On the Ruderman-Kittel-Kasuya-Yosida interaction in graphene

TL;DR

This paper investigates the RKKY interaction in graphene, revealing unique decay, oscillation, and sublattice-dependent magnetic properties due to graphene's linear band structure and two-dimensionality.

Contribution

It provides a detailed analysis of the RKKY interaction in graphene using linear response theory, highlighting its distinctive decay, interference effects, and sublattice dependence.

Findings

RKKY interaction in graphene decays as 1/R^3

Interaction exhibits interference from Dirac cones

Ferromagnetic on same sublattice, antiferromagnetic on opposite

Abstract

The two dimensionality plus the linear band structure of graphene leads to new behavior of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, which is the interaction between two magnetic moments mediated by the electrons of the host crystal. We study this interaction from linear response theory. There are two equivalent methods both of which may be used for the calculation of the susceptibility, one involving the integral over a product of two Green's functions and the second that involves the excitations between occupied and unoccupied states, which was followed in the original work of Ruderman and Kittel. Unlike the $J \propto (2k_FR)^{-2} \sin (2k_FR) $ behavior of an ordinary two-dimensional (2D) metal, $J$ in graphene falls off as $1/R^3$, shows the $1 + \cos ((\bm{K}-\bm{K'}).\bm{R})$-type of behavior, which contains an interference term between the two Dirac cones, and it oscillates for certain directions and not for others. Quite interestingly, irrespective of any oscillations, the RKKY interaction in graphene is always ferromagnetic for moments located on the same sublattice and antiferromagnetic for moments on the opposite sublattices, a result that follows from particle-hole symmetry.