Theoretical perspective on structural, electronic and magnetic properties of 3d metal tetraoxide clusters embedded into single and di-vacancy graphene

Theoretical perspective on structural, electronic and magnetic properties of 3d metal tetraoxide clusters embedded into single and di-vacancy graphene

Accepted Manuscript Title: Theoretical perspective on structural, electronic and magnetic properties of 3d metal tetraoxide clusters embedded into sin...

4MB Sizes 0 Downloads 30 Views

Accepted Manuscript Title: Theoretical perspective on structural, electronic and magnetic properties of 3d metal tetraoxide clusters embedded into single and di-vacancy graphene Authors: Muhammad Rafique, Yong Shuai, He-Ping Tan, Hassan Muhammad PII: DOI: Reference:

S0169-4332(17)30612-8 http://dx.doi.org/doi:10.1016/j.apsusc.2017.02.239 APSUSC 35348

To appear in:

APSUSC

Received date: Accepted date:

9-1-2017 27-2-2017

Please cite this article as: Muhammad Rafique, Yong Shuai, He-Ping Tan, Hassan Muhammad, Theoretical perspective on structural, electronic and magnetic properties of 3d metal tetraoxide clusters embedded into single and di-vacancy graphene, Applied Surface Science http://dx.doi.org/10.1016/j.apsusc.2017.02.239 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Theoretical perspective on structural, electronic and magnetic properties of 3d metal tetraoxide clusters embedded into single and di-vacancy graphene

Rafique Muhammad(a),b), Yong Shuai(a),*, He-Ping Tan(a), Hassan Muhammad(a)

(a) (b)

*

School of Energy Science and Engineering, Harbin Institute of Technology,92 West Dazhi Street, Harbin 150001, PR China

M.U.E.T, S.Z.A.B, Campus Khairpur Mir's, Sindh, Pakistan

Corresponding author: Tel: +86451 86412308. E-mail: [email protected] (Yong Shuai, Dr)

Graphical abstract

Abstract Structural, electronic and magnetic properties of 3d transition metal tetraoxide TMO4 superhalogen clusters doped single vacancy (SV) and divacancy (DV) monolayer graphene have been studied using first-principles calculations. We found that in both cases of TMO4 cluster substitution, all the impurity atoms are tightly bonded with graphene, having significant formation energy and large charge transfer occurs from graphene to TMO4 clusters. CrO4 and MnO4 substituted SV graphene structures exhibit dilute magnetic semiconductor behavior in their spin down channel with 2.15 µB and 3.51 µB magnetic moment, respectively. However, CoO4, FeO4, TiO4 and NiO4 substitution into SV graphene, leads to Fermi level shifting to conduction band, thereby causing the Dirac cone to move into valence band and a band gap appears at high symmetric K-point. Interestingly, CoO4, CrO4, FeO4 and MnO4 substituted DV graphene structures exhibit dilute magnetic semiconductor behavior in their spin up channel with 1.74 µB, 3.27 µB, 3.09 µB and 1.99 µB magnetic moment, respectively. Detailed analysis of density of states (DOS) plots show that d orbitals of 3d TM atoms should be responsible for inducing magnetic moments in graphene. We believe that our results are appropriate for experimental exploration and graphene-based spintronic and magnetic storage devices.

Keywords: First-principles; Doping; Graphene; Magnetic Moments; Transition Metals

1. Introduction In recent times, graphene [1, 2] has drawn a course of attention from researchers and experimentalists due to its potential applications in nanoscience, condensed matter physics and spintronic data storage devices. Due to its unique electrical, electronic, mechanical and other outstanding properties [3-7], various graphene devices have been designed and utilized to facilitate catalysis [8, 9], to design efficient energy storage, nanoelectronics, sensor and spintronic devices [10-17]. Given the unique structure of graphene, with planar sp2 bonding and π bonding with perpendicular pz orbitals, it is a nonmagnetic semimetal with a linear dispersion of energy near the Fermi energy (EF) level [3]. In order to broaden the applications of graphene as a magnetic material, to be used for novel spintronic devices, various approaches have been

utilized to functionalize the graphene for introducing ferromagnetism behavior in graphene [1719]. For example, producing defects in graphene layer by electron or ion beam [20-22] can produce magnetism in graphene. Recently, metal ad-atoms on monolayer graphene, nanotubes and silicene have been widely studied to analyze their ferromagnetism behavior using firstprinciples study calculations [23-25]. Presently, there are two main approaches broadly utilized for substituting TM atoms into graphene to induce magnetic moments in graphene layer. The first approach is to adsorb TM atoms on graphene sheet, studies indicate that adsorbed TM atoms bind strongly to graphene sheet [26] and their calculated migration barrier is low enough to be mobile at room temperatures [27]. The second approach is to incorporate TM atoms into graphene vacancies namely, single vacancy (SV) or divacancy (DV). Various studies have been performed to determine the structural, electronic and magnetic properties of individual TM atoms embedded into SV and DV graphene sheets [28-30]. These studies indicate that, binding energies obtained for TM atoms embedded into SV and DV graphene are far better than that of TM atoms adsorbed at graphene sheet. These studies also predict that, doping TM atoms into SV and DV graphene is more suitable than TM atoms adsorption on graphene, for its applications in graphene-based devices operating at room temperatures and above. In all cases of TM atoms adsorption or doping into SV and DV graphene produces ferromagnetic behavior due to strong interaction between TM atoms and defective graphene [23-30]. However, all these studies are focused only on individual TM atom doping into SV or DV graphene. Recently, Dan Li et al. [31] performed first-principles calculations on various complexes of MnO3(4) superhalogen clusters embedded into SV and DV monolayer graphene. Authors predicted that, MnO3(4) superhalogen clusters are easily embedded in SV and DV graphene layer. Neutral MnO3(4) cluster doping was thermodynamically favored with exothermic energy and the direction of charge transfer was always from graphene to MnO3(4) clusters because of highly electronegative nature of halogen cluster. Since this study is focused on various MnO3(4) complexes substituted in graphene, therefore, a well-defined and systematic study is required for 3d metal tetraoxide superhalogen cluster substitution into SV and DV graphene and their effects on structural, electronic and magnetic properties of graphene. Our study aims to obtain the electronic properties and ferromagnetism coupling of the TMO4 superhalogen clusters embedded into SV and DV graphene sheet.

In this study, we incorporated 3d metal tetraoxide (TMO4) superhalogen clusters in SV and DV monolayer graphene and their structural, electronic, and magnetic properties were investigated using first-principles calculations based on density functional theory (DFT) method. Given their negative formation energy and strong binding energy, TMO4-doped structures are suitable for use in magnetic substrates to induce magnetism in graphene. To the best of our knowledge, the structural, electronic and magnetic properties of such a system has not been well understood. These new findings can enable to tune the band gap and magnetic properties of graphene for engineering applications, in particular, in nanoelectronics and in graphene spin field effect transistors (spin-FETs) that are distinct from those of pristine graphene. 2. Computational Method The structural, electronic and magnetic properties of 3d TMO4 superhalogen clusterdoped SV and DV monolayer graphene were calculated using first-principles calculations based on density functional-theory (DFT) method. The DFT method has proven to be one of the most accurate methods for the computation of the electronic structure of solids [32-37]. All the calculations were performed in spin-polarized mode. The projector augmented wave (PAW) potentials [38] with Perdew–Burke–Ernzerhof (PBE) functional [39] was utilized by Vienna Abinitio simulation package (VASP) [40]. A kinetic energy cutoff of 500 eV was used for wave function expansion. Our structure model consists of a 4 × 3 monolayer graphene supercell (20 carbon atoms with 5 impurity atoms in case of TMO4 cluster embedded into SV graphene) and (18 carbon atoms with 5 impurity atoms in case of TMO4 cluster embedded into DV graphene) with a vacuum layer of 15 Å in Z-direction to eliminate the interaction between adjacent layers. The Brillouin zone (BZ) was sampled using a 7 × 7 × 1 Γ-centered k-point mesh. All the structures were fully optimized until the Hellmann–Feynman forces were less than 0.01 eV/Å and the total change in energy was less than 10-6 eV. Gaussian smearing method was utilized to deal with the partial occupancies. Bader analysis was used to calculate the charge transfer [41, 42]. 3. Results and discussions 3.1 Geometric structures and magnetic properties Different 3d metal tetraoxide halogen clusters i.e. (CoO4, CrO4, FeO4, MnO4, NiO4, TiO4 and VO4) were embedded into monolayer graphene with two different approaches. In first case,

individual TM atom was embedded into SV graphene at the defect site in graphene sheet, three C atoms were substituted by three O atoms around the SV and remaining one O atom was attached on top of the TM atom as shown in Figs.1(a) and 1(b). In second case, individual TM atom was incorporated into DV graphene at the defect site and four C atoms were substituted by four O atoms around the DV site in the graphene sheet as shown in Figs.1(c) and 1(d), and comprehensive comparison is made between these two models throughout our work. In all cases of TMO4 superhalogen clusters incorporated into SV monolayer graphene, TM atom bulges out of the graphene plane after geometry optimization, causing minute upward drift of O atoms present in the graphene planar structure. Fig.2. represents bond distances of TMO and bond distances of C-O atoms after geometry relaxation of TMO4 clusters embedded into SV monolayer graphene. It is observed that substitutional TM atoms with large atomic radii caused the local deformation and significant elevations above the 2D plane of honey comb structure of graphene. It is also found that, the elevation in individual TM atom also causes small displacement in the O atoms around the SV site of graphene, resulting change in the bond lengths between C-O atoms. The structural parameters calculated for TMO4 clusters embedded in SV graphene are consistent with the previous studies carried out on 2D materials [31, 43-45]. These results depict that the employed computational methods and structural models used in the present work are enough accurate. By contrast, the positions of C atoms around the TMO4 clusters were unaffected, and the planar structure of graphene was maintained in the TMO4 clusters incorporated into SV monolayer graphene. In case of TMO4 clusters-doped into SV graphene structures, the C-O bond lengths were almost equal at 1.38-1.40 Å and the amount of the change in C-O bond lengths were less than 0.03 Å. In addition, the Jahn-teller distortion lowered the D3h local symmetry of monolayer graphene to C3v or Ci symmetry of TMO4 cluster doped SV graphene structures. Fig. 3. represents TM-O bond distances and C-O bond distances after geometry relaxation of TMO4 clusters incorporated into DV monolayer graphene. In this case TM atoms are embedded at the DV site of graphene and four C atoms are substituted by four O atoms around the DV site. In all cases of TMO4 superhalogen clusters incorporated into DV monolayer graphene as shown in Fig. 3, respectively, it is observed that the TM atoms placed at DV site maintain their position in the planar structure of 2D graphene without getting elevated above the 2D plane. It is due to strong covalent bonding between four O atoms around the DV site,

however a minute local deformation is observed and a small change in bond length between C-O atoms is obtained. Similar to TMO4 cluster-doped SV graphene structures, the positions of C atoms surrounding the TMO4 cluster embedded into DV graphene is unchanged, and the planar structure of graphene layer is maintained. In case of TMO4 clusters embedded into DV monolayer graphene, the C–O bond lengths were found to be in range of equal at 1.39–1.41 Å, and the amounts of change in the C–O bond lengths were less than 0.02 Å. All TMO4 clustersdoped DV graphene structures had similar fourfold rotational symmetry. However, the equatorial TM–O bond lengths of the TMO4 cluster-doped DV graphene structures were all significantly shorter than those of the TMO4 cluster-doped SV graphene structures. The structural parameters calculated for TMO4 cluster-doped DV graphene complexes are consistent with the previous reports [27, 31, 46]. Table 1 given below lists the average equatorial bond lengths between TM-O atoms, bond lengths between C-O atoms, the elevation "h" of TM atoms above the monolayer graphene surface for TMO4 cluster-doped SV graphene structures, the total magnetization μtot of the supercell and the magnetic moment of individual TM atoms μTM for both approaches of TMO4 clusters incorporated into SV and DV monolayer graphene. The results obtained for MnO4 clusters doped in SV and DV graphene are consistent with the Ref. [31]. However minor variations in results can be attributed to difference between the size of supercell and utilization of k-point mesh. The magnetic moments of the graphene supercell given in the table below indicate that, TMO4 clusters doping into DV graphene produces larger ferromagnetic behavior as compared to TMO4 doped into SV graphene. Increase in ferromagnetic behavior of TMO4 clusters embedded in DV graphene can be attributed to the weaker interaction of impurity atoms/molecules with the ligand bonds resulting in higher spin state of the complex. These results are consistent with the previous studies available [27, 31, 43, 44]. Total magnetic moments μtot and magnetic moments of TM atoms μTM presented in table 1 indicate that larger magnetic moments per supercell can be obtained for TMO4 clusters embedded in SV graphene structures, except CoO4 and NiO4 doped SV graphene. Total magnetic moments for TMO4 clusters embedded into SV graphene structures are 0.65 μB, 2.15 μB, 3.27 μB, 3.51 μB, 0.04 μB, 0.35 μB, and 2.75 μB for CoO4, CrO4, FeO4, MnO4, NiO4, TiO4 and VO4 complexes, respectively. We analyzed the magnetic coupling behavior for the TMO4 clusterdoped SV graphene structures. Figs. 4(a)-(d) show spin densities (ρ↑ - ρ↓) of TMO4 (CrO4, FeO4,

MnO4 and VO4) doped SV graphene structures. CoO4, NiO4 and TiO4 doped SV graphene structures spin densities were omitted due to their weak ferromagnetism coupling behavior with the graphene supercell. All the TMO4 doped SV graphene structures presented similar magnetic coupling behavior between TM atoms and graphene layer. Significant magnetic coupling behavior was obtained between TM atoms and neighboring three C and three O atoms. However Cr, Fe, Mn and V, atoms contain large positive spin density which is due to their unfilled d orbital configuration. In CrO4, FeO4 and MnO4 complexes, direction of polarization between TM atoms and nearest O atoms substituted into graphene layer are parallel, whereas those are antiparallel in VO4 doped graphene. In FeO4 complex the direction of polarization between Fe and O atom attached on top is anti-parallel. The magnetic coupling was not localized, it was distributed along the graphene layer. These results are consistent with the previous reports available [27, 31, 43, 44]. Figs. 5(a)-(g) show the spin densities (ρ↑ - ρ↓) of TMO4 clusters incorporated into DV monolayer graphene. All the TMO4 clusters embedded into DV graphene structures show similar magnetic coupling behavior between TMO4 cluster and graphene layer. Significant magnetic coupling behavior was obtained between TM atoms and neighboring C and O atoms. In all cases of TMO4 cluster doped structures, magnetic coupling was not localized, it was distributed along the graphene layer. Total magnetic moments for TMO4 clusters embedded into DV graphene structures are 1.74 μB, 3.27 μB, 3.09 μB, 1.99 μB, 1.03 μB, 2.47 μB, and 3.48 μB for CoO4, CrO4, FeO4, MnO4, NiO4, TiO4 and VO4 complexes, respectively. It is observed that the direction of spin polarization on TM atom and neighboring O atoms is parallel in case CoO4, FeO4, NiO4, TiO4 and VO4 clusters doped graphene structures as shown in Figs. 5(a), 5(c), 5(e), 5(f) and 5(g), respectively. However TiO4 and VO4 clusters doped into DV graphene induce larger positive spin in the graphene layer. The direction of polarization between TM atoms and neighboring O atoms is anti-parallel for that of CrO4 and MnO4 clusters doped DV graphene structures as shown in Figs. 5(b) and 5(d), respectively. From the total magnetic moments given in table 1 and spin density diagrams shown in Figs. 5(a)-(g), one can clearly observe that the obtained results are consistent with the crystal field theory: A larger "hole" at the DV is responsible for the weaker interaction of the impurity clusters with the ligand bonds, which in turn gives rise to

higher spin states of the TMO4 clusters doped DV monolayer graphene complex structures. These obtained results are consistent with the previous studies available [27, 31, 46-48] . In order to further understand the behavior of TMO4 clusters embedded in SV monolayer graphene, we examined the charge transfer using Bader analysis [41, 42] for TMO4 clusterdoped SV graphene structures. The charge density difference is defined as ΔρTMO4 = ρTMO4(sv/dv)graphene

- ρgraphene - ρTMO4. Where ρTMO4-(sv/dv)graphene, ρgraphene and ρTMO4 represent the charge

density of TMO4 cluster-doped SV/DV graphene, charge density of graphene with vacancy and charge density of TMO4 clusters respectively. Figs. 6(a)-(g) show the electron charge density of TMO4 clusters doped SV graphene structures. The yellow and cyan isosurfaces correspond to electron rich and electron depleted zone with the isosurfaces value of 0.003 e/Å3 respectively. In Figs. 6(a)-(g), all TMO4 clusterdoped SV graphene structures i.e. CoO4, CrO4, FeO4, MnO4, NiO4, TiO4 and VO4 doped structures show similar pattern of charge density difference. The electron density around the O atoms is increased whereas the adjacent C atoms has decreased charge density as depicted by yellow and cyan colors, respectively. It depicts that charge transfer occurs from monolayer graphene to TMO4 clusters. These results suggest that the TMO4 clusters embedded into SV graphene complexes have stronger electronegativity, thereby maintaining superhalogen characteristics. Stronger electronegativity of superhalogen clusters embedded in SV graphene can result in lower formation energies producing stable TMO4 cluster-doped SV graphene complexes. The trend of charge density diagrams obtained in our study is consistent with previous literature available [25, 27, 31, 43, 44]. .

Using similar technique as mentioned above, we investigated the charge density difference of TMO4 clusters embedded into DV monolayer graphene as shown in Figs. 7(a)-(g), respectively. Results given below suggest that, all TMO4 cluster-doped DV graphene structures show the same characteristics of charge density difference. TMO4 clusters embedded into DV graphene show similar behavior of charge density difference to that of TMO4 clusters embedded into SV graphene i.e. the electron density around the substituted O atoms and TM atoms is increased whereas the adjacent C atoms has decreased charge density as depicted by yellow and cyan colors, respectively. The yellow and cyan isosurfaces correspond to electron rich and electron depleted zone with the isosurfaces value of 0.003 e/Å3 respectively. Interestingly, in

case of TMO4 clusters embedded into DV graphene structures, a large portion of graphene layer has electron depleted configuration, which supports the prediction that large amount of charge transfer occurs from monolayer graphene to TMO4 clusters embedded into DV graphene as compared to that of TMO4 cluster-doped SV graphene, this increase in charge transfer from graphene to TMO4 clusters can be attributed to the presence of four O atoms and one TM atom directly in the planar structure of graphene, rather than that of TM and O atoms elevated above the planar structure as that of TMO4 cluster-doped SV graphene. Increase in charge transfer further supports the prediction of stronger electronegativity of superhalogen clusters, thereby having lower formation energies and stable TMO4 cluster doped DV graphene complexes. These results are consistent with the previous reports available [25, 27, 31, 43, 44]. .

3.2 Electronic properties In this section, band structure and density of states plots are investigated for TMO4 clusters incorporated into SV and DV monolayer graphene structure. For band structure calculations, 20 points are collected along each high symmetry lines using path Γ- M - K - Γ in the irreducible Brillouin zone to obtain the band structure with very fine grid. Total and projected density of states (PDOS) is calculated for all TMO4 cluster-doped structures using a 11 × 11 × 1 Gamma centered Brillouin-zone sampling, and the energy eigenvalues are smeared with Gaussians of width 0.2 eV. We used spin polarized mode for calculating band structure and DOS plots. 3.2.1 Band structure and PDOS plots for TMO4 clusters-doped SV monolayer graphene Fig.8 (a)-(g) presents spin polarized band structure diagrams of TMO4 (CoO4, CrO4, FeO4, MnO4, NiO4, TiO4 and VO4) clusters incorporated into SV monolayer graphene. For comparison of band structure diagrams after TMO4 cluster doping, spin un-polarized band structure diagram of pure graphene is also shown named as graphene. Band structure of pure graphene demonstrates a zero band gap semiconductor which is in good agreement with the previous results available [1-5]. Pure graphene π and π* bands are shown at high symmetric kpoint. Fermi energy (EF) level is set at zero and is shown by dotted purple line in the given band structure diagrams.

Since TMO4 clusters had excess of charge which causes the Fermi level (EF) to shift up into conduction band, the π* band of monolayer graphene shifts into valence band and a band gap appears at high symmetric K-point, as shown in Figs.8 (a)-(g), respectively. All TMO4 clusters i.e. CoO4, CrO4, FeO4, MnO4, NiO4, TiO4 and VO4 doped SV graphene structures exhibit metallic characteristics in spin up channel polarization condition by introducing very small band gap in spin up channel. However, CrO4 and MnO4 cluster-doped SV graphene structures exhibit dilute magnetic semiconductor properties introducing band gap of approximately 0.9 eV and 0.7 eV in case of spin down band channel as shown in Figs. 8(b) and 8(d). It is important to note here that, the spin up and spin down states in these bands are polarized which indicates the existence of magnetic moments (we will further elaborate the origins of magnetism in DOS plots below). The emergence of finite band gap in the band structure diagrams of TMO4 cluster-doped SV graphene structures can be attributed to the local distortion of the graphene induced by impurity atoms, which breaks the symmetry of the sub lattices of graphene. These obtained results are consistent with the previous studies [26, 49-51]. Spin polarized total density of states (TDOS) and projected density of states (PDOS) plots for all the TMO4 clusters embedded into SV graphene structures are analyzed to understand the different effects of TMO4 cluster doping into SV graphene. TDOS and PDOS on the TM atoms, adjacent C atom p orbital and adjacent O atom p orbitals for all TMO4 cluster-doped SV graphene structures are shown in Figs.9 (a)-(g), respectively. Fermi energy level (EF) is marked by thin grey line in the PDOS plots appearing at the 0 eV energy level. Impurity states induced by all TMO4 clusters near the top of the valence band and bottom of the conduction band are observed as shown in Figs.9 (a)-(g), respectively. Clearly, these impurity states appear due to hybridization between 3d orbitals of TM atoms and p orbitals of O atoms. Since we know that CrO4, FeO4, MnO4 and VO4 cluster doping induced larger magnetic moments of 2.15 µB, 3.27 µB, 3.51 µB and 2.75 µB, respectively, therefore their d orbitals have larger spin polarization as shown in PDOS plots for given structures. However, other three CoO4, NiO4 and TiO4 complexes induce very small magnetic moments of 0.65 µB, 0.04 µB and 0.35 µB, respectively, hence their d orbitals show less spin polarization as shown in their PDOS plots. From the PDOS plots we can further analyze that the five different orbitals namely (dxy, dyz, dz2, dxz and dx2-y2 ) of 3d TM atoms give rise to magnetic moments of TMO4 clusters doped SV graphene structures. For all the TMO4 clusters incorporated into SV graphene complexes, dz2, and dxy orbitals of TM atoms

almost did not hybridize with p orbitals of O atoms, but dxz, dyz and dx2-y2 orbitals of TM atoms interacted softly with p orbitals of O atoms as shown in Figs. 9(a)-(g). From the given PDOS plots we can clearly observe the band gap opening in TMO4 cluster-doped SV graphene structures, which is described in band structure diagrams shown in Figs. 8(a)-(g). However, an important factor to note here is that the appearing of band gap in spin up and spin down states shown in DOS plots is at different energy levels, due to the polarization of spin state bands, thereby introducing the concept of spintronics. From obtained results we can predict that 2D magnetic semiconductors can be synthesized by doping TMO4 clusters into SV graphene. 3.2.2 Band structure and PDOS plots for TMO4 clusters-doped DV monolayer graphene Fig.10 (a)-(g) presents spin polarized band structure diagrams of TMO4 clusters embedded into DV monolayer graphene. For the sake of comparison, spin un-polarized band structure diagram of pure graphene is also given, named as graphene. Pure graphene π and π* bands are shown at k-point. From the given band structure diagrams for all TMO4 clusters doped DV graphene structures, we can predict that, after TMO4 cluster doping, linear dispersion of energy at the Dirac point is maintained for all the structures. Since TMO4 clusters embedded into DV graphene structure had excess of charge than monolayer graphene, therefore TMO4 clusterdoping can be regarded as donor impurity doping. Since the impurity atoms have donor nature, they cause the Fermi level (EF) to shift up into conduction band, and the π* band of monolayer graphene shifts into valence band also introducing band gap at high symmetric K-point, as shown in Figs.10 (a)-(g), respectively. The shift in the Dirac point is about 1 eV, which is close to the electron transfer quantitatively. It is observed that the band gap appearing at the Dirac point in spin up channel is higher than the band gap appearing at the Dirac point in spin down channel in all the TMO4 cluster-doped graphene structures. Similar to TMO4 cluster-doped SV graphene structures, the spin up and spin down states in these bands of TMO4 cluster-doped DV graphene complexes are also polarized which indicates the existence of ferromagnetism. The origin of magnetism in these structures is explained in detail in their corresponding PDOS plots. Our results obtained for band structure calculations are consistent with previous studies [29, 52-56] Spin polarized TDOS and PDOS plots for all the TMO4 clusters embedded into DV graphene structures are analyzed to understand the different effects of TMO4 cluster doping into DV graphene. TDOS and PDOS on the TM atoms, adjacent C atom p orbital and adjacent O

atom p orbitals for all the TMO4 cluster-doped DV monolayer graphene structures are shown in Figs.11 (a)-(g), respectively. Fermi energy level (EF) is marked by thin grey line in the PDOS plots appearing at the 0 eV energy level. Impurity states induced by TMO4 clusters at the Fermi level are observed, which are induced due to hybridization between 3d orbitals of TM atoms and p orbitals of O atoms as shown in Figs.11(a)-(g). Since we know that, all the TMO4 clusters (CoO4, CrO4, FeO4, MnO4, NiO4, TiO4, and VO4) embedded into DV graphene structures induced magnetic moments of 1.74 µB, 3.27 µB, 3.09 µB, 1.99 µB, 1.03 µB, 2.47 µB, and 3.48 µB, respectively, therefore their d orbitals have larger spin polarization as shown in PDOS plots for given structures. Similar to TMO4 cluster-doped SV graphene structures, same five different orbitals namely (dxy, dyz, dz2, dxz and dx2-y2 ) of 3d TM atoms give rise to magnetic moments of TMO4 clusters doped DV graphene structures. For all the TMO4 clusters incorporated into DV graphene complexes, dz2, and dx2-y2 orbitals of TM atoms almost did not hybridize with p orbitals of O atoms, but dxz, dyz and dxy orbitals of TM atoms interacted softly with p orbitals of O atoms as shown in Figs. 11(a)-(g). An important factor to note here is that the appearing of band gap in spin up channel at Dirac point has higher value than band gap of spin down channel, which suggests that the TMO4 cluster-doped structures can exhibit metallic or dilute magnetic semiconductor properties depending upon the polarization of magnetic field. 3.3 Formation energies of TMO4 cluster-doped SV and DV graphene To verify the stability of our TMO4 cluster-doped SV and DV monolayer graphene structures we calculated the formation energies for each system using following equation [31]: 𝐸𝑓(𝑔𝑝𝑇𝑀𝑂3 ) = 𝐸(𝑔𝑝𝑇𝑀𝑂3 ) − 𝐸𝑝𝑔𝑝 + 𝑚µ𝑐 − 𝑛µ𝑂 − µ 𝑇𝑀 where 𝐸𝑓(𝑔𝑝𝑇𝑀𝑂3 ) is the total energy of TMO4 doped graphene structures, 𝐸𝑝𝑔𝑝 is the total energy of pure graphene; 𝑚 is the number of C atoms substituted by O and TM atoms, and 𝑛 is the number of O atoms in the TMO4 clusters, respectively. The chemical potentials of carbon µ𝑐 , oxygen µ𝑂 and TM atoms µ 𝑇𝑀 were obtained from pristine graphene, O2 gas molecules and standard phases of various TM crystals. For TMO4 cluster-doped SV graphene complexes 𝑚 and 𝑛 = 4 and for TMO4 cluster-doped DV graphene complexes 𝑚 =6 and 𝑛 =4, respectively. The calculated formation energies for all TMO4 cluster-doped SV and DV monolayer graphene structures are given in table 2. All TMO4 cluster-doped SV and DV graphene structures showed negative formation energies. The negative formation energies indicate that TMO4 cluster doping in SV and DV

graphene is thermodynamically favored with exothermic energy. By contrast, TMO4 clusterdoped DV graphene structures have lower formation energies as compared to TMO4 clusterdoped SV graphene structures. These results suggest that TMO4 cluster doping in DV graphene is more thermodynamically favorable than SV graphene structures. These results are consistent with the previous studies available [25, 27, 31, 43, 44].

4. Conclusion The structural, electronic and magnetic properties of TMO4 clusters embedded into SV and DV monolayer graphene structures were investigated by means of first-principles study calculations based on density functional theory (DFT) method. Two different approaches were utilized for substituting TMO4 clusters into monolayer graphene; i) Individual TM atom was embedded in single vacancy (SV) of graphene, three carbon (C) atoms were substituted by three oxygen (O) atoms around the SV and remaining O atom was attached to TM atom. ii) individual TM atom was embedded in divacancy (DV) of graphene and four C atoms were substituted by four O atoms around the DV of graphene. TMO4 cluster doping into SV and DV graphene introduced ferromagnetism in monolayer graphene. From obtained results it is predicted that TMO4 clusters embedded into DV graphene produce larger magnetic moments as compared to that of TMO4 cluster-doped SV graphene structures. We calculated the spin densities (ρ↑ - ρ↓) and charge density difference for all TMO4 cluster-doped structures. Significant ferromagnetic couplings were observed between a TM atom and neighboring C and O atoms on the graphene layer in all TMO4 cluster-doped SV and DV graphene structures. The direction of charge transfer was always from monolayer graphene to TMO4 clusters. Band structure and PDOS plots were obtained in order to understand the effect of TMO4 cluster doping on the electronic properties of SV and DV monolayer graphene. The band gap was sensitively dependent on the doped clusters, which offers a reasonable approach to tune the gap of monolayer graphene. In addition, band gaps differed between spin up and spin down channels. Thus, they have potential applications for the development of spintronic devices. From the PDOS plots it was observed that, in both cases of TMO4 cluster-doped into SV and DV graphene, five different orbitals (dxy, dyz, dz2, dxz and dx22 y

) of 3d TM atoms give rise to magnetic moments in monolayer graphene. All TMO4 cluster-

doped structures have negative formation energies, which suggests that TMO4 cluster-doping is

thermodynamically favorable with exothermic energy. However TMO4 cluster-doped DV graphene have lower formation energies as compared to TMO4 cluster-doped SV graphene. From the results given above we can conclude that some of TMO4 cluster-doped SV and DV graphene structures introduce band gap and magnetic moments converting semimetal graphene into metallic/semiconductor structures. Therefore we can predict that TMO4 cluster-doped graphene complexes are suitable for the magnetic substrate to induce magnetism in graphene for its practical applications in high speed spin-FETs. It would be motivating to pertain our calculations in future experimental studies.

Acknowledgments This work was supported by the National Natural Science Foundation of China (Nos. 51276049, 51522601) and the program for New Century Excellent Talents in University (No. NCET-13-0173).

References [1] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Electric field effect in atomically thin carbon films, science, 306 (2004) 666-669. [2] K. Novoselov, D. Jiang, F. Schedin, T. Booth, V. Khotkevich, S. Morozov, A. Geim, Twodimensional atomic crystals, Proceedings of the National Academy of Sciences of the United States of America, 102 (2005) 10451-10453. [3] K. Novoselov, A.K. Geim, S. Morozov, D. Jiang, M. Katsnelson, I. Grigorieva, S. Dubonos, A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, nature, 438 (2005) 197200. [4] F. Guinea, N. Peres, K. Novoselov, A. Geim, A.C. Neto, The electronic properties of graphene, Rev. Mod. Phys., 81 (2009) 109-162. [5] A.K. Geim, K.S. Novoselov, The rise of graphene, Nature materials, 6 (2007) 183-191. [6] C. Lee, X. Wei, J.W. Kysar, J. Hone, Measurement of the elastic properties and intrinsic strength of monolayer graphene, science, 321 (2008) 385-388.

[7] A.A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, C.N. Lau, Superior thermal conductivity of single-layer graphene, Nano letters, 8 (2008) 902-907. [8] Y. Li, Z. Zhou, G. Yu, W. Chen, Z. Chen, CO catalytic oxidation on iron-embedded graphene: computational quest for low-cost nanocatalysts, The Journal of Physical Chemistry C, 114 (2010) 6250-6254. [9] M. Kaukonen, A. Krasheninnikov, E. Kauppinen, R. Nieminen, Doped graphene as a material for oxygen reduction reaction in hydrogen fuel cells: a computational study, ACS Catalysis, 3 (2013) 159-165. [10] I. Cabria, M. López, J. Alonso, Enhancement of hydrogen physisorption on graphene and carbon nanotubes by Li doping, The Journal of chemical physics, 123 (2005) 204721. [11] I. López-Corral, E.a. Germán, A. Juan, M.a.A. Volpe, G.P. Brizuela, DFT study of hydrogen adsorption on palladium decorated graphene, The Journal of Physical Chemistry C, 115 (2011) 4315-4323. [12] M. Pumera, Graphene-based nanomaterials for energy storage, Energy & Environmental Science, 4 (2011) 668-674. [13] Y.-M. Lin, C. Dimitrakopoulos, K.A. Jenkins, D.B. Farmer, H.-Y. Chiu, A. Grill, P. Avouris, 100-GHz transistors from wafer-scale epitaxial graphene, Science, 327 (2010) 662-662. [14] L. Liao, Y.-C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K.L. Wang, Y. Huang, X. Duan, High-speed graphene transistors with a self-aligned nanowire gate, Nature, 467 (2010) 305-308. [15] F. Schedin, A. Geim, S. Morozov, E. Hill, P. Blake, M. Katsnelson, K. Novoselov, Detection of individual gas molecules adsorbed on graphene, Nature materials, 6 (2007) 652655. [16] Y.-W. Son, M.L. Cohen, S.G. Louie, Half-metallic graphene nanoribbons, Nature, 444 (2006) 347-349. [17] O.V. Yazyev, M. Katsnelson, Magnetic correlations at graphene edges: basis for novel spintronics devices, Physical Review Letters, 100 (2008) 047209. [18] N. Tombros, C. Jozsa, M. Popinciuc, H.T. Jonkman, B.J. Van Wees, Electronic spin transport and spin precession in single graphene layers at room temperature, Nature, 448 (2007) 571-574.

[19] W. Han, K. Pi, K. McCreary, Y. Li, J.J. Wong, A. Swartz, R. Kawakami, Tunneling spin injection into single layer graphene, Physical review letters, 105 (2010) 167202. [20] F. Banhart, J. Kotakoski, A.V. Krasheninnikov, Structural defects in graphene, ACS nano, 5 (2010) 26-41. [21] O. Lehtinen, J. Kotakoski, A. Krasheninnikov, A. Tolvanen, K. Nordlund, J. Keinonen, Effects of ion bombardment on a two-dimensional target: atomistic simulations of graphene irradiation, Physical review B, 81 (2010) 153401. [22] J. Kotakoski, A. Krasheninnikov, U. Kaiser, J. Meyer, From point defects in graphene to two-dimensional amorphous carbon, Physical Review Letters, 106 (2011) 105505. [23] H. Sahin, F.M. Peeters, Adsorption of alkali, alkaline-earth, and 3 d transition metal atoms on silicene, Physical Review B, 87 (2013) 085423. [24] S. Lisenkov, A.N. Andriotis, M. Menon, Magnetic anisotropy and engineering of magnetic behavior of the edges in Co embedded graphene nanoribbons, Physical review letters, 108 (2012) 187208. [25] A.T. Lee, J. Kang, S.-H. Wei, K. Chang, Y.-H. Kim, Carrier-mediated long-range ferromagnetism in electron-doped Fe-C 4 and Fe-N 4 incorporated graphene, Physical Review B, 86 (2012) 165403. [26] M. Sun, W. Tang, Q. Ren, S. Wang, Y. Du, Y. Zhang, First-principles study of the alkali earth metal atoms adsorption on graphene, Applied Surface Science, 356 (2015) 668-673. [27] A. Krasheninnikov, P. Lehtinen, A.S. Foster, P. Pyykkö, R.M. Nieminen, Embedding transition-metal atoms in graphene: structure, bonding, and magnetism, Physical review letters, 102 (2009) 126807. [28] D. Boukhvalov, M. Katsnelson, Destruction of graphene by metal adatoms, Applied Physics Letters, 95 (2009) 023109. [29] E.J. Santos, D. Sánchez-Portal, A. Ayuela, Magnetism of substitutional Co impurities in graphene: Realization of single π vacancies, Physical Review B, 81 (2010) 125433. [30] V.V. Nelayev, A.I. Mironchik, Magnetism of graphene with vacancy clusters, Materials, Physics and Mechanic, 9 (2010) 26-34. [31] D. Li, C. Wang, Y. Niu, H. Zhao, C. Liang, Structural and electronic properties of MnO 3 (4) superhalogen clusters embedded in graphene, Chemical Physics Letters, 601 (2014) 16-20.

[32] A.H. Reshak, D. Stys, S. Auluck, I. Kityk, Dispersion of linear and nonlinear optical susceptibilities and the hyperpolarizability of 3-methyl-4-phenyl-5-(2-pyridyl)-1, 2, 4-triazole, Physical Chemistry Chemical Physics, 13 (2011) 2945-2952. [33] G. Davydyuk, O.Y. Khyzhun, A. Reshak, H. Kamarudin, G. Myronchuk, S. Danylchuk, A. Fedorchuk, L. Piskach, M.Y. Mozolyuk, O. Parasyuk, Photoelectrical properties and the electronic structure of Tl 1− x In 1− x Sn x Se 2 (x= 0, 0.1, 0.2, 0.25) single crystalline alloys, Physical Chemistry Chemical Physics, 15 (2013) 6965-6972. [34] A. Reshak, Y. Kogut, A. Fedorchuk, O. Zamuruyeva, G. Myronchuk, O. Parasyuk, H. Kamarudin, S. Auluck, K. Plucinski, J. Bila, Linear, non-linear optical susceptibilities and the hyperpolarizability of the mixed crystals Ag 0.5 Pb 1.75 Ge (S 1− x Se x) 4: experiment and theory, Physical Chemistry Chemical Physics, 15 (2013) 18979-18986. [35] A. Reshak, Ab initio study of TaON, an active photocatalyst under visible light irradiation, Physical Chemistry Chemical Physics, 16 (2014) 10558-10565. [36] A.H. Reshak, Fe 2 MnSi x Ge 1− x: influence thermoelectric properties of varying the germanium content, RSC Advances, 4 (2014) 39565-39571. [37] A.H. Reshak, Thermoelectric properties for AA-and AB-stacking of a carbon nitride polymorph (C 3 N 4), RSC Advances, 4 (2014) 63137-63142. [38] P.E. Blöchl, Projector augmented-wave method, Physical Review B, 50 (1994) 17953. [39] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Physical review letters, 77 (1996) 3865. [40] G. Kresse, D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Physical Review B, 59 (1999) 1758. [41] W. Tang, E. Sanville, G. Henkelman, A grid-based Bader analysis algorithm without lattice bias, Journal of Physics: Condensed Matter, 21 (2009) 084204. [42] G. Henkelman, A. Arnaldsson, H. Jónsson, A fast and robust algorithm for Bader decomposition of charge density, Computational Materials Science, 36 (2006) 354-360. [43] J. Meng, D. Li, Y. Niu, H. Zhao, C. Liang, Z. He, Structural, electronic, and magnetic properties of 3D metal trioxide and tetraoxide superhalogen cluster-doped monolayer BN, Physics Letters A, 380 (2016) 2300-2306.

[44] D. Li, Y. Niu, H. Zhao, C. Liang, Z. He, Electronic and magnetic properties of 3d-metal trioxides superhalogen cluster-doped monolayer MoS 2: A first-principles study, Physics Letters A, 378 (2014) 1651-1656. [45] M. Rafique, Y. Shuai, H.-P. Tan, H. Muhammad, Structural, electronic and magnetic properties of 3d metal trioxide clusters-doped monolayer graphene: A first-principles study, Applied Surface Science. [46] Y. Chen, H. Wang, H. Wang, J.-x. Zhao, Q.-h. Cai, X.-G. Wang, Y.-h. Ding, Divacancyassisted transition metal adsorption on the BN graphene and its interaction with hydrogen molecules: a theoretical study, Applied Surface Science, 273 (2013) 293-301. [47] M. Oubal, S. Picaud, M.T. Rayez, J.C. Rayez, Adsorption of atmospheric oxidants at divacancy sites of graphene: A DFT study, Computational and Theoretical Chemistry, 1016 (2013) 22-27. [48] X.-D. Tan, X.-P. Liao, L. Sun, The electronic and magnetic properties of corrugated zigzag graphene nanoribbons with divacancy defects, Physica E: Low-dimensional Systems and Nanostructures, 85 (2017) 302-307. [49] K. Sato, L. Bergqvist, J. Kudrnovský, P.H. Dederichs, O. Eriksson, I. Turek, B. Sanyal, G. Bouzerar, H. Katayama-Yoshida, V. Dinh, First-principles theory of dilute magnetic semiconductors, Reviews of modern physics, 82 (2010) 1633. [50] E.J. Santos, A. Ayuela, D. Sánchez-Portal, First-principles study of substitutional metal impurities in graphene: structural, electronic and magnetic properties, New Journal of Physics, 12 (2010) 053012. [51] T. Alonso-Lanza, A. Ayuela, F. Aguilera-Granja, Substitutional 4d and 5d Impurities in Graphene, arXiv preprint arXiv:1606.00165, (2016). [52] A.W. Robertson, B. Montanari, K. He, J. Kim, C.S. Allen, Y.A. Wu, J. Olivier, J. Neethling, N. Harrison, A.I. Kirkland, Dynamics of single Fe atoms in graphene vacancies, Nano letters, 13 (2013) 1468-1475. [53] Z. He, K. He, A.W. Robertson, A.I. Kirkland, D. Kim, J. Ihm, E. Yoon, G.-D. Lee, J.H. Warner, Atomic structure and dynamics of metal dopant pairs in graphene, Nano letters, 14 (2014) 3766-3772.

[54] E.J. Santos, A. Ayuela, S. Fagan, J. Mendes Filho, D. Azevedo, A. Souza Filho, D. Sánchez-Portal, Switching on magnetism in Ni-doped graphene: density functional calculations, Physical Review B, 78 (2008) 195420. [55] J. Kang, H.-X. Deng, S.-S. Li, J. Li, First-principles study of magnetic properties in Modoped graphene, Journal of Physics: Condensed Matter, 23 (2011) 346001. [56] M. Wu, C. Cao, J. Jiang, Electronic structure of substitutionally Mn-doped graphene, New Journal of Physics, 12 (2010) 063020.

(a)

(c)

(b)

(d)

h Fig.1- (a) Top view of atomic structures of TMO4 cluster-doped (b) side view of TMO4 cluster incorporated into SV monolayer graphene. (c) top view of atomic structures of TMO4 cluster-doped and (d) side view of TMO4 clusterembedded into DV monolayer graphene. The small brown and red balls represent C and O atoms, and big light blue ball represents dopant TM atom.

1.39

CoO4

CrO4

1.38

2.28

FeO4

1.40

2.16

2.06

2.08

2.17

2.28 1.38

1.39

NiO4

1.39 2.21

TiO4

1.40

1.40

VO4

1.40 2.28

2.28

2.29

2.20

2.30

2.78 1.39

2.27 1.39

2.29

2.21

2.24 2.24

2.24 2.61

2.06

MnO4

1.40

1.43

1.40

Fig. 2- Top views of atomic structures of TMO4 clusters incorporated into SV monolayer graphene showing bond lengths of TM–O and C–O atoms. Bond length is shown in Å

CoO4 1.39 1.93 1.94 1.39

1.39 1.93

CrO4 1.41

1.94 1.39

1.41

1.94

1.94

1.95

1.95

1.41

FeO4 1.39 1.94

1.39 1.94

1.40 1.92

1.39 1.92

1.95

1.95 1.39

1.93 1.39

1.93 1.40

1.39

1.41

MnO4

NiO4

TiO4

VO4

1.39 1.94

1.39 1.93

1.41 1.96

1.41 1.96

1.40 1.95

1.40 1.95

1.93 1.39

1.94 1.39

1.97 1.41

1.97 1.41

1.96 1.40

1.96 1.40

Fig. 3- Top views of atomic structures of TMO4 cluster incorporated into DV monolayer graphene showing bond lengths of TM–O and C–O atoms. Bond length is shown in Å

CrO4

(a)

(b) CrO4

MnO4

FeO4

(d)

(c) FeO4

VO4

MnO4

VO4

Fig. 4- Top and side views of spin density for TMO4 clusters incorporated into a 4 × 3 SV monolayer graphene supercell. Yellow and cyan isosurfaces represent positive and negative spin densities, respectively. The isosurfaces value is 0.0003 e/Å3

CoO4

(a)

CrO4

(b)

(c)

NiO4

(e)

FeO4

(d)

TiO4

(f)

MnO4

VO4

(g)

Fig. 5- Top and side views of spin density for TMO4 clusters incorporated into a 4 × 3 DV monolayer graphene supercell. Yellow and cyan isosurfaces represent positive and negative spin densities, respectively. The isosurfaces value is 0.0003 e/Å3

CoO4

(a)

CrO4

(b)

(c) NiO4

(e)

FeO4

(d) VO4

TiO4

(f)

MnO4

(g)

Fig.6- Top views of charge density for TMO4 clusters-doped SV monolayer graphene (4 × 3) supercell structure. Yellow and cyan isosurfaces (0.003 e/ Å3) correspond to electron-rich and electron-depleted zones, respectively.

CoO4

(a)

CrO4

(b)

FeO4

(c) NiO4

(e)

MnO4

(d) VO4

TiO4

(f)

(g)

Fig.6- Top views of charge density for TMO4 clusters-doped SV monolayer graphene (4 × 3) supercell structure. Yellow and cyan isosurfaces (0.003 e/ Å3) correspond to electron-rich and electron-depleted zones, respectively

CoO4

(a)

(b)

(c) NiO4

(e)

FeO4

CrO4

(d) VO4

TiO4

(f)

MnO4

(g)

Fig.7- Top views of charge density for TMO4 clusters-doped DV monolayer graphene (4 × 3) supercell structure. Yellow and cyan isosurfaces (0.003 e/ Å3) correspond to electron-rich and electron-depleted zones, respectively

Fig.8- Spin polarized band structure diagrams for all TMO4 clusters-doped SV monolayer graphene (4 × 3) supercell structures. The black and red lines represent the spin up and spin down bands, respectively.

Fig. 9- Total and projected densities of states (DOSs) of TMO4 clusters incorporated into SV monolayer graphene. Fermi level is denoted by the vertical solid grey line at 0 eV energy level.

Fig. 10- Spin polarized band structure diagrams for all TMO 4 clusters-doped DV monolayer graphene (4 × 3) supercell structures. The black and red lines represent the spin up and spin down bands, respectively.

Fig. 11- Total and projected densities of states (DOSs) of TMO4 clusters incorporated into DV monolayer graphene. Fermi level is denoted by the vertical solid grey line at 0 eV energy level.

Table 1 Total magnetization of the supercell (μtot, in μB); magnetic moment of individual TM atoms (μTM, in μB); average equatorial bond distances of TM-O (dTM–O, in Å), C-O (dC-O, in Å) and elevation (h, in Å) of TM atom above the graphene surface for all TMO4 clusters embedded into SV and DV monolayer graphene. Impurity

μtot, in μB

μTM, in μB

dTM-O Å

dC-O Å



CoO4 (SV)

0.65

1.31

2.06

1.39

1.26

CoO4 (DV)

1.74

2.26

1.93

1.39

--

CrO4 (SV)

2.15

2.88

2.17

1.38

1.81

CrO4 (DV)

3.27

3.21

1.94

1.41

--

FeO4 (SV)

3.27

3.28

2.25

1.40

1.85

FeO4 (DV)

3.09

2.76

1.94

1.39

--

MnO4 (SV)

3.51

3.68

2.24

1.40

1.83

MnO4 (DV)

1.99

1.984

1.92

1.40

--

NiO4 (SV)

0.04

0.12

2.21

1.39

1.72

NiO4 (DV)

1.03

0.925

1.93

1.39

--

TiO4 (SV)

0.35

0.16

2.29

1.41

1.88

TiO4 (DV)

2.47

1.788

1.96

1.41

--

VO4 (SV)

2.75

2.39

2.28

1.40

1.86

VO4 (DV)

3.48

2.965

1.95

1.40

--

Table 2 Formation energies (Ef in eV) for all TMO4 clusters embedded into SV and DV monolayer graphene structures. Structure

CoO4

CrO4

FeO4

MnO4

NiO4

TiO4

VO4

SV graphene

-1.12

-3.05

-2.32

-5.07

-2.13

-4.26

-3.69

DV graphene

-0.46

-1.05

-1.68

-2.46

-1.55

-2.29

-2.12