Ab initio calculations for structural, electronic and magnetic behaviors of nitrogenized monolayer graphene decorated with 5d transition metal atoms

Physica E 93 (2017) 26–38

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Physica E journal homepage: www.elsevier.com/locate/physe

Ab initio calculations for structural, electronic and magnetic behaviors of nitrogenized monolayer graphene decorated with 5d transition metal atoms

MARK

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Muhammad Rafiquea,b, Yong Shuaia, , Meng Xua, Guohua Zhanga, Yanming Guoa a b

School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, PR China Mehran University of Engineering and Technology, S.Z.A.B, Campus Khairpur Mir's, Sindh, Pakistan

A R T I C L E I N F O

A BS T RAC T

Keywords: Dilute magnetic semiconductor Magnetic moments Transition metal Graphene

Graphene-based magnetic materials have revealed great potential for developing high-performance electronic units at sub-nanometer such as spintronic data storage devices. However, a significant ferromagnetism behavior and ample band gap in the electronic structure of graphene is required before it can be used for actual engineering applications. Based on first-principles calculations, here we demonstrate the structural, electronic and magnetic behaviors of 5d transition metal (TM) atom-substituted nitrogenized monolayer graphene. We find that, during TMN(3)4 cluster-substitution, tight bonding occurs between impurity atoms and graphene with significant binding energies. Charge transfer occurs from graphene layer to the TMN(3)4 clusters. Interestingly, PtN3, TaN4 and ReN4 cluster-doped graphene structures exhibit dilute magnetic semiconductor behavior with 1.00 µB, 1.04 µB and 1.05 µB magnetic moments, respectively. While, OsN4 and PtN4 cluster-doped structures display nonmagnetic direct band gap semiconductor behavior. Remaining, TMN(3)4 cluster-doped graphene complexes exhibit half metal properties. Detailed analysis of density of states (DOS) plots indicate that d orbitals of TM atoms should be responsible for arising magnetic moments in graphene. Given results pave a new route for potential applications of dilute magnetic semiconductors and half-metals in spintronic devices by employing TMN(3)4 cluster-doped graphene complexes.

1. Introduction Two dimensional (2D) materials, graphene, hexagonal boron nitride (h-BN) and silicene are currently under intense experimental and theoretical research due to their unique and outstanding electronic device applications [1–3]. Graphene has demonstrated various exquisite phenomena instigated from the characteristic of linear dispersion of energy and chiral behavior of its valence and conduction bands around the Fermi energy level [4]. Given these novel electronic properties of graphene, graphene-based magnetic devices are expected to be more stable, adaptable and economical than contemporary transition-metal (TM) based magnetic devices. Among the various graphene properties, ferromagnetism in graphene has been widely studied due to its rising potential applications for nanoelectronics and spintronic devices [5–7]. The metal ad-atom on graphene, h-BN and silicene has been extensively studied for introducing magnetic properties using first-principles calculations [8–10]. At present, there are two approaches being utilized widely for substituting TM atoms into graphene. First is to adsorb TM atoms on graphene sheets. Studies reveal that, adsorbate TM atoms strongly bond to graphene [11] and

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Corresponding author. E-mail address: [email protected] (Y. Shuai).

http://dx.doi.org/10.1016/j.physe.2017.05.015 Received 17 February 2017; Received in revised form 21 May 2017; Accepted 23 May 2017 Available online 25 May 2017 1386-9477/ © 2017 Elsevier B.V. All rights reserved.

the obtained migration barriers are low enough [12]. Another approach is to incorporate TM atoms into graphene containing single vacancy (SV) or divacancy (DV) of C atoms in graphene layer. Structural, electronic and magnetic properties of TM atoms embedded into SV and DV in graphene have been extensively investigated [12–15]. These studies reveal that, obtained binding energies in these cases are far better than the binding energies of adsorbed TM atoms on graphene sheet. In addition, TM atoms embedded graphene complex structures are more suitable that adsorbate TM atom graphene complex structures for utilization in graphene-based devices working at room temperatures and above. Ferromagnetism in graphene can be obtained by substituting TM atoms into SV and DV in graphene, due to strong interaction between the impurity atom and defective graphene layer [5–10,15,16]. Recently, a third approach has been largely utilized by various researchers to introduce ferromagnetism in 2D materials and getting lower formation energies i.e. by incorporating various halogen and superhalogen clusters in graphene vacancies [17–19]. Superhalogen clusters are highly electronegative and their electron affinities are far better than halogen atoms [20–22]. Studies carried out on superhalogen cluster-doped graphene reveal that larger magnetic

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Fig. 1. (a) Top view of atomic structures of TMN3 cluster-doped (b) side view of TMN3 cluster-doped monolayer graphene. (c) top view of TMN4 cluster-doped and (d) side view of TMN4 cluster-doped monolayer graphene. The small brown and light green balls represent C and N atoms, and big ball represents dopant TM atom. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

[33] were utilized to describe core-electron and Perdew–Burke– Ernzerhof (PBE) functional [34] was adopted for exchange-correlation energy. The kinetic energy cutoff of 500 eV was used for wave function expansion. For structural optimization, the convergence of Hellmann– Feynman forces less than 0.01 eV/Å per atom and the total change in energy less than 10−6 eV were achieved. Since the convergence with respect to the number of K-points was very critical to obtain accurate results, we utilized a 9 × 9 × 1 Γ-centered k-point mesh for Brillouin zone (BZ) sampling. Our structure model consists of a 4 × 3 monolayer graphene supercell (20 carbon atoms with 4 impurity atoms in case of TMN3 cluster embedded into graphene) and (18 carbon atoms with 5 impurity atoms in case of TMN4 cluster embedded into graphene) with a vacuum layer of 15 Å in Z-direction to eliminate the interaction between adjacent layers. Gaussian smearing method was utilized to deal with the partial occupancies. Bader analysis was used to calculate the charge transfer [35,36].

moments and lower formation energies can be easily obtained. We also performed first-principles calculations on TMO3 cluster-doped monolayer graphene [22] in order to introduce ferromagnetism in graphene. Results of our study reveal that TMO3 cluster-doping is thermodynamically favorable in graphene and the band gap of graphene is sensitively dependent on impurity clusters. Keeping that in mind, we try to introduce 5d TMN(3)4 clusters into graphene to determine the ferromagnetism behavior in graphene. As we know that introducing N atoms in graphene can alter the band structure of graphene [23,24] thereby adding 5d TM atom into nitrogenized graphene can obtain our purpose of introducing magnetism as well as a well-defined band gap in graphene. In this study, we incorporated 5d transition metal (TM) nitrides TMN3 and TMN4 clusters into monolayer graphene. In our calculations, all TM atoms are placed at SV and DV site containing N atoms around the SV and DV, hence we can represent these dopant impurities as TM@NSV and TM@NDV. However, this representation will not clarify the number of N atoms doped in graphene layer. For that particular reason, we define TM@NSV as TMN3 cluster and TM@NDV as TMN4 cluster. Since we are substituting different 5d TM atoms (TM=Hf, Ta, W, Re, Os, Ir and Pt) in SV and DV graphene containing 3 N and 4 N atoms respectively, So these structures are simply defined as TMN3 and TMN4 clusters-doped monolayer graphene complexes. The structural, electronic and magnetic behaviors of 5d TMN3 and TMN4 substituted monolayer graphene were investigated by firstprinciples calculations based on density-functional theory method. Our work is organized as follows. After a brief description of the computational method, we describe the geometry structures and magnetic properties of all the 5d TMN(3)4 cluster substituted graphene complexes. We also analyze the magnetic coupling behavior and charge transfer for the TMN(3)4 cluster-doped structures. Then we explain the effect of impurity cluster-doping on the electronic properties of graphene. Finally, we provide the summary with some general conclusions. To the best of our knowledge, the structural, electronic and magnetic properties of such a system has not been extensively investigated. These new results can facilitate to tune the band gap and magnetic properties of graphene for engineering applications, in particular, in nanoelectronics and spintronics that are distinct from those of pristine graphene and pristine hexagonal boron nitride.

3. Results and discussions 3.1. Structural and magnetic properties Different 5d transition metal (TM) trinitride and tetranitride clusters i.e. (HfN(3)4, TaN(3)4, WN(3)4, ReN(3)4, OsN(3)4, IrN(3)4 and PtN(3)4) were embedded into monolayer graphene with two different approaches. In first case of 5d TMN3 cluster substitution, three C atoms were substituted by three N atoms and one C atom was substituted by one 5d TM atom as shown in Figs. 1(a) and 1(b). In second case of 5d TMN4 cluster substitution, two C atoms were substituted by one 5d TM atom and four C atoms were substituted by four N atoms around the 5d TM atom as presented in Figs. 1(c) and 1(d), respectively. The comparison was made between these two models throughout our work. After geometry optimization of all TMN3 and TMN4 cluster-doped graphene complexes, it is found that in case of TMN3 cluster-doping, TM atom is elevated above the 2D layer of graphene planar structure and a very minute drift occurs in the N atoms. In case of TMN4 clusterdoped graphene complexes, TM atom maintains its position in the planar structure of graphene without getting elevated above the graphene layer due to strong covalent bonding between neighboring four N atoms and the larger vacancy hole present in the graphene layer also makes TM atom to stay in the planar structure. Typical geometries after relaxation of TMN3 cluster substituted graphene complexes are shown in Fig. 2. The bond lengths of TM-N atoms and bond lengths of C-N atoms of relaxed TMN3 cluster-doped graphene complexes are also shown in Fig. 2. The structural diagrams of 5d TMN3 cluster-doped graphene complexes given in Fig. 2. clearly indicate that the 5d TM impurity atoms with large atomic radii produced the local deformation in the graphene plane and obtained a significant elevation (h) above the 2D

2. Computational method The present first-principles DFT calculations were performed to calculate the structural, electronic and magnetic properties of 5d TMN(3)4 cluster-doped monolayer graphene using Vienna Ab-initio simulation package (VASP) [25]. The DFT method is known as the most accurate method for the computation of the electronic structure of solids [24,26–32]. The projector augmented wave (PAW) potentials 27

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Fig. 2. Top views of atomic structures of 5d TMN3 clusters incorporated into monolayer graphene showing bond lengths of TM–N and C–N atoms. Bond length is shown in Å.

tional symmetry. The structural properties calculated for TMN4 cluster-doped DV graphene structures are consistent with the previous studies carried out on 2D materials [12,17,37]. Table 1 presents the average equatorial bond lengths between TM-N atoms, bond lengths between C-N atoms, the elevation "h" of TM atoms above the monolayer graphene surface for TMN3 cluster-doped graphene structures, the total magnetization μtot of the supercell and the magnetic moment of individual TM atoms μTM for both approaches of TMN(3)4 clusters incorporated into monolayer graphene. Our result obtained for the magnetic moment of WN4 cluster-doped DV graphene are consistent with the results of Ref. [38], though slight difference in results can be credited to difference between the size of supercell and utilization of k-point mesh. The magnetic moments obtained for TMN(3) 4 cluster-doped graphene supercell as given in Table 1 indicate that TMN3 cluster-doped graphene structures produce larger ferromagnetism behavior in comparison to TMN4 cluster-doped graphene complexes. The increase in ferromagnetic behavior of TMN3 clusters-doped graphene complexes can be attributed to the weaker interaction of impurity atoms/molecules with the ligand bonds and larger number of unfilled d orbitals resulting in higher spin state of the complex. However, in case of TMN4 cluster-doped graphene structures, more number of d orbitals are hybridized to the p orbitals of N atoms, therefore the number of unfilled d orbitals is reduced in comparison to TMN3 clusters, resulting in lower spin magnetic moments. These results are consistent with the previous studies available [12,17–19,38]. Total magnetic moments μtot and magnetic moments of 5d TM atoms μTM presented in Table 1 predict that significant magnetic moments per supercell can be achieved for most of the TMN3 clusterdoped graphene complexes, except HfN3 and OsN3 doped graphene structures. Here we examine the magnetic coupling behavior for the 5d TMN3 cluster-doped graphene structures. Fig. 4(a)-(e) show spin densities (ρ↑ - ρ↓) of TMN3 (TaN3, WN3, ReN3, IrN3 and PtN3) doped graphene complexes. HfN3 and OsN3 spin densities were omitted due to their zero magnetic moments. From the spin density diagrams given in Fig. 4(a)-(e) we can observe that all the TMN3 doped graphene structures presented similar magnetic coupling behavior between TM

plane of honeycomb lattice of graphene. It is found that the elevation in TM atoms also caused minor displacement in the N atoms neighboring the TM impurity atom, resulting change in the bond distances of C-N atoms. However, the positions of C atoms around the TMN3 cluster were unchanged which indicates that the planar structure of monolayer graphene was intact after TMN3 cluster substitution into graphene. We also found that, after 5d TMN3 cluster substitution into graphene, the C-N bond distances were almost equal at 1.37–1.38 Å and the amount of the change in C-N bond lengths were less than 0.01 Å. In addition to that, the Jahn-teller distortion lowered the D3h local symmetry of monolayer graphene to C3v or Ci symmetry of TMN3 cluster doped graphene complexes. The structural parameters calculated for 5d TMN3 clusters incorporated into graphene are consistent with the previous reports available [17–19,22]. Typical geometries after relaxation of TMN4 cluster substituted graphene complexes are shown in Fig. 3. The bond distances of TM-N atoms and bond distances of C-N atoms of relaxed TMN4 cluster-doped graphene complexes are also shown in Fig. 3. In this approach we incorporated one TM atom at the divacancy (DV) site and four C atoms were substituted by four N atoms around the DV site of graphene. It is observed that in all TMN4 cluster-doped DV graphene complexes as presented in Fig. 3, respectively, the TM atoms embedded at DV site preserve their spots in the planar structure of 2D graphene without getting elevated above the plane which can be attributed to the strong covalent bonding of four N atoms to the 5d TM atom present around the DV site of graphene. Although a minute deformation occurs in the C and N atoms around the DV site which results in the change in bond distances of C-N atoms as the bond lengths are described in Fig. 3, respectively. Similar to TMN3 clusterdoped graphene complexes, the positions of C atoms surrounding the TMN4 clusters embedded into DV graphene is unaffected which indicates that in this approach also the 2D planar structure of graphene layer is preserved. In this case, bond lengths of C-N atoms were found to be in range of equal at 1.37–1.39 Å and the corresponding change in C-N bond lengths were less than 0.02 Å. It is also found that, TMN4 clusters-doped DV graphene structures contain similar fourfold rota28

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Fig. 3. Top views of atomic structures of 5d TMN4 clusters incorporated into monolayer graphene showing bond lengths of TM–N and C–N atoms. Bond length is shown in Å.

behavior between TM atoms and graphene layer. Significant magnetic coupling behavior was observed between TM atoms and neighboring four N atoms. However Hf, Ta, W, Re and Ir display large positive spin density attributed to their unfilled d orbital configuration. In case of HfN4, TaN4, WN4 and ReN4 cluster-doped graphene complexes, the direction of polarization between TM atoms and nearest N atoms is parallel, whereas the direction of polarization is antiparallel between TM atoms and nearest N atoms in case of IrN3 doped graphene structure. Another factor to note here is that the spin density is localized at the impurity atoms in HfN4 and TaN4 cluster-doped graphene complexes as shown in Figs. 5(a) and 5(b), respectively. However in remaining three cases the spin density is distributed along the graphene layer as shown in Figs. 5(c), 5(d) and 5(e), respectively. Our obtained results are consistent with the previous reports available [12,17,37,39,40]. In order to further understand the behavior of TMN(3)4 clusters embedded into monolayer graphene, we investigated the charge transfer using Bader analysis [35,36] for TMN(3)4 cluster-doped graphene complexes. The charge density difference is defined as ΔρTMN(3)4 = ρTMN(3)4-graphene - ρgraphene - ρTMN(3)4. Where ρTMN(3)4graphene, ρgraphene and ρTMN(3)4 represent the charge density of TMN(3) 4 clusters-doped graphene, charge density of graphene with vacancy and charge density of TMN(3)4 clusters, respectively. Firstly, we analyze the charge density difference results for TMN3 cluster doped graphene. Fig. 6(a)-(g) describe the electron charge densities of TMN3 clusters embedded into graphene. The electron rich and electron depleted zones are presented by yellow and cyan isosurfaces, respectively. The isosurfaces value is 0.003 e/Å3. From the given charge density difference results, we can predict that all the TMN3 doped graphene complexes i.e. (HfN3, TaN3, WN3, ReN3, OsN3, IrN3 and PtN3) show similar behavior of charge density difference. The electron charge density on impurity N and 5d TM atoms is increased as depicted by yellow color whereas on the adjacent C atoms which are directly bonded to N atoms is decreased as depicted by cyan color, respectively. This behavior suggests that charge transfer occurs from monolayer graphene to the TMN3 clusters. Another way to justify this

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-N (dTM–N, in Å), C-N (dC-N, in Å) and elevation (h, in Å) of TM atom above the graphene surface for all TMN(3)4 clusters embedded into monolayer graphene. Impurity

μtot, in μB

μTM, in μB

dTM-N Å

dC-N Å

hÅ

HfN3 HfN4 TaN3 TaN4 WN3 WN4 ReN3 ReN4 OsN3 OsN4 IrN3 IrN4 PtN3 PtN4

0.00 0.74 2.42 1.04 2.78 2.37 1.56 1.05 0.00 0.00 1.30 0.75 1.00 0.00

0.00 0.46 1.58 0.85 2.17 2.10 0.94 1.08 0.00 0.00 1.01 0.62 0.57 0.00

1.98 2.1 1.97 2.0 1.95 1.98 1.93 1.97 1.93 1.95 1.97 1.97 1.93 1.97

1.38 1.39 1.37 1.38 1.38 1.39 1.37 1.37 1.37 1.38 1.36 1.37 1.38 1.37

1.56 – 1.61 – 1.65 – 1.63 – 1.52 – 1.68 – 1.66 –

atoms and graphene layer. Significant magnetic coupling behavior was observed between TM atoms and neighboring three C and three N atoms. However Ta, W, Re, Ir and Pt atoms hold large positive spin density attributed to their unfilled d orbital configuration. In case of TaN3 and WN3 cluster-doped graphene complexes, the direction of polarization between TM atoms and nearest N atoms is antiparallel, whereas the direction of polarization is parallel between TM atoms and nearest N atoms in case of ReN3, IrN3 and PtN3 doped graphene structures. These results are consistent with the previous studies [12,17–19,38]. Fig. 5(a)-(e) present the spin densities (ρ↑ - ρ↓) of TMN4 (HfN4, TaN4, WN4, ReN4 and IrN4) doped graphene complexes. OsN4 and PtN4 spin densities were omitted due to their zero magnetic moments. Spin density diagrams presented in Fig. 5(a)-(e) describe that all the TMN4 doped graphene structures show similar magnetic coupling 29

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Fig. 4. Top and side views of spin density for TMN3 clusters embedded into a 4 × 3 monolayer graphene supercell. Yellow and cyan isosurfaces represent positive and negative spin densities, respectively. The isosurfaces value is 0.0003 e/Å3. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

structure of graphene layer rather than getting elevated above the 2D plan. This increase in charge transfer further supports the prediction of stronger electronegativity of TMN4 clusters, thereby having lower formation energies and stable TMN4 cluster-doped graphene structures. IrN4 and PtN4 doped graphene complexes exhibit different charge transfer behavior in comparison to other TMN4 cluster-doped graphene complexes. In case of IrN4 and PtN4 doping, the graphene layer is covered by larger yellow isosurface, which represents reduction in charge transfer. This is due to the covalent bonding of Ir and Pt with N atoms, and the formation of IrN4 and PtN4 nitrides occurs. Thereby, showing the different charge transfer behavior in comparison to other TMN4 clusters [42]. The electronegativity of these two clusters is lower than the other TMN4 clusters. These results are consistent with the previous reports available [12,17–21,43].

charge transfer is the difference of electronegativity between C atoms, impurity N and 5d TM atoms. As we know that N atom is more electronegative than C atom, hence N atoms has higher tendency to attract electrons thereby defining the behavior of charge transfer in TMN3 cluster-doped graphene. These results suggest that the TMN3 clusters-doped graphene complexes have stronger electronegativity, which can result in lower formation energies and stable TMN3 clusterdoped graphene complexes. These results are consistent with the previous studies [17,18,20,21,38,41]. Using similar technique described earlier, here we investigated the charge density difference of TMN4 clusters-doped monolayer graphene as presented in Fig. 7(a)-(g), respectively. Charge density difference diagrams given in Fig. 7(a)-(g), suggest that, all the TMN4 i.e. (HfN4, TaN4, WN4, ReN4, OsN4, IrN4 and PtN4) cluster-doped graphene complexes present similar pattern of charge density difference as that of TMN3 cluster-doped graphene complexes. The electron charge density around the substituted N atoms and 5d TM atoms is increased whereas the adjacent C atoms has decreased charge density as revealed 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. However, in TMN4 cluster-doped graphene complexes, the N and 5d TM atoms are covered by larger yellow isosurfaces, which suggests that these atoms accumulated more charge carriers in comparison to the N and TM atoms of TMN3 cluster-doped graphene complexes. This increase in the charge transfer on N and 5d TM atoms can be attributed to the presence of four N atoms and one TM atom directly in the planar

3.2. Electronic properties In this section, we try to investigate the band structure and density of states plots of TMN(3)4 cluster-doped graphene structures. We utilized 30 K-points grid for band structure calculation along the 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) plots are generated for all TMN(3)4 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. Band structure diagrams and DOS plots were obtained in spin polarized calculation mode. 30

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Fig. 5. Top and side views of spin density for TMN4 clusters embedded into a 4 × 3 monolayer graphene supercell. Yellow and cyan isosurfaces represent positive and negative spin densities, respectively. The isosurfaces value is 0.0003 e/Å3. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

these clusters can be regarded as donor impurities. Since the impurity clusters have donor nature which causes the Fermi level (EF) to shift up into conduction band and the π* band of graphene creeps into the valence band. However, even after the shift in the Fermi level (EF) and the π* band, a band gap appears at the high symmetric K-point as shown in Fig. 8(a)-(g), respectively. The finite band gap appearing at high symmetric K-point is attributed to the distortion in π electron net of pure graphene due to addition of foreign electrons which trap some of massless π electrons thereby adding some energy gap at the high symmetric K-point. Given band structure diagrams indicate that, the HfN3, TaN3, WN3, ReN3, OsN3 and IrN3-doped graphene structures display half metallic properties as shown in Fig. 8(a)-(f), respectively. Interestingly, PtN3-doped structure exhibits dilute magnetic semiconductor (DMS) behavior, having band gap of 0.3 eV during spin up (black lines) channel and a band gap of 0.08 eV during spin down (red lines) channel as shown in Fig. 8(g). An important factor to note here that, the spin up and spin down state bands are polarized for the TMN3 clusterdoped graphene structures having magnetic moments, which indicates the existence of ferromagnetism behavior (we will further elaborate the origins of magnetism in DOS plots). Since, we described earlier that, both HfN3 and OsN3 doped graphene structure has 0.0 µB magnetic moments, therefore their band states are un-polarized. The emergence of finite band gap in the band structure diagrams of TMN3 cluster-doped graphene complexes can also be attributed to the local distortion of the graphene induced by impurity clusters which break the symmetry of the sub lattices of graphene. These results obtained for the band structure diagrams of TMN3 cluster-doped graphene structures are consistent with the previous studies [8,16,50,51].

3.2.1. Band structure and PDOS plots for TMN3 cluster-doped graphene complexes Spin polarized band structure diagrams for 5d TMN3 (HfN3, TaN3, WN3, ReN3, OsN3, IrN3 and PtN3) cluster-doped graphene complexes are shown in Fig. 8(a)-(g), respectively. In order to determine the effect of TMN3 cluster-doping on the band structure of graphene, we added the band structure diagram of pure graphene for the sake of comparison and is presented in Fig. 8 named as graphene. Pure graphene valence band (π) and conduction band (π*) are shown at k-point. Valence and conduction bands of pure graphene are straddling with each other at Dirac point, making graphene a zero band gap semiconductor. Our calculated band structure of pure graphene is in good agreement with the previous studies in terms of gapless behavior and linear dispersion of energy at the Fermi level [1,44–47]. In addition, if we compare our calculated band structure diagram of pure graphene to the band structure diagram of pure graphene presented in recent studies [8,48,49], it can be seen that our calculated band structure diagram is in consensus with these reports in case of π bands of graphene touching each other at the Fermi level (EF), thereby making graphene zero bandgap semiconductor. However, our calculated band structure shows a little indifference to these reports in case of α (Flat) bands. This difference can be attributed to the size of supercell and the number of k-point utilized in our calculations. In summarized way, we can define that our calculated band structure diagram of pure graphene is consistent with previous studies, regarding the obtained behavior of graphene π bands at the Fermi level (EF). Fig. 8(a)-(g) represents the spin polarized band structure diagrams for TMN3 cluster-doped graphene. As described earlier, TMN3 clusters have access of charge, hence 31

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Fig. 6. Top views of charge density for TMN3 clusters-doped monolayer graphene (4 × 3) supercell structures. Yellow and cyan isosurfaces (0.003 e/Å3) correspond to electron-rich and electron-depleted zones, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

PDOS on the 5d TM atoms, adjacent C atom p orbital and adjacent N atom p orbitals for all TMN3 cluster-doped monolayer graphene complexes are presented in Fig. 9(a)-(g), respectively. The Fermi energy level (EF) is indicated by a vertical thin grey line appearing at the 0 eV energy

In this section, we try to analyze the spin polarized total density of states (TDOS) and projected density of states (PDOS) plots for all the TMN3 clusters-doped graphene structures in order to comprehend different effects of TMN3 cluster-doping into graphene. TDOS and

Fig. 7. Top views of charge density for TMN4 clusters-doped monolayer graphene (4 × 3) supercell structures. Yellow and cyan isosurfaces (0.003 e/ Å3) correspond to electron-rich and electron-depleted zones, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

32

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Fig. 8. Spin polarized band structure diagrams for all 5d TMN3 clusters-doped monolayer graphene (4 × 3) supercell structures. The black and red lines represent the spin up and spin down bands, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

From the given PDOS plots we can further suggest that the five different orbitals namely (dxy, dyz, dz2, dxz and dx2-y2) of 5d TM atoms give rise to magnetic moments of TMN3 clusters-doped graphene structures. For all TMN3 cluster-doped graphene, dz2, dx2-y2 and dxy orbitals of TM atoms almost did not hybridize with p orbitals of N atoms, but dxz and dyz orbitals of TM atoms interacted softly with p orbitals of N atoms as presented in Fig. 9(a)-(g). An important factor to note here is that the appearing of band gap in spin up states and spin down states is at different energy levels, which is due to the polarization of spin state bands, thereby introducing the concept of spintronics. These obtained results suggest that 2D magnetic semiconductors can be synthesized by doping TMN3 clusters into monolayer graphene.

level in the given PDOS plots. From the PDOS plots given in Fig. 9(a)-(g), we can clearly observe some impurity states appearing near the top of valence band and the bottom of conduction band. These impurity states also known as the surface states appear due to the occurrence of robust hybridization between d orbitals of TM atoms and p orbitals of N atoms. Different d orbitals of TM atoms and p orbitals N atoms are clearly shown by labeled color lines in the given PDOS plots. Since we know that TaN3, WN3, ReN3, IrN3 and PtN3 cluster doping induced magnetic moments of 2.42 µB, 2.78 µB, 1.56 µB, 1.30 µB and 1.00 µB, respectively, therefore their d orbitals have larger spin polarization as shown in PDOS plots for given structures. While, the other two HfN3 and OsN3 doped graphene complexes contain 0.00 µB magnetic moments, therefore their d orbitals are spin un-polarized as shown in their respective PDOS plots. 33

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Fig. 9. Total and projected densities of states (DOSs) of TMN3 clusters embedded into monolayer graphene. Fermi level is indicated by the vertical solid grey line at 0 eV energy level.

structures show half metal properties with 0.74 µB and 2.37 µB magnetic moments, respectively. Interestingly, TaN4 and ReN4 substituted graphene structures exhibit dilute magnetic semiconductor behavior with a band gap of approximately 0.2 eV and 0.4 eV appearing at high symmetric K-point, respectively. While OsN4 and PtN4 substituted graphene structures display nonmagnetic direct band gap semiconductor behavior having a band gap of approximately 0.3 eV and 0.7 eV, respectively. Since HfN4, TaN4, WN4, ReN4 and IrN4 contain sufficient magnetic moments, hence spin polarization is observed in their spin up state and spin down state band channels indicating the existence of ferromagnetism behavior. The emergence of finite band gap in the band structure diagrams of TMN4 cluster-doped graphene complexes can be attributed to the distortion in π electron net of pure graphene caused by addition of foreign electrons which trap

3.2.2. Band structure and PDOS plots for TMN4 cluster-doped graphene complexes Spin polarized band structure diagrams for all the TMN4 i.e. (HfN4, TaN4, WN4, ReN4, OsN4, IrN4 and PtN4) cluster-doped graphene complexes are presented in Fig. 10(a)-(g), respectively. Spin unpolarized band structure diagram of pure graphene is also given in order to determine the effects of TMN4 cluster-doping on graphene. Similar to TMN3 clusters, TMN4 clusters also contain access of charge and can be considered as donor impurity clusters. Consequently, the Fermi level (EF) shifts up into conduction band, the π* band of graphene creeps into the valence band and a band gap appears at high symmetric K-point as presented in Fig. 10(a)-(g), respectively. Given band structure diagrams of TMN4 cluster-doped graphene complexes reveal that, HfN4 and WN4 substituted graphene 34

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Fig. 10. Spin polarized band structure diagrams for all TMN4 clusters-doped monolayer graphene (4 × 3) supercell structures. The black and red lines represent the spin up and spin down bands, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

some of massless π electrons and the local distortion of the graphene induced by impurity clusters which break the symmetry of the sub lattices of graphene. Our obtained results of band structure diagrams of TMN4 cluster-doped graphene complexes are consistent with the previous studies [14,41,52–55]. Spin polarized TDOS and PDOS plots for all the TMN4 clusters incorporated into graphene structures are examined to comprehend the different effects of TMN4 cluster-doping into graphene. TDOS and PDOS on the TM atoms, adjacent C atom p orbital and neighboring N atom p orbitals for all the TMN4 cluster-doped DV monolayer graphene structures are presented in Fig. 11(a)-(g), respectively. Fermi energy level (EF) is denoted by vertical thin grey line in the PDOS plots visible

at the 0 eV energy level. Some impurity surface states are observed at the Fermi level induced by TMN4 clusters due to the robust hybridization between d orbitals of TM atoms and p orbitals of N atoms as presented in Fig. 11(a)-(g). As we know that, some of the TMN4 i.e. (HfN4, TaN4, WN4, ReN4 and IrN4) cluster-doped graphene complexes produced ferromagnetism coupling behavior with 0.74 µB, 1.04 µB, 2.37 µB, 1.05 µB and 0.75 µB magnetic moments respectively. Therefore, d orbitals of respective 5d TM atoms contain spin polarization as described in the PDOS of plots of given structures. Similar to TMN3 cluster-doped graphene complexes, same five different orbitals namely (dxy, dyz, dz2, dxz and dx2-y2) of 5d TM atoms are the cause for arising of magnetic moments in TMN4 clusters-doped monolayer 35

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Fig. 11. Total and projected densities of states (DOSs) of TMN4 clusters incorporated into monolayer graphene. Fermi level is indicated by the vertical solid grey line at 0 eV energy level.

3.3. Binding energies of TMN(3)4 clusters incorporated into monolayer graphene

graphene structures. For all the TMN4 clusters embedded into monolayer graphene complexes, dz2, dx2-y2 and dyz orbitals of TM atoms roughly did not hybridize with p orbitals of N atoms, except that dxz and dxy orbitals of TM atoms interacted lightly with p orbitals of N atoms as presented in Fig. 11(a)-(g), respectively. It is also important to note here is that the TMN4 cluster-doped graphene structures having magnetic moments have the appearing of band gap in spin up and spin down channels at different energy levels along with difference of band gap value during spin up and spin down channels, which is due to the polarization of spin state bands, thereby introducing the concept of spintronics. These obtained results suggest that 2D magnetic semiconductors can be synthesized by doping TMN4 clusters into monolayer graphene.

In order to verify the stability of our TMN(3)4 cluster-doped monolayer graphene structures we calculated the binding energies for each system using following equation [38].

Eb (gpTMN(3)4) = −E(gpTMN(3)4) + EgpN(3)4 + ETM where E(gpTMN(3)4) , EgpN(3)4 and ETM describe the total energies of TMN(3)4 cluster-doped graphene structures, N doped graphene structures and TM atoms, respectively. The calculated biding energies for all TMN3 and TMN4 clusters-doped monolayer graphene structures are given in Table 2. 36

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Acknowledgments

Table 2 Binding energies (Eb in eV) for all TMN3 and TMN4 clusters embedded into monolayer graphene structures. Structure

Hf

Ta

W

Re

Os

Ir

Pt

N3 -doped N4 -doped

3.1 5.578

6.17 7.06

6.48 8.76

6.22 8.915

5.46 8.486

4.756 8.614

2.866 7.741

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All TMN3 and TMN4 cluster-doped monolayer graphene structures presented positive binding energies. The positive binding energies indicate that TMN(3)4 cluster-doping into graphene can be considered as thermodynamically favorable and the resultant complex structures can be stable enough to be adopted for future applications. An important factor to consider here is that the binding energies obtained for TMN3 cluster-doped graphene complexes are lower than the binding energies obtained for TMN4 clusters substituted graphene structures, which indicates that the TMN4 cluster-doped graphene structures are more stable in comparison to TMN3 cluster-doped structures. Our obtained results for binding energies of TMN3 and TMN4 clusters-doped monolayer graphene structures are consistent with the previous studies. [9,38,43,56]. 4. Conclusion In this paper we investigated the structural, electronic and magnetic properties of TMN3 and TMN4 clusters-doped monolayer graphene structures by means of first-principles study calculations based on density functional theory (DFT) method. We utilized two different approaches for substituting 5d TM and nitrogen (N) atoms into monolayer graphene; i) One carbon (C) atom was substituted by one TM atom and three C atoms were substituted by three N atoms. ii) Two C atoms were substituted by one TM atom and four C atoms were substituted by four N atoms in graphene. It was found that TMN(3)4 cluster doping into graphene produced ferromagnetism behavior in graphene. The results obtained during our study, revealed that TMN3 clusters embedded into graphene induce larger magnetic moments in comparison to that of TMN4 cluster-doped graphene structures. We computed the spin densities (ρ↑ - ρ↓) and charge density difference for all TMN(3)4 cluster-doped graphene complexes. Considerable ferromagnetic couplings were observed between 5d TM atom and neighboring C and N atoms on the graphene layer in all TMN(3)4 cluster-doped graphene structures. Charge transfer occurs from monolayer graphene to TMN(3)4 clusters. We calculated the band structure and PDOS plots in order to comprehend the effects of TMN(3)4 cluster doping on the electronic properties of monolayer graphene. Through our calculations it was observed that the band gap was sensitively dependent on the doped clusters, which offers a reasonable approach to tune the band gap of monolayer graphene. In addition, band gaps differed between spin up and spin down channels. Hence, it can be predicted that these graphene complex structures carry potential applications for the development of future spintronic devices. Detailed analysis of PDOS plots reveal that, in all cases of TMN(3)4 cluster-doped graphene structures, five different orbitals (dxy, dyz, dz2, dxz and dx2-y2) of 5d TM atoms introduce magnetic moments in monolayer graphene. All TMN(3)4 cluster-doped structures present positive binding energies, which suggests that TMN(3)4 clusterdoping is thermodynamically favorable and stable graphene structures can be obtained. However TMN4 cluster-doped graphene structures contain higher binding energies as compared to TMN3 cluster-doped graphene structures. After analyzing the results of our calculations, we can conclude that most of TMN(3)4 cluster-doped graphene structures exhibit direct/indirect band gap semiconductor, half-metal and dilute magnetic semiconductor behavior. Therefore we can predict that TMN(3) 4 cluster-doping can be suitable for manipulating the electronic and magnetic properties of graphene. It would be interesting to apply our predictions in experimental studies. 37

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