Strain induced second-order Jahn–Teller reconstruction and magnetic moment modulation at monovacancy in graphene

Abstract

Using density functional theory simulations, we examine the electronic structure of an isolated monovacancy defect in graphene under symmetry-breaking deformation. Results show that the defect experiences a second-order Jahn–Teller reconstruction at a critical strain of 1.7%. It stabilizes the orientation of the JT bond relative to the loading direction and breaks the threefold degeneracy of the defect structure. We call it Jahn–Teller re-reconstruction (JTRR), and it is mechanically reversible. The reversibility and stabilization of the orientation depend on the direction cosine between the JT bond and the loading direction. Also, a change in the loading direction by 90° can change the orientation of the JT bond by 120°. An atomic-scale analysis suggests that the maximum bond force arising from “the derivative of the kinetic energy of electrons” defines the critical strain. JTRR alters the electron occupation in the individual electronic orbitals at the defect site. The electronic charge redistribution and the density of states at the defective sites reveal that the pz orbitals dominate the reconstruction process. Furthermore, JTRR changes the magnitude of the magnetic moment at the defective site from 1.36 μB to 1.22 μB. This unravels a new way of controlling the magnetic behavior of monovacancy by applying symmetry-breaking mechanical strain. Results also show that passivation of the dangling bond can subside or eliminate the reconstruction process depending on the number of valence electrons available in the passivating atom.

Strain-Tuneable Magnetism and Spintronics of Distorted Monovacancies in Graphene

“…The most stable nonmagnetic V 1 (55–66) structure is identified and studied, while the magnetic properties of monovacancies at other positions are discussed. This investigation clarifies the origin of the inconsistent magnetic moments of a freestanding monovacancy reported in the previous literature. ,,− It re-confirms the existence and the essential stabilizing effect of the V 1 (55–66) bond reconstruction, previously reported by Santos et al, now using a more rigorous a priori approach that determines the ripple configurations before adding the defects. The relationship between the local geometry of monovacancies and the magnetic moment of the system is also explored in detail.…”

“…The calculated magnetic moment of the monovacancy is 2 μ B , which comprises one unpaired electron from the dangling sp 2 bond and 1/3 of an electron from each 2p z orbital of the 3 neighbors of the monovacancy . The computed magnetic moments of a monovacancy in periodic systems have frequently been reported as fractional values between 1 and 2 μ B in previous studies. ,,, This was considered to originate from the finite size effects in periodic calculations and Rodrigo et al suggested that the magnetic moment of an isolated monovacancy converges to 2 μ B using large-scale DFT up to 30 × 30 supercell. However, the current study suggests that an alternative explanation for the inconsistency lies in the well-known electron self-interaction error of DFT, which is significant for the previously used (semi-)­local functionals based on local spin density approximation (LSDA) and GGA. ,, The consequences of this error have been widely documented in strongly correlated systems resulting from the electron confinement that occurs in dangling bonds or n-doped systems. ,− Pisani et al estimated a significant Hubbard U parameter of ∼3.25 eV for graphene ribbons with the GGA–PBE functional, indicating the large self-interaction that exists in the nonbonding localized orbitals when the π band of graphene is disrupted.…”

“…The monovacancy disrupts the delocalized π band and may lead to unpaired electron density that potentially results in a net magnetization of graphene, , making it a potential candidate for use in spintronic devices. However, there are debates over the exact magnetic moment of monovacancy, ,,− and Rodrigo et al argued that it is an artifact that originates from the finite-size effects in periodic calculations. Although the overall magnetization is usually regarded as zero when multiple monovacancies exist in graphene, , the ferromagnetic hysteresis of proton irradiated graphite is observed at room temperature when an external field is applied …”

“…Strains beyond this limit are experimentally achieved by confining graphene monolayers in a polymer matrix or a diamond anvil cell. , However, previous theoretical studies have found difficulties that the prediction of ripple wavelengths is predetermined by the choice of periodic simulation cell. ,− The nature of the interplay between monovacancies and strain-induced ripples remains an open question. Some preliminary results have been obtained by either applying tensile strains , or under the assumption that the strained graphene sheet is ideally flat . The most noticeable finding is the strain-induced bond reconstruction of monovacancies, indicating the probable existence of novel strain-tuneable properties.…”

Designing 3d metal oxides: selecting optimal density functionals for strongly correlated materials

“…151–155 Naturally, it follows that Mulliken population analysis is basis-dependent, which is significant in molecular systems because of the local nature of basis sets, but reduced in ionic systems, for which the basis set is optimized for crystal orbitals. 156–159 Since the calculated the TMOs μ B with all DFs were compared using the same basis set, any error should be systematic.…”