First-order ferromagnetic phase transition in the low electronic density regime of a biased graphene bilayer

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 first-order phase transition between paramagnetic and ferromagnetic phases induced by doping at zero temperature.