Theory of inter-edge superexchange in zigzag edge magnetism

TL;DR

This paper develops a theoretical model for inter-edge superexchange in zigzag graphene nanoribbons, predicting how the interaction strength and charge gap depend on ribbon width, and revealing the energetic favorability of opposite edge spins.

Contribution

It introduces a novel Dirac-model-based theory predicting width-dependent superexchange and charge gap behaviors in zigzag edge graphene nanoribbons.

Findings

Superexchange strength scales as W^{-2} with ribbon width.

Charge gap scales as W^{-1} with ribbon width.

Opposite edge spins are energetically favored by kinetic and interaction energies.

Abstract

A graphene nanoribbon with zigzag edges has a gapped magnetic ground state with an antiferromagnetic inter-edge superexchange interaction. We present a theory based on asymptotic properties of the Dirac-model ribbon wavefunction which predicts $W^{-2}$ and $W^{-1}$ ribbon-width dependencies for the superexchange interaction strength and the charge gap respectively. We find that, unlike the case of conventional atomic scale superexchange, opposite spin-orientations on opposite edges of the ribbon are favored by both kinetic and interaction energies.