Graphene with adatoms: tuning the magnetic moment with an applied voltage

We show that, in graphene with a small concentration of adatoms, the total magnetic moment $\mu_T$ can be switched on and off by varying the Fermi energy $E_F$, either by applying a gate voltage or by suitable chemical doping. Our calculation is carried out using a simple tight-binding model described previously, combined with a mean-field treatment of the electron-electron interaction on the adatom. The values of $E_F$ at which the moment is turned on or off are controlled by the strength of the hopping between the graphene sheet and the adatom, the on-site energy of the adatom, and the strength of the electron-electron correlation energy U. Our result is in qualitatively consistent with recent experiments by Nair {\it et al.} [Nat.\ Commun.\ {\bf 4}, 2010 (2013)].