  We systematically study magnetic correlations in graphene within Hubbard
model on a honeycomb lattice by using quantum Monte Carlo simulations. In the
filling region below the Van Hove singularity, the system shows a short-range
ferromagnetic correlation, which is slightly strengthened by the on-site
Coulomb interaction and markedly by the next-nearest-neighbor hopping integral.
The ferromagnetic properties depend on the electron filling strongly, which may
be manipulated by the electric gate. Due to its resultant controllability of
ferromagnetism, graphene-based samples may facilitate the development of many
applications.
