RKKY coupling in graphene

TL;DR

This paper investigates the RKKY exchange interaction between magnetic moments in graphene using exact diagonalization, revealing detailed distance-dependent behaviors and edge effects in nanoribbons, with implications for magnetic properties.

Contribution

It provides a precise calculation of RKKY coupling in graphene avoiding momentum cut-offs and explores edge effects in nanoribbons, offering new insights into magnetic interactions in graphene structures.

Findings

RKKY coupling in bulk graphene scales as 1/|R|^3 with oscillations.

A-A sublattice coupling is ferromagnetic; A-B is antiferromagnetic and larger.

Edge impurities exhibit exponential decay of RKKY coupling due to localized edge states.

Abstract

We study the carrier-mediated exchange interaction, the so-called RKKY coupling, between two magnetic moments in graphene using exact diagonalization on the honeycomb lattice. By using the tight-binding nearest neighbor band structure of graphene we avoid the use of a momentum cut-off which plagues results in the Dirac continuum model formulation. We extract both the short and long impurity-impurity distance behavior and show several corrections to earlier long distance results. In the bulk the RKKY coupling is proportional to $1/|{\bf R}|^3$ and displays $(1+\cos(2{\bf k}_D\cdot {\bf R})$-type oscillations. A-A sublattice coupling is always ferromagnetic whereas A-B subattice coupling is always antiferromagnetic and three times as large. We also study the effect of edges in zigzag graphene nanoribbons (ZGNRs) and find that for impurities on the edge, the RKKY coupling decays exponentially because of the localized zero energy edge states. For impurities inside a ZGNR the bulk characteristics are quickly regained.