π Magnetism of Carbon Monovacancy in Graphene by Hybrid Density Functional Calculations

Understanding magnetism in defective graphene is paramount to improve and broaden its technological applications. A single vacancy in graphene is expected to lead to a magnetic moment with both a σ (1 μB) and a π (1 μB) component. Theoretical calculations based on standard LDA or GGA functional on periodic systems report a partial quenching of the π magnetization (0.5 μB) due to the crossing of two spin split bands at the Fermi level. In contrast, STS experiments ( Phys. Rev. Lett. 2016, 117, 166801) have recently proved the existence of two defect spin states that are separated in energy by 20–60 meV. In this work, we show that self-interaction corrected hybrid functional methods (B3LYP-D*) are capable of correctly reproducing this finite energy gap and, consequently, provide a π magnetization of 1 μB. The crucial role played by the exact exchange is highlighted by comparison with PBE-D2 results and by the magnetic moment dependence with the exact exchange portion in the functional used. The ground state ferromagnetic planar solution is compared to the antiferromagnetic and to the diamagnetic ones, which present an out-of-plane distortion. Periodic models are then compared to graphene nanoflakes of increasing size (up to C383H48). For large models, the triplet spin configuration (total magnetization 2 μB) is the most stable, independently of the functional used, which further corroborates the conclusions of this work and puts an end to the long-debated issue of the magnetic properties of an isolated C monovacancy in graphene