Localized magnetic states in biased bilayer and trilayer graphene

We study the localized magnetic states of an impurity in biased bilayer and trilayer graphene. It is found that the magnetic boundary for bilayer and trilayer graphene shows mixed features of Dirac and conventional fermions. For zero gate bias, as the impurity energy approaches the Dirac point, the impurity magnetization region diminishes for bilayer and trilayer graphene. When a gate bias is applied, the dependence of impurity magnetic states on the impurity energy exhibits a different behavior for bilayer and trilayer graphene due to the opening of a gap between the valence and the conduction band in the bilayer graphene with an applied gate bias. The magnetic moment and the corresponding magnetic transition of the impurity in bilayer graphene are also investigated.