Anisotropic RKKY interaction in spin polarized graphene

TL;DR

This paper investigates how spin polarization affects the RKKY interaction in graphene, revealing anisotropic XXZ-type interactions and oscillation patterns influenced by doping and lattice directions.

Contribution

It introduces the concept of anisotropic RKKY interactions in spin-polarized graphene and analyzes the effects of doping and lattice orientation on oscillation patterns.

Findings

Spin polarization induces anisotropic XXZ interaction in graphene.

Doping causes oscillations in the RKKY interaction with distance.

Beating patterns in oscillations depend on chemical potential and spin polarization.

Abstract

We study the Ruderman-Kittle-Kasuya-Yosida (RKKY) interaction in the presence of spin polarized two dimensional Dirac fermions. We show that a spin polarization along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. For undoped graphene, while the $x$ part of interaction keeps its constant ferromagnetic sign, its $z$ part oscillates with the distance of magnetic impurities, $R$. A finite doping causes that both parts of the interaction oscillate with $R$. We explore a beating pattern of oscillations of the RKKY interaction along armchair and zigzag lattice directions, which occurs for some certain values of the chemical potential. The two characteristic periods of the beating are determined by inverse of the difference and the sum of the chemical potential and the spin polarization.