  The electronic properties of graphene decorated with Ni, Co, Cu and Zn
adatoms is studied with the density functional theory approach. Within the
analysis the spin-orbit interaction is taken into account. We focus on the case
when the indicated $3d$ metallic adatoms form a perfect, close-packed
single-atomic layer above the graphene surface. The two configurations are
examined, namely the adatoms in the on-top, and the hollow positions on
graphene. First, we verify that the metallic adatoms in the close-packed
structure do not form a covalent bonds with the graphene substrate. However,
due to the proximity of the metallic adatoms to the graphene, the charge
transfer from the adatom layer to the graphene takes place, and in consequence
the graphene becomes $n$-doped. The observed charge transfer results from the
arising hybridization between the graphene $2p$ and transition metal $3d$
orbitals. The proximity of metallic adatoms modifies the magnetic state of the
graphene. This effect is especially pronounced for the decoration with magnetic
atoms, when the magnetic moments on the graphene sublattices are induced. The
analysis of the band structure demonstrates that the charge transfer, as well
as the induced magnetism on graphene, modify the graphene electronic properties
near high symmetry points, especially the Dirac cones. The presence of the
metallic adatoms breaks graphene $K-K^{'}$ symmetry and splits the bands due to
the exchange coupling. We show that for the hollow configuration the gap
opening arises at the $K(K^{'})$-point due to the Rashba-like spin-orbit
interaction, while in the case of the on-top configuration the energy gap opens
mainly due to the staggered potential. We also mapped the parameters of an
effective Hamiltonian on the results obtained with the density functional
theory approach.
