illustrated in table II. It is clear that N atom has the same stable position in both monolayer and bilayer graphene, so does the O atom. C adatom is stable at the bridge site in monolayer graphene, and Hollow site in bilayer graphene. We believe the different stable positions for C atom results from its interaction with the upper graphene layer. The C$_{Hol}$ structure is favored as the ground state for C atom intercalated in the bilayer graphene. The spin-resolved band structures and density of states (DOS) for C$_{Hol}$ system are shown in Fig. 3. Fig. 3(a) and (b) are the band structures for the majority spin and minority spin, respectively. It is clearly seen that impurity bands for the majority and minority spin components lie, respectively, lower and higher than the Fermi level. In the spin-resolved total DOS (see Fig. 3(c)), two narrow peaks at the opposite side of the Fermi level are observed, indicating the itinerant magnetism triggered by the intercalated C atom. In the following, we will find the itinerant magnetism comes from not only the foreign C atom, but also the carbon atoms of the bilayer graphene. In the orbital-resolved PDOS of the foreign C atom, s state and p state have peaks in the same energy range, which is indicative of the sp 3 hybridization. The C-C bonding between the foreign C and the nearest carbon atoms with the value of 1.54 ˚ A , is also a proof of the sp 3 hybridization, which has been pointed in the previous analysis. When the spin degree of freedom is neglected, our calculation from first principle predicts a twofold degenerate peak at the Fermi level (Fig. 3(e)), but the spin unpolarized state is not the ground state. Including the spin degree of freedom, the balance between the majority and minority spin components will be destroyed. The spin density distribution of the lower graphene layer of the C$_{Hol}$ system are shown in Fig. 3(f). Both the foreign C atom and the pushed down carbon atom are magnetic, yet we cannot see their magnetic moment distribution in Fig. 3(f), because they are not in the lower graphene plane. Seen from the top-view, these two carbon atoms occupy coinciding positions, which are noted in Fig. 3(f) by the letter ‘C’. The three nearest carbon atoms bonded with the foreign C atom are nearly nonmagnetic and the next-near-neighbors are magnetic. On the whole, the total magnetic moment of the C$_{Hol}$ system is about 1.32 µB , and the magnetic moment distributions show threefold symmetry, which is similar with the hydrogen adsorption on the graphene plane [23]. Spin-resolved band structure and density of states for N$_{Bri}$ system are shown in Fig. 4, where Fig. 4(a) and (b) show the band structure for majority and minority spin, respec- 5