Spin susceptibilities in zigzag graphene nanoribbons

TL;DR

This paper investigates the spin susceptibilities and energy band structures of zigzag graphene nanoribbons using the Hubbard model, revealing doping-dependent magnetic configurations and their electronic properties.

Contribution

It provides a detailed analysis of spin susceptibilities and magnetic states in zigzag graphene nanoribbons within a mean field Hubbard framework, highlighting doping effects.

Findings

Antiferromagnetic state exhibits an energy gap proportional to Hubbard parameter.

Ferromagnetic state shows intersecting spin bands at Fermi level.

Transverse spin susceptibilities depend on electron doping levels.

Abstract

The simple Hubbard Hamiltonian with the mean field approximation is used to know about the energy bands and spin susceptibilities of zigzag graphene nanoribbons. Depending on the electron doping, antiferromagnetic or ferromagnetic configurations are possible; in the former, an energy gap exits which is proportional to the Hubbard parameter, while in the latter the up and down spin bands intersect the Fermi level. Due to the two dimensional nature of the system, a susceptibility square matrix is necessary to explain the self-correlations and correlations between spins in the ribbon unit cell. The transverse spin susceptibilities are computed and the static case for ferromagnetic solutions is examined, as a function of the electron doping.