  Electron-electron interactions are intrinsically long ranged, but many models
of strongly interacting electrons only take short-ranged interactions into
account. Here, we present results of atomistic calculations including both
long-ranged and short-ranged electron-electron interactions for the magnetic
phase diagram of twisted bilayer graphene and demonstrate that qualitatively
different results are obtained when long-ranged interactions are neglected. In
particular, we use Hartree theory augmented with Hubbard interactions and
calculate the interacting spin susceptibility at a range of doping levels and
twist angles near the magic angle to identify the dominant magnetic
instabilities. At the magic angle, mostly anti-ferromagnetic order is found,
while ferromagnetism dominates at other twist angles. Moreover, long-ranged
interactions significantly increase the twist angle window in which strong
correlation phenomena can be expected. These findings are in good agreement
with available experimental data.
