Inducing and optimizing magnetism in graphene nanomeshes

Abstract

Using first-principles calculations, we explore the electronic and magnetic properties of graphene nanomesh (GNM), a regular network of large vacancies, produced either by lithography or nanoimprint. When removing an equal number of A and B sites of the graphene bipartite lattice, the nanomesh made mostly of zigzag (armchair) -type edges exhibit antiferromagnetic (spin unpolarized) states. In contrast, in situations of sublattice symmetry breaking, stable ferri(o)magnetic states are obtained. For hydrogen-passivated nanomesh, the formation energy is dramatically decreased, and ground state is found to strongly depend on the vacancies shape and size. For triangular-shaped holes, the obtained net magnetic moments increase with the number difference of removed A and B sites in agreement with Lieb's theorem for even A + B. For odd A + B triangular meshes and all cases of nontriangular nanomeshes, including the one with even A + B, Lieb's theorem does not hold anymore, which can be partially attributed to the introduction of armchair edges. In addition, large triangular-shaped GNMs could be as robust as nontriangular GNMs, providing a possible solution to overcome one of the crucial challenges for the sp magnetism. Finally, significant exchange-splitting values as large as ∼ 0.5 eV can be obtained for highly asymmetric structures evidencing the potential of GNM for room-temperature carbon-based spintronics. These results demonstrate that a turn from zero-dimensional graphene nanoflakes throughout one-dimensional graphene nanoribbons with zigzag edges to GNM breaks localization of unpaired electrons and provides deviation from the rules based on Lieb's theorem. Such delocalization of the electrons leads the switch of the ground state of a system from an antiferromagnetic narrow gap insulator discussed for graphene nanoribons to a ferromagnetic or nonmagnetic metal.

Energy gaps in graphene nanomeshes

“…We fully relax all the GNMs until the maximum atomic force is less than 0.02 eV/Å, using a 2 × 2 × 1 k-mesh which leads to good convergence for the large unit cells. All the calculations are spin polarized, and the antiferromagnetic state is found to have the lowest energy for the systems considered here, in agreement with previous works 15,22,23 . We have checked the effects of vacuum spacing, and the 4 nm spacing is found to be well converged since further increasing it makes no change in all results.…”

Thermoelectric properties of finite graphene antidot lattices

“…Our calculations have been carried out in the ballistic limit, which gives a reasonable first estimate for short devices whose dimensions are smaller than the various scattering lengths (important scattering mechanisms include the anharmonic phonon-phonon interactions, electron-phonon scattering, and electron-electron scattering). Also, spin polarization may turn important: recent studies have shown that one can have spin-splitting and a magnetic moment in triangular [77][78][79] antidots with pure zigzag edges. Above all, the most important future task is a systematic study of disorder effects.…”

Formation and Physical Properties of h-BN Atomic Layers: A First-Principles Density-Functional Study

“…In Figure 1 are calculated to be 1, 0, and 3 , respectively. Unlike graphene [48], the behavior of vacancies N in the magnetic properties does not follow Lieb's theorem because of the structural reconstructions with the N-N bond formation [49]. When the N-N bond formation is broken, the total magnetic moment increases.…”