RKKY interactions in graphene: Dependence on disorder and Fermi energy

Abstract

International audienceWe report, how the indirect exchange interaction JRKKY(R) between magnetic moments at a distance R in graphene depends on nonmagmetic disorder strength W and gate voltage. First, a semiclassical method is used to rederive JRKKY in clean graphene, yielding the asymptotic decay 1/R2+α, where α=1 is the power of the pseudogap at the Dirac point. Next, we perform numerical calculations with the Anderson tight-binding model on a honeycomb lattice. We observe that along the armchair direction JRKKY is more robust to nonmagnetic disorder than in other directions. This is explained semiclassically by the presence of more than one shortest path between two lattice sites in armchair directions, which is shown to reduce the disorder sensitivity compared to other directions. The distribution of JRKKY is calculated. We identify three different distribution shapes, repeated periodically along the zigzag direction, while only one kind, more narrow distribution, is observed along the armchair direction. We explain this by the different sensitivity to scattering phases. When increasing W, we find that the distribution crosses over to a logarithm-normal distribution. Its width is found to increase linearly with W. Moving away from the Dirac point, Friedel oscillations appear in addition to the one caused by the interference between two Dirac points. This results in a beating pattern. We study how this is effected by nonmagnetic disorder

Critical temperature of two-dimensional hydrogenated multilayer graphene-based diluted ferromagnet

“…This strong disorder due to randomly distributed hydrogen impurities influences the electronic wavefunctions by causing the tendency to localization and, therefore, may limit the range of interaction. Such a phenomenon is known for example from the studies of indirect RKKY coupling in disordered systems [45], including the case of indirect coupling in graphene [46,47]. The conclusion can be drawn that the disorder causes damping of amplitude of indirect interaction and also shifts the phase [45].…”

Prospects of spintronics based on 2D materials

“…In principle, due to the π bonding and availability of itinerant charges, coupling between localized magnetic moments at various defect sites can be achieved through the Ruderman–Kittel–Kasuya–Yoshida (RKKY) interaction . However, earlier studies concluded that such an interaction in graphene is too weak to result in high T C , and can be even suppressed . Yazyev and Helm found from their early study that the coupling between the magnetic moments can be either FM or AFM, depending on whether the defects are located on the same or different hexagonal sublattices of the graphene lattice, respectively .…”

Spin-polarized electronic current induced by sublattice engineering of graphene sheets with boron/nitrogen

“…Although the range of our data is very limited due to computational expense, our results are in general agreement with previous analytical and numerical studies of RKKY interaction in graphene. [26][27][28][29][30][31] Hence, the RKKY is the dominant magnetic coupling interaction that induces the ferromagnetic spin-alignment for configurations with half-metallic electronic structures in Fig.1. When the separation is shorter than 0.3 nm, the magnetic coupling cannot be interpreted simply by the RKKY interaction due to the strong direct interaction between the nitrogen atoms.…”