Effect of long-ranged Coulomb interactions on magnetic ordering in twisted bilayer graphene

Using an atomistic approach, we investigate the magnetic phase diagram of twisted bilayer graphene as function of twist angle and doping. Specifically, we calculate the magnetic susceptibility and determine the critical value of the Hubbard parameter at which the susceptibility diverges. As a starting point, we use either a non-interacting tight-binding model or a Hartree approach that captures effects of the long-range part of the Coulomb interaction. We find leading instabilities that correspond to ferromagnetic and anti-ferromagnetic states. Importantly, the different approaches result in qualitatively different phase diagrams. In particular, the band structure of twisted bilayer graphene from Hartree theory depends sensitively on the doping level and exhibits an interaction-induced band flattening which enhances magnetic instabilities and increases the twist-angle window where strong correlation effects can be observed. We also study quasiparticle properties of the magnetic phases using a mean-field Hubbard model.