Unrestricted Hartree-Fock analysis of the Hubbard model on single-layer graphene and Bernal bilayer graphene

We perform unrestricted Hartree-Fock calculations on the two-dimensional Hubbard model on a honeycomb and bilayer honeycomb lattice at both zero and finite temperatures. Finite-size real-space calculations are supplemented with random-phase approximation calculations in the thermodynamic limit. Our motivation comes from high doping levels achieved in graphene and Bernal bilayer graphene by intercalation. We present phase diagrams in doping and temperature for a moderate Hubbard interaction. The magnetic states we find are classified systematically based on the dominant Fourier components of their spin patterns, their average magnetization and spin incommensurabilities. The dominant spin patterns are Néel order and various types of stripes. Around Van Hove filling, we resolve the competition between stripe and chiral spin density waves in the symmetry-broken regime. We also investigate the effect of an applied external displacement field on the spin patterns of Bernal bilayer graphene.