  We explore possible ways to manipulate the intrinsic edge magnetism in
hexagonal graphene nanoflake with zigzag edges, using density functional theory
supplemented with on-site Coulomb interaction. The effect of carrier doping,
chemical modification at the edge, and finite temperature on the edge magnetism
has been studied. The magnetic phase diagram with varied carrier doping, and
on-site Coulomb interaction is found to be complex. In addition to the
intrinsic antiferromag- netic solution, as predicted for charge neutral
hexagonal nanoflake, fully polarized ferromagnetic, and mixed phase solutions
are obtained depending on the doped carrier concentration, and on-site Coulomb
interaction. The complexity arises due to the competing nature of local Coulomb
in- teraction and carrier doping, favoring antiferromagnetic and ferromagnetic
coupling, respectively. Chemical modification of the edge atoms by hydrogen
leads to partial quenching of local moments, giving rise to a richer phase
diagram consisting of antiferromagnetic, ferromagnetic, mixed, and nonmagnetic
phases. We further report the influence of temperature on the long-range
magnetic ordering at the edge using ab initio molecular dynamics. In agreement
with the recent experimental observations, we find that temperature can also
alter the magnetic state of neutral nanoflake, which is otherwise
antiferromagnetic at zero temperature. These findings will have important
implications in controlling magnetism in graphene based low dimensional
structures for technological purpose, and in understanding varied experimental
reports.
