Spin coupling around a carbon atom vacancy in graphene

TL;DR

This study explores the electronic and magnetic structure of a carbon vacancy in graphene, revealing a triplet ground state with decoupled local magnetic moments and potential for spin-half paramagnetism under certain conditions.

Contribution

It combines density-functional theory and multi-reference perturbation theory to detail the magnetic states and bistability of a carbon vacancy in graphene, a novel insight into defect magnetism.

Findings

Ground state is a triplet with planar geometry.

Vacancy exhibits bistability with two equivalent configurations.

Bare vacancy is a spin-one paramagnetic species.

Abstract

We investigate the details of the electronic structure in the neighborhoods of a carbon atom vacancy in graphene by employing magnetization-constrained density-functional theory on periodic slabs, and spin-exact, multi-reference, second-order perturbation theory on a finite cluster. The picture that emerges is that of two local magnetic moments (one \pi-like and one \sigma-like) decoupled from the \pi- band and coupled to each other. We find that the ground state is a triplet with a planar equilibrium geometry where an apical C atom opposes a pentagonal ring. This state lies ~0.2 eV lower in energy than the open-shell singlet with one spin flipped, which is a bistable system with two equivalent equilibrium lattice configurations (for the apical C atom above or below the lattice plane) and a barrier ~0.1 eV high separating them. Accordingly, a bare carbon-atom vacancy is predicted to be a spin-one paramagnetic species, but spin-half paramagnetism can be accommodated if binding to foreign species, ripples, coupling to a substrate, or doping are taken into account.