Variable range of the RKKY interaction in edged graphene

TL;DR

This study investigates how the RKKY interaction's range varies in edged graphene, revealing rapid decay at specific impurity sites near edges, combining analytical and numerical methods.

Contribution

It provides new insights into the decay behavior of RKKY interactions in graphene with armchair edges, especially at sites multiple of three atoms from the edge.

Findings

Rapid decay of RKKY interaction at sites multiple of three atoms from the edge.

Bulk decay rate observed in semi-infinite graphene.

One-dimensional decay rate in graphene nanoribbons.

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.