Ruderman-Kittel-Kasuya-Yosida interactions on a bipartite lattice

TL;DR

This paper revisits the RKKY interaction on bipartite lattices, revealing that zero modes significantly influence the exchange coupling, which differs from previous theoretical predictions, especially in graphene nanoribbons.

Contribution

The study demonstrates that zero modes alter the RKKY interaction predictions on bipartite lattices, challenging existing theorems and providing numerical insights into graphene nanoribbons.

Findings

Zero modes significantly affect RKKY interactions.

Effective exchange coupling is largest at the edges of graphene nanoribbons.

Theoretical predictions do not fully match numerical results due to zero mode contributions.

Abstract

Carrier-mediated exchange coupling, known as Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, plays a fundamental role in itinerant ferromagnetism and has great application potentials in spintronics. A recent theorem based on the imaginary-time method shows that the oscillatory RKKY interaction becomes commensurate on bipartite lattice and predicts that the effective exchange coupling is always ferromagnetic for the same sublattice but antiferromagnetic for opposite sublattices. We revisit this important problem by real- and imaginary-time methods and find the theorem misses important contributions from zero modes. To illustrate the importance of zero modes, we study the spin susceptibility in graphene nanoribbons numerically. The effective exchange coupling is largest on the edges but does not follow the predictions from the theorem.