The importance of electron-electron interactions in the RKKY coupling in graphene

TL;DR

This paper demonstrates that electron-electron interactions significantly alter the RKKY coupling in graphene, changing its oscillatory behavior and range, especially in nanoribbons, and suggests graphene is near an antiferromagnetic phase.

Contribution

It reveals how electron-electron interactions modify RKKY coupling in graphene, showing suppression of oscillations and increased range, with implications for magnetic properties.

Findings

Oscillations in RKKY coupling disappear with interactions.

Long-range RKKY becomes more extended as U increases.

Graphene is close to an antiferromagnetic instability.

Abstract

We show that the carrier-mediated exchange interaction, the so-called RKKY coupling, between two magnetic impurity moments in graphene is significantly modified in the presence of electron-electron interactions. Using the mean-field approximation of the Hubbard-$U$ model we show that the $(1+\cos(2{\bf k}_D\cdot {\bf R})$-oscillations present in the bulk for non-interacting electrons disappear and the power-law decay becomes more long ranged with increasing electron interactions. In zigzag graphene nanoribbons the effects are even larger with any finite $U$ rendering the long-distance RKKY coupling distance independent. Comparing our mean-field results with first-principles results we also extract a surprisingly large value of $U$ indicating that graphene is very close to an antiferromagnetic instability.