Variable range of the RKKY interaction in edged graphene

Abstract

Abstract. The indirect exchange interaction is one of the key factors in determining the overall alignment of magnetic impurities embedded in metallic host materials. In this work we examine the range of this interaction in magnetically-doped graphene systems in the presence of armchair edges using a combination of analytical and numerical Green function (GF) approaches. We consider both a semi-infinite sheet of graphene with a single armchair edge, and also quasi-one-dimensional armchair edged graphene nanoribbons (GNRs). While we find signals of the bulk decay rate in semi-infinite graphene and signals of the expected one-dimensional decay rate in GNRs, we also find an unusually rapid decay for certain instances in both, which manifests itself whenever the impurities are located at sites which are a multiple of three atoms from the edge. This decay behavior emerges from both the analytic and numerical calculations, and the result for semi-infinite graphene can be interpreted as an intermediate case between ribbon and bulk systems.Variable range of the RKKY interaction in edged graphene 2

Exclusive sub-lattices for extended and localized states in graphene ribbons: their role in Klein tunneling, disorder and magnetic field effects

“…In previous works [27][28][29], destructive interference effects were reported at each three sites starting from the armchair graphene nanoribbon edge. This interference generate an armchair configuration for the available wavefunction of the system.…”

Noncollinear exchange interaction in transition metal dichalcogenide edges

“…2(a) for level 1. The effective 1D character of states in the gap is evident, not unlike states in carbon nanotubes [48][49][50] or graphene edges [19,22,24,25]. However, as these states can be seen to arise from the mixing of 2D-bulk states with strong SOC, different states in the vicinity of a given energy carry information on the spin and spatial structure that result in subtle effective interactions between the embedded magnetic impurities.…”

“…This has been studied on finite two-dimensional (2D) materials, such as graphene nanoflakes [19,20] and nanoribbons [21][22][23][24][25], where impurities lie close to or on zigzag and armchair edges. On graphene, RKKY interactions with a dominant 1D character have been identified for impurities near the sample edges [25] and line defects [26]. Magnetic impurities, such as Mn, Fe [27,28], Co [28], or Ti [29], can be introduced by STM and/or associated with Mo or S vacancies.…”

Long range of indirect exchange interaction on the edges of MoS2flakes

“…For impurities on graphene nanoribbon edges, both zigzag [59] and armchair [65], the decay has been found to be slower than r −2 but only for small impurity separations, while for larger separations there is an exponential decay; for impurities interacting in the bulk of the nanoribbon the r −2 decay is naturally recovered. Silicine shows a topological insulator phase, and when impurities sit on zigzag edges, the interaction decays as r −1 and is much stronger than in the bulk [66].…”