Effect of interaction between impurities on localized magnetic states in graphene

We study effect of interaction between impurities on localized magnetic states in graphene. It is shown that the modifications of the impurity self-energy induced by the inter-impurity interaction can push the impurity energy across the zero energy point, which leads to splitting of the impurity magnetization boundary into the three peaks. With increasing the inter-impurity interaction strength, the two side peaks in the magnetic region are sharply skewed away from the central one, and their amplitudes exhibit the different dependence on interaction strength. The magnetic moment and corresponding magnetic transition of the impurities are also investigated.