Strength of effective Coulomb interactions and origin of ferromagnetism in hydrogenated graphene

Hydrogenation provides a novel way to tune the electronic properties of graphene. Recent scanning tunneling microscopy experiments have demonstrated that local graphene magnetism can be selectively switched on and off by hydrogen (H) dimers. Employing first-principles calculations in conjunction with the constrained random-phase approximation we determine the strength of the effective Coulomb interaction $U$ in hydrogenated graphene. We find that the calculated $U$ parameters are smaller than the ones in graphene and depend on the H concentration. Moreover, the $U$ parameters are very sensitive to the position of H atoms adsorbed on the graphene lattice. We discuss the instability of the paramagnetic state of the hydrogenated graphene towards the ferromagnetic one on the basis of calculated $U$ parameters within the Stoner model. Spin-polarized calculations reveal that the itinerant ferromagnetism in hydrogenated graphene can be well accounted for by the Stoner model.

Figure 1

The crystal structure of the two-dimensional $3\times 3$ supercell with (a) a single H atom on sublattice $A$ (${\mathrm{C}}_{18}\mathrm{H}$); (b) an AA dimer $\left[{\mathrm{C}}_{18}{\mathrm{H}}_2\left(\mathrm{nn}\right)\right]$, H atoms are next-nearest neighbors; (c) an AB dimer $\left[{\mathrm{C}}_{18}{\mathrm{H}}_2\left(\mathrm{n}\right)\right]$, H atoms are nearest neighbors; and (d) an AB dimer $\left[{\mathrm{C}}_{18}{\mathrm{H}}_2\left(\mathrm{nnn}\right)\right]$, H atoms are next-next-nearest neighbors. Dark and light circles are carbon atoms in different sublattices. Circles with $\times$ denote carbon atoms bonded to H.

Figure 2

Frequency dependence of the (a) on-site $U_{00}\left(\omega \right)$ and (b) nearest-neighbor $U_{01}\left(\omega \right)$ effective Coulomb interaction for graphene, graphone, and graphane.

Figure 3

Calculated partially screened $U$ and fully screened $W$ Coulomb interaction parameters for C $2p_z$ electrons in the cases of (a) a single H atom on sublattice $A$ (${\mathrm{C}}_{18}\mathrm{H}$), (b) AA dimer $\left[{\mathrm{C}}_{18}{\mathrm{H}}_2\left(\mathrm{nn}\right)\right]$, (c) AB dimer $\left[{\mathrm{C}}_{18}{\mathrm{H}}_2\left(\mathrm{n}\right)\right]$ with nearest-neighbor separation, and (d) AB dimer $\left[{\mathrm{C}}_{18}{\mathrm{H}}_2\left(\mathrm{nnn}\right)\right]$ with next-next-nearest-neighbor separation (see Fig. 1).

Figure 4

(a) DOS at the Fermi level for the nonmagnetic case, (b) Stoner criterion, and (c) magnetic moments (in ${\mu }_{\mathrm{B}}$) of different carbon atoms in the case of a single H atom on $A$ sublattice (${\mathrm{C}}_{18}\mathrm{H}$) and the AA dimer $\left[{\mathrm{C}}_{18}{\mathrm{H}}_2\left(\mathrm{nn}\right)\right]$. C atoms 1 to 9 (10 to 18) belong to the sublattice $A$ ($B$).