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 AnAn (R) and J BnBn (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 * Corresponding author. Tel./fax: +98 831 427 4569, Tel: +98 831 427 4569. E-mail address:yawar.mohammadi@gmail.com 1 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 (R) and J B 1 A 2 (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.

Ruderman-Kittel-Kasuya-Yosida interaction in Weyl semimetals

“…Non-trivial electronic states of carriers along with dimensions of space containing itinerant carriers result in an interesting behavior of the RKKY interaction between magnetic spins in graphene [42][43][44][45][46][47][48][49][50][51][52][53][54], topological insulators [55][56][57][58][59], transition-metal dichalcogenides [60,61] and silicene [62,63]. The aforementioned features of WSMs would provide an important effect on the interaction of dilute impurities located inside these materials with the itinerant Weyl fermions.…”

“…Due to recent development of new materials with non-trivial topology, the investigation of indirect exchange interactions between magnetic impurities through carriers of a host material, known as the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction [39][40][41], has become an interesting issue. Non-trivial electronic states of carriers along with dimensions of space containing itinerant carriers result in an interesting behavior of the RKKY interaction between magnetic spins in graphene [42][43][44][45][46][47][48][49][50][51][52][53][54], topological insulators [55][56][57][58][59], transition-metal dichalcogenides [60,61] and silicene [62,63]. The aforementioned features of WSMs would provide an important effect on the interaction of dilute impurities located inside these materials with the itinerant Weyl fermions.…”

Ferrimagnetic and antiferromagnetic phase in bilayer graphene nanoflake controlled with external electric fields

“…Within the broad field of graphene physics, its magnetism offers particularly exciting prospects for developing carbon-based spintronics [12]. As a result, also magnetic properties of bilayer graphene are widely explored in the literature [13][14][15][16][17][18][19][20]. In addition to the infinite, two-dimensional bilayers, bilayer graphene nanostructures constitute a class of highly promising systems due to additional possibility of shaping their edge geometry to engineer the desired properties.…”