RKKY interaction in triangular graphene nanobubble

Abstract

Using the Lanczos method as a numerically exact theoretical framework, we investigate the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction in the triangular graphene nanobubble. Our results demonstrate that Saremi’s rule remains valid in the charge-neutral triangular graphene nanobubble. However, the characteristic $R^{-3}$ decay of the RKKY interaction observed in pristine graphene is disrupted when both magnetic impurities are located within the nanobubble. This decay behavior is restored when one impurity is positioned far from the nanobubble center, regardless of the other impurity’s location. By tuning the height of the nanobubble, the strength of the RKKY interaction can be enhanced by up to three orders of magnitude compared to that in pristine graphene. Moreover, we reveal that carrier doping, which shifts the Fermi level away from the Dirac point, can induce a transition from anti-ferromagnetic to ferromagnetic RKKY coupling between impurities on opposite sublattices, depending on the nanobubble height. These findings provide new insights into the manipulation of magnetic interactions in nanostructured graphene systems and pave the way for potential applications in graphene-based spintronic devices.