Magnetism in graphene flakes with edge disorder

Abstract

The magnetization of graphene flakes as a function of size, shape, boundary type, and edge defects is computed in a tight-binding model. Flakes with Klein boundaries exhibit a smaller orbital magnetization than flakes with other boundaries. The difference in magnitude is significant for flakes with a few hundred to a few thousand atoms. One can tune the magnetization of a zigzag or Klein flake quasicontinuously by adding atoms, one by one, to the edges of the zigzag flake, or removing atoms from a Klein flake. Flakes with an odd number of atoms show a paramagnetic spin response due to particle-hole symmetry. The addition of a next-nearest neighbor term to the Hamiltonian, which breaks particle-hole symmetry, does not destroy this effect as long as there is approximate particle-hole symmetry. Other defects that affect the chemical potential, such as edge atoms with an onsite potential, or doping, can affect the paramagnetism but preserve the difference in magnetization between Klein and non-Klein flakes. These results are consistent with experiments which see paramagnetic response at low magnetic fields crossing over to diamagnetic response at higher fields.