Coulomb interactions and ferromagnetism in pure and doped graphene

We study the presence of ferromagnetism in the phase diagram of the two-dimensional honeycomb lattice close to half-filling (graphene) as a function of the strength of the Coulomb interaction and doping. We show that exchange interactions between Dirac fermions can stabilize a ferromagnetic phase at low doping when the coupling is sufficiently large. In clean systems the zero-temperature phase diagram shows both first-order and second-order transition lines and two distinct ferromagnetic phases: one phase with only one type of carriers (either electrons or holes) and another with two types of carriers (electrons and holes). Using the coherent potential approximation we argue that disorder further stabilizes the ferromagnetic phase. This work should estimulate Monte Carlo calculations in graphene dealing with the long-range nature of the Coulomb potencial.

Figure 1

(Color online) Zero-temperature phase diagram of a clean graphene plane as a function of the coupling constant $g$, Eq. (1), and doping away from half-filling. The dashed line corresponds to a first order, and the continuous line a second-order phase transition between the paramagnetic and ferromagnetic phases. The dotted curve corresponds to the value of $g$ with ${ϵ}_0=1$ and a Dirac-Fermi velocity of $\hslash v_F=5.7\mathrm{eV}\mathrm{\AA }$, as defined by Eq. (1). The points labeled 1–4 in the figure are discussed ahead in the text in connection with Fig. 3.

Figure 2

(Color online) Occupied and empty states in the paramagnetic and ferromagnetic ground states of Dirac fermions (a) half-filling case, (b) finite doping and one type of carrier in the ferromagnetic phase, and (c) finite doping and two types of carriers in the ferromagnetic phase.

Figure 3

(Color online) Behavior of the energy curves as function of the magnetization for the points marked in the phase diagram of Fig. 1.