Edge-state-mediated RKKY coupling in graphene nanoflakes

Abstract We investigate the long-range behavior and size dependence of the Ruderman-Kittel-Kasuya-
Yosida (RKKY) interaction in hexagonal and triangular graphene nanoflakes with zigzag and arm-
chair edges. We employ the tight-binding model with exact diagonalization to calculate the RKKY
interaction as a function of the distance between magnetic impurities, nanoflake size, and edge ge-
ometry. Our findings demonstrate a strong dependency of the RKKY interaction on edge geometry
and flake size, with notable changes in the RKKY interaction strength. We further analyze the
influence of structural defects on the interaction strength of exchange interactions.