  In this article we study the ferromagnetic behavior of ABC-stacked trilayer
graphene. This is done using a nearest-neighbor tight-binding model, in the
presence of long-range Coulomb interactions. For a given electron-electron
interaction g and doping level n, we determine whether the total energy is
minimized for a paramagnetic or ferromagnetic configuration of our variational
parameters. The g versus n phase diagram is first calculated for the unscreened
case. We then include the effects of screening using a simplified expression
for the fermion bubble diagram. We show that ferromagnetism in ABC-trilayer
graphene is more robust than in monolayer, in bilayer, and in ABA-trilayer
graphene. Although the screening reduces the ferromagnetic regime in
ABC-trilayer graphene, the critical doping level remains one order of magnitude
larger than in unscreened bilayer graphene.
