RKKY interaction in bilayer graphene

Abstract

We study the RKKY interaction between two magnetic impurities located on same layer (intralayer case) or on different layers (interlayer case) in undoped bilayer graphene in the four-bands model, by directly calculating the Green functions in the eigenvalues and eigenvectors representation. Our results show that both intra- and interlayer RKKY interactions between two magnetic impurities located on same (opposite) sublattice are always ferromagnetic (antiferromagnetic). Furthermore we find unusual long-distance decay of the RKKY interaction in BLG. The intralyer RKKY interactions between two magnetic impurities located on same sublattice, $J^{A_n{A}_n}(\mathbf{R})$ and $J^{B_n{B}_n}(\mathbf{R})$, decay closely as $1/R^6$ and $1/R^2$ at large impurity distances respectively, but when they are located on opposite sublattices the RKKY interactions exhibit $1/R^4$ decays approximately. In the interlayer case, the RKKY interactions between two magnetic impurities located on same sublattice show a decay close to $1/R^4$ at large impurity distances, but if two magnetic impurities be on opposite sublattices the RKKY interactions, $J^{A_1{B}_2}(\mathbf{R})$ and $J^{B_1{A}_2}(\mathbf{R})$, decay closely as $1/R^6$ and $1/R^2$ respectively. Both intra- and interlayer RKKY interactions have anisotropic oscillatory factors which for intralayer case is equal to that for single layer graphene. Our results at weak and strong interlayer coupling limits reduce to the RKKY interaction of SLG and that of BLG in the two-bands approximation respectively.

28 pages, 7 figures

References in corpus (14)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Chiral tunneling and the Klein paradox in graphene
• Unconventional Integer Quantum Hall effect in graphene
• Asymmetry gap in the electronic band structure of bilayer graphene
• Strong suppression of weak (anti)localization in graphene
• Quantum-limited shot noise in graphene
• Non-adiabatic Kohn-anomaly in a doped graphene monolayer
• Transport in Bilayer Graphene: Calculations within a self-consistent Born approximation
• RKKY in half-filled bipartite lattices: graphene as an example
• RKKY Interaction in Graphene from Lattice Green's Function
• Screening, Kohn anomaly, Friedel oscillation, and RKKY interaction in bilayer graphene
• Localized states at zigzag edges of bilayer graphene
• Electric field control of spins in bilayer graphene: Local moment formation and local moment interactions

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