes. Beyond a
critical doping, crossover from antiferromagnetic to ferromagnetic phase is
observed for the flakes without sublattice imbalance, while suppression of
magnetism, and a possible crossover from magnetic to nonmagnetic phase is
observed for flakes with sublattice imbalance. Simultaneous to magnetic phase
changes, a semiconductor to (half) metal transition is observed, upon carrier
doping.
