Single vacancy defect in graphene: Insights into its magnetic properties from theoretical modeling

• Published in: Physical review. B 2017-09, Vol.96 (12), Article 125431
• Main Authors: Valencia, A. M., Caldas, M. J.
• Format: Article
• Language: English
• Subjects: Boundary conditions; Computer simulation; Crystal defects; Defects; Density functional theory; Exchanging; Graphene; Lattice vacancies; Magnetic moments; Magnetic properties; Magnetism
• ISSN: 2469-9950; 2469-9969
• DOI: 10.1103/PhysRevB.96.125431

Magnetic properties of a single vacancy in graphene is a relevant and still much discussed problem. The experimental results point to a clearly detectable magnetic defect state at the Fermi energy, while calculations based on density functional theory (DFT) yield widely varying results for the magnetic moment, in the range of μ=1.04–2.0μB. We present a multitool ab initio theoretical study of the same defect, using two simulation protocols for a defect in a crystal (cluster and periodic boundary conditions) and different DFT functionals-bare and hybrid DFT, mixing a fraction of the Hartree-Fock (HF) exchange. We find that due to the π character of the Fermi-energy states of graphene, delocalized in the in-plane and localized in the out-of-plane direction, the inclusion of the HF exchange is crucial, and moreover, that defect-defect interactions are long-range and have to be carefully taken into account. Our main conclusions are two-fold. First, for a single isolated vacancy we can predict an integer magnetic moment μ=2μB. Second, we find that due to the specific symmetry of the graphene lattice, periodic arrays of single vacancies may provide interesting diffuse spin-spin interactions.