Spin and band ferromagnetism in trilayer graphene

We study the ground-state properties of an ABA-stacked trilayer graphene. The low-energy band structure can be described by a combination of both a linear and a quadratic particle-hole symmetric dispersion, reminiscent of monolayer and bilayer graphene, respectively. The multiband structure offers more channels for instability toward ferromagnetism when the Coulomb interaction is taken into account. Indeed, if one associates a subband-index 1/2 degree of freedom to the bands (parabolic and linear), it is possible to realize also a band-ferromagnetic state, where there is a shift in the energy bands since they fill up differently. By using a variational procedure, we compute the exchange energies for all possible variational ground states and identify the parameter space for the occurrence of spin- and band-ferromagnetic instabilities as a function of doping and interaction strength