Critical analysis of vacancy-induced magnetism in monolayer and bilayer graphene

Abstract

The observation of intrinsic magnetic order in graphene and graphene-based materials relies on the formation of magnetic moments and a sufficiently strong mutual interaction. Vacancies are arguably considered the primary source of magnetic moments. Here we present an in-depth density functional theory study of the spin-resolved electronic structure of (monoatomic) vacancies in graphene and bilayer graphene. We use two different methodologies: supercell calculations with the SIESTA code and cluster-embedded calculations with the ALACANT package. Our results are conclusive: The vacancy-induced extended π magnetic moments, which present long-range interactions and are capable of magnetic ordering, vanish at any experimentally relevant vacancy concentration. This holds for σ -bond passivated and unpassivated reconstructed vacancies, although, for the unpassivated ones, the disappearance of the π magnetic moments is accompanied by a very large magnetic susceptibility. Only for the unlikely case of a full σ -bond passivation, preventing the reconstruction of the vacancy, a full value of 1 μ B for the π extended magnetic moment is recovered for both monolayer and bilayer cases. Our results put on hold claims of vacancy-induced ferromagnetic or antiferromagnetic order in graphene-based systems, while still leaving the door open to σ -type paramagnetism.

Spin coupling around a carbon atom vacancy in graphene

“…This is a standard E ⊗e problem which is described by the so-called tricorn when such vibrations are included up to second-order 31,32 . Accordingly, a distorted geometry with a "pentagonal" ring and a "apical" carbon atom opposite to it (see Fig.1), can be predicted to be the equilibrium configuration (three-fold degenerate), as indeed found in several previous investigations [21][22][23][24][25][26] . Out of plane, E vibrations do not lift degeneracy at first-order, but may affect energetics at higher orders, especially if coupling to the low-lying excited states is considered 32 .…”

“…The ensuing lattice re-arrangement leaves two unpaired electrons, and a magnetic moment in the range 2.0 − 1.0 µ B has been found by (ensemble) density functional theory (DFT) calculations [21][22][23][24][25][26] , with a clear tendency to 1.0 µ B (and vanishing dependence of the energy on the magnetization) in the low-density limit which signals the absence of any order at experimentally relevant concentrations 26 . Apart from the possible role of electron-hole symmetry, this apparently contrasts with the situation described above for a π moment only, since the presence of an additional unpaired electron in a very localized σ orbital is expected to give either a triplet or a singlet state.…”

Interaction between single vacancies in graphene sheet: An ab initio calculation

“…Recently theoretical works [9][10][11][12][13][14] have revealed that the magnetic properties in graphene-based systems are associated with the occurrence of defects such as atomic vacancies, substitutional and chemisorbed species. In particular, vacancies in graphene sheet giving rise to magnetism depend on the density of defects [15].…”

Monovacancy paramagnetism in neutron-irradiated graphite probed by13C NMR

“…The theoretical modeling of the local-moment formation in the related materials is still controversial [12,[25][26][27][28]. For example, a density functional theory (DFT) study by Palacios et al showed that the vacancy-induced π moments in graphene quench at any experimentally relevant vacancy density [25], whereas Nanda et al suggested that both the σ and π electrons of the vacancy defects contribute and favor an S = 1 state with a reduced net magnetic moment of 1.7 µ B [12]. Experimentally, there is emerging consensus on magnetism in carbon-based systems.…”

“…As one of the main reasons, it offers a new conceptual framework to study the unconventional magnetism of the sp-electrons [12,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. The theoretical modeling of the local-moment formation in the related materials is still controversial [12,[25][26][27][28]. For example, a density functional theory (DFT) study by Palacios et al showed that the vacancy-induced π moments in graphene quench at any experimentally relevant vacancy density [25], whereas Nanda et al suggested that both the σ and π electrons of the vacancy defects contribute and favor an S = 1 state with a reduced net magnetic moment of 1.7 µ B [12].…”