Magnetic moment of a single vacancy in graphene and semiconducting nanoribbons

Abstract

Calculations of single-vacancy-induced magnetism in graphene have found different values within a large range, which restricts the understanding of magnetism in defected graphene. Here we report first-principles simulations to examine the accuracy of magnetic moment calculations of a single vacancy with respect to the smearing width and $k$-points sampling in calculations of total density of states, based on which the magnetic moment is calculated. We show that the magnetic moment of a single vacancy arises from the asymmetry between spin-up and spin-down electrons in a small energy window of 1 eV that contains a sharp resonance close to the Fermi level. A small smearing width is important to accurately describe the sharp resonance. However, we find that even with a very large number of $k$ points (thousands per unit cell), the magnetic moment value is still sensitive to the smearing width, and that the total density of states still shows spikes, which leads to unreliable evaluation of the magnetic moment. Calculations of a single vacancy in semiconducting graphene nanoribbons further illustrate the balance between smearing width and $k$-points sampling, and indicate a 2 ${\ensuremath{\mu}}_{B}$ ground state as in semiconducting graphene nanoflakes.