Indirect exchange of magnetic impurities in zigzag graphene ribbon

TL;DR

This study investigates how the indirect magnetic coupling between impurities on zigzag graphene edges varies with chemical potential, revealing suppression at zero-energy and complex magnetic behavior depending on impurity placement and doping levels.

Contribution

The paper provides a detailed quantum Monte Carlo analysis of impurity interactions on zigzag graphene edges, highlighting the effects of doping and sublattice positioning on magnetic correlations.

Findings

Spin-spin correlation is suppressed near zero-energy.

Antiferromagnetic correlation peaks away from half-filling.

Crossover from ferromagnetic to antiferromagnetic correlation near zero-energy.

Abstract

We use quantum Monte Carlo method to study the indirect coupling between two magnetic impurities on the zigzag edge of graphene ribbon, with respect to the chemical potential $\mu$. We find that the spin-spin correlation between two adatoms located on the nearest sites in the zigzag edge are drastically suppressed around the zero-energy. As we switch the system away from half-filling, the antiferromagnetic correlation is first enhanced and then decreased. If the two adatoms are adsorbed on the sites belonging to the same sublattice, we find similar behavior of spin-spin correlation except for a crossover from ferromagnetic to antiferromagentic correlation in the vicinity of zero-energy. We also calculated the weight of different components of d-electron wave function and local magnet moment for various values of parameters, and all the results are consistent with those of spin-spin correlation between two magnetic impurities.