  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)].
