Competition of exchange and correlation energies in two-dimensional N -component electron gas ferromagnetism

Motivated by recent observations of symmetry-broken phases in lightly doped multilayer graphene, we investigate magnetic phase transitions in a generalized electron gas model with four-component electron spin. This model simplifies the problem with a parabolic dispersion band, abstracting away the details of the graphene band structure to focus solely on the effects of the Coulomb interaction. We report four findings: (i) In the Hartree-Fock approximation, we observe that the paramagnetic state undergoes a sequence of density-driven, first-order phase transitions, progressively depopulating electrons from each spin component until achieving complete polarization within a very a narrow density window where 1.2<rs<2 (rs being the electron gas parameter). (ii) Further incorporating the correlation energy via the Bohm-Pines random-phase approximation shows that the cascade of transitions obtained within the Hartree-Fock approximation is replaced by a single ferromagnetic phase transition at rs=6.12. (iii) The disappearance of cascade is due to the correlation energy difference between the four-component paramagnetic state and symmetry-broken phases, which is nearly an order of magnitude more negative than the corresponding Hartree-Fock energy difference for 1.2<rs<2. (iv) The transition from the paramagnetic state to the fully polarized state at rs=6.12 is governed by the balance between exchange and correlation energies, a competition that cannot be captured by mean-field approximations to models featuring effective (density-dependent) δ-function interactions, such as the Stoner model. We use the insights from our model to comment on the phase diagram of multilayer graphene electron gas.