Magnetic gap opening in rhombohedral-stacked multilayer graphene from first principles

We investigate the occurrence of magnetic and charge density wave instabilities in rhombohedral-stacked multilayer (three to eight layers) graphene by first principles calculations including exact exchange. Neglecting spin polarization, an extremely flat surface band centered at the special point K of the Brillouin zone occurs at the Fermi level. Spin polarization opens a gap in the surface state by stabilizing an antiferromagnetic state. The top and the bottom surface layers are weakly ferrimagnetic in-plane (net magnetization smaller than 10(-3) mu B) and are antiferromagnetic coupled to each other. This coupling is propagated by the out-of-plane antiferromagnetic coupling between the nearest neighbors. The gap is very small in a spin-polarized generalized gradient approximation, while it is proportional to the amount of exact exchange in hybrid functionals. For trilayer rhombohedral graphene it is 38.6 meV in PBE0, in agreement with the 42 meV gap found in experiments. We study the temperature and doping dependence of the magnetic gap. At electron doping of n similar to 7 x 10(11) cm(-2) the gap closes. Charge density wave instabilities with root 3 x root 3 periodicity do not occur.