Effect of pressure on the magnetism of bilayer graphene

We study the effect of pressure on the localized magnetic moments induced by vacancies in bilayer graphene in the presence of topological defects breaking the bipartite nature of the lattice. By using a mean-field Hubbard model, we address the two inequivalent types of vacancies that appear in the Bernal stacking bilayer graphene. We find that by applying pressure in the direction perpendicular to the layers the critical value of the Hubbard interaction needed to polarize the system decreases. When combined with an external electric field applied perpendicularly to bilayer graphene the effect becomes sizable and can be detected experimentally. The effect is particularly enhanced for one type of vacancies, and admits straightforward generalization to multilayer graphene in Bernal stacking and graphite. The results clearly demonstrate that the magnetic behavior of multilayer graphene can be affected by mechanical transverse deformation.

Figure 1

(a) Bilayer lattice structure and main tight-binding parameters. Left: $\alpha$ vacancy. Right: $\beta$ vacancy. (b) Reconstructed vacancies modeled by a pentagonal link.

Figure 2

(a) Critical value of the Hubbard parameter $U$ needed to polarize the cluster as a function of the strength of the pentagonal link $t_p$, for different values of the perpendicular hopping $t_{\perp }$ in units of $t$. From lower to upper curves: $t_{\perp }/t$ $=$ 1, 0.5, 0.1. (b) Dependence of the critical $U$ on the perpendicular hopping $t_{\perp }$ for fixed values of the pentagonal link.