  The phase diagram of a biased graphene bilayer is computed and the existence
of a ferromagnetic phase is discussed both in the critical on-site interaction
$U_{c}$ versus doping density and versus temperature. We show that in the
ferromagnetic phase the two planes have unequal magnetization and that the
electronic density is hole like in one plane and electron like in the other. We
give evidence for a \emph{first-order} phase transition between paramagnetic
and ferromagnetic phases induced by doping at zero temperature.
