  By applying tight binding model of adatoms in graphene, we study
theoretically the localized aspects of the interaction between transition metal
atoms and graphene. Considering the electron-electron interaction by adding a
Hubbard term in the mean-field approximation, we find the spin-polarized
localized and total density of states. We obtain the coupled system of
equations for the occupation number for each spin in the impurity and we study
the fixed points of the solutions. By comparing the top site and hollow site
adsorption, we show that the anomalous broadening of the latter allows to
obtain magnetization for small values of the Hubbard parameter. Finally, we
model the magnetic boundaries in order to obtain the range of Fermi energies at
which magnetization starts.
