Stability, Electronic and Magnetic Properties of In-Plane Defects in

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Stability, Electronic and Magnetic Properties of In-Plane Defects in Graphene: A First-Principles Study Shyam Kattel,† Plamen Atanassov,‡ and Boris Kiefer*,† †

Department of Physics, New Mexico State University, Las Cruces, New Mexico 88003, United States Department of Chemical & Nuclear Engineering, University of New Mexico, Albuquerque, New Mexico 87131, United States

‡

S Supporting Information *

ABSTRACT: The electronic and magnetic properties of graphene can be modified through combined transition-metal and nitrogen decoration of vacancies. In this study, we used density functional theory to investigate the following defect motifs: nitrogen doping, nitrogen decoration of single and double vacancies (SVs and DVs), TM doping (TM = Co, Fe), TM adsorption on nitrogen-doped graphene, and combined TM− nitrogen chemistries in SV and DV (TM−Nx) configurations. The results show that the highest magnetic moments are supported in TM−Nx defect motifs. Among these defects, Co−N3, Fe−N3, and Fe−N4 defects are predicted to show ferromagnetic spin structures with high magnetic moments and magnetic stabilization energies, as well as enhanced stability as expressed by favorable formation energies, and high TM binding energies.

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INTRODUCTION Graphene is a material with applications in areas ranging from energy production1−3 to electronic circuitry elements,4−6 spintronic devices,7,8 and sensors.9,10 This versatility can at least partially be attributed to its electronic structure. A vanishing electronic density of states exactly at the Fermi energy (Dirac point) suggests that the electronic properties of graphene can easily be altered.11−14 Several previous studies reported edge functionalization as an effective way to tailor the magnetic and electronic properties of graphene.15−17 However, geometrical scaling shows that, with increasing sheet size, the number of edge atoms relative to the number of atoms in the interior of the sheets diminishes as C/l, where l is a characteristic length scale and C is a geometry-dependent constant. Thus, nonedge defects can provide additional modes of functionalization that are currently being explored for a wide range of applications in nanoelectronics,11−13 spintronics,14 and platinum-free electrocatalysts in fuel cell applications.18 We use the term “in-plane” defects to describe nonedge defects in a two-dimensional graphene sheet. Spin polarization in carbon-based materials has gained significant interest19 since the first synthesis of graphene in 2004.20 Previous computations have shown that a single vacancy (SV) in graphene is magnetic, with a magnetic moment that increases from 1.12 to 1.53 μB as the defect concentration decreases from 20% to 0.5% and vacancies become more isolated.19 The observation of magnetism in defective graphene is consistent with the predictions of Lieb’s theorem.21 Ferromagnetic transition metals (TMs) such as Co and Fe are attractive modifiers for graphene because they allow the magnetic moment to be increased significantly beyond that obtained in the SV-carbon-only case.14,22 However, the interactions between magnetic dopants can be complex, and the stability of energetically competing ferromagnetic (fm) and © 2012 American Chemical Society

antiferromagnetic (afm) spin states, at least in nitrogen-free TM-doped graphene, depends strongly on the TM distribution.23 Alternatively, doping with nitrogen has been shown to be an effective chemical route to tune the electronic properties of carbon nanostructures.13,24−27 Importantly, TMs in SVs and double vacancies (DVs) in graphene have previously been synthesized.28 At present, the combined effect of TMs and nitrogen on the electronic structure and magnetism of graphene remains largely unexplored. In the present density functional theory (DFT) study, we explored the effects of the chemistry and geometry of nitrogendoped, nitrogen-decorated SV and DV, TM-doped (TM = Co, Fe), TM adsorbed on nitrogen doped graphene and combined TM-nitrogen chemistries in SV and DV (TM−Nx) configurations on the stability, electronic and magnetic properties of graphene.

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COMPUTATIONAL METHODS The spin-polarized computations were based on density functional theory (DFT).29 Electronic exchange and correlation effects were described within the generalized gradient approximation (GGA) in the Perdew−Burke−Ernzerhof (PBE) parametrization.30 The interactions between electrons and nuclei were treated with all-electron-like projectoraugmented-wave (PAW) potentials.31,32 The electrons explicitly included in the calculations (core radii in atomic units) were 4s23d7 (2.300aB), 4s23d6 (2.300aB), 2s22p2 (1.500aB), and 2s22p3 (1.500aB) for Co, Fe, C, and N respectively. The defect motifs were modeled as 4 × 4 orthorhombic graphene supercells with lattice parameters of a = 9.842 Å and b = Received: December 16, 2011 Revised: March 8, 2012 Published: March 12, 2012 8161

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2). Defect formation energies (ΔE) were calculated relative to pristine graphene according to eq 2 x C32 + N2 + TM → C32 − x − yNxTM + Cx + y (1) 2

8.524 Å (containing 32 atoms) subjected to periodic boundary conditions. For nitrogen doping, this model corresponds to ∼3 at. % doping. Our geometry-optimized graphene sheet (Figure 1a) had an in-plane C−C distance of 1.421 Å, which agrees well

ΔE = EC32 − x − yNxTM + (x + y)μC − [EC32 + xμN + E TM(g)]

(2)

Here, μC is the chemical potential of carbon, defined as the total energy of graphene per carbon atom;40−42 EC32 and EC32−x−yNx (EC32−x−yNxTM) are the energies before and after nitrogen (and TM) incorporation, respectively; and μN is the chemical potential of nitrogen, taken as one-half of the total energy of the N2 molecule in the gas phase, following previous work.40,43,44 Following previous work, to allow a more direct comparison, the reference energy for the transition metal, ETM(g), was computed for an isolated TM atom in the gas phase.14,18,38,39,41 x is the number of nitrogen atoms introduced, and (x + y) is the number of carbon atoms removed from the perfect graphene sheet during defect formation. Throughout this article, we follow the convention that a higher (more positive) formation energy means a lower likelihood of the presence of a defect in equilibrium. TM binding energies were calculated as

Figure 1. Graphene configurations without and with N decoration considered in this study: (a) reference graphene supercell, (b) single vacancy (SV), (c) double vacancy (DV), d) N-substituted graphene (sub-N), (e) pyrrolic N (Py-N), (f) pyridinic N3 (P-N3), (g) pyridinic N2 (P-N2), and (h) pyridinic N4 (P-N4). Gray, carbon; blue, nitrogen.

with previous theoretical observations.33,34 The electronegativity differences between system components led to an electrical dipole moment perpendicular to the modeled sheet. The associated spurious interactions were minimized by introducing a vacuum layer of 14-Å thickness and applying a dipole correction to the total energy of the system.35,36 A planewave energy cutoff of Ecut = 800 eV and a 4 × 4 × 1 Monkhorst−Pack grid37 were sufficient to obtain energy convergence to better than 1 meV/atom. During the calculations, all atoms were allowed to relax while the cell shape was held fixed using our DFT-optimized parameters for defect-free graphene. The Fermi level was slightly broadened by using a Fermi−Dirac smearing of σ = 25 meV. This approach is similar to that used in previous computational studies of electronic and magnetic properties of graphene with TMs in SV and DV.14,23 For Co and Fe adsorption on defect freegraphene, we found the hollow site to be most favorable, consistent with previous work.38,39 The in-plane defects were generated by the following procedure: Remove the appropriate number of carbon atoms from graphene (Figure 1a), substitute nitrogen (x > 0, Figure 1b−h), and add one TM in the center of each remaining vacancy (TM−Nx defect) as needed (Figure

BE = EC32 − x − yNxTM − [EC32 − x − yNx + E TM(g)]

(3)

and the magnetic stabilization energy was evaluated as ΔEm = Enonmagneticconfiguration − Emagneticconfiguration (4)

where Enonmagnetic configuration is the energy of the constrained nonmagnetic calculation and Emagnetic configuration is the energy of the free magnetic moment calculation. ΔEm > 0 indicates that a state with finite magnetic moment is the electronic ground state. However, simulation cells with a single defect motif allowed only for ferromagnetic or nonmagnetic solutions. Thus, we doubled the simulation cell (SC) along the y direction (SC 1 × 2 × 1) to explore the energetically competing antiferromagnetic spin state. The electronic density of states was computed for the most stable configurations on a 16 × 16 × 1 k-point grid with a Gaussian smearing of the Fermi level of σ = 0.1 eV, following ref 39. The computations were static, and zero-point motion and vibrational effects were neglected, as in previous studies.14,23 All calculations were performed using the Vienna ab initio simulation package (VASP).45,46

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RESULTS AND DISCUSSION Transition-Metal-Free Defects without and with Nitrogen. SV (Figure 1b) and DV (Figure 1c) formation in graphene is energetically unfavorable (Table 1), consistent with previous computations.22 Nitrogen decoration of the vacancies reduces the number of electronically unfavorable dangling electrons, leading to more favorable energetics. Pyridinic N is energetically more favorable than pyrrolic N for a configuration with equal concentrations of carbon and nitrogen (Py-N, Figure 1e; P-N3, Figure 1f and Table 1). We find that the N-doped graphene configuration (Figure 1d) has the lowest formation energy of all carbon-only or nitrogen-only defects considered in this study because it causes the least perturbation of the

Figure 2. (a) TM-adsorbed N-doped graphene, (b) TM−N3 defect, (c) TM−N2 defect, and (d) TM−N4 defect configurations. Gray, carbon; blue, nitrogen; brown, cobalt or iron. 8162

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because they have high magnetic moments, but only the P-N2 defect also shows a favorable high magnetic stabilization energy (Table 1). However, all three defects have high defect formation energies, which most likely render these defects inferior to the same defect motifs in the presence of Co or Fe (discussed below). Transition Metal−Nitrogen (TM−Nx) Defects. The formation energies of nitrogen-free Co- and Fe-doped graphene configurations are 0.14 and 0.48 eV, respectively. The computed binding energies (BEs) and magnetic moments of the nitrogen-free Co- and Fe-doped graphene configurations (Table 2) are consistent with previously reported values of BEs

Table 1. Formation Energies (ΔE), Magnetic Moments Per Simulation Cell (m), and Magnetic Stabilization Energies (ΔEm) of in-Plane Defects in Graphene without and with N Decorationa

a

defect

ΔE (eV)

m (μB)

ΔEm (eV)

SV (Figure 1b) DV (Figure 1c) sub-N (Figure 1d) Py-N (Figure 1e) P-N3 (Figure 1f) P-N2 (Figure 1g) P-N4 (Figure 1h)

7.85 8.51 0.87 5.88 3.53 7.05 3.99

1.51 0.00 0.00 1.00 0.46 2.00 0.00

0.13 0.00 0.00 0.19 0.01 0.75 0.00

For further explanation and computational details, see text.

Table 2. Formation Energies (ΔE), Binding Energies (BE), Magnetic Moments for Single Defect Per Simulation Cell (m), and Magnetic Stabilization Energies (ΔEm) of TM−Nx (x = 0, 1, 2, 3, 4; TM = Co, Fe) Defects on Graphenea,b

graphene π-electron system. This observation is similar to the previous theoretical prediction of favorable N doping over pyridinic N defects in carbon nanotubes (CNTs).47,48 In the case of carbon defects without nitrogen, the dangling electronic orbitals are only half-filled, which destabilizes the defective carbon structure. In contrast, N electronic orbitals are filled and are less destabilizing, consistent with the DFT-predicted order of the defect formation energies (Table 1). The magnetic states of SV (m = 1.51 μB) and DV (m = 0.00 μB) are consistent with Lieb’s theorem (ref 21) and previous computations.19 The relaxed SV and DV geometries show that the carbon atoms closest to the vacancies undergo a Jahn− Teller distortion and form a weak bond between carbon atoms bordering defects (dotted lines in Figure 1b,c). However, Lieb’s theorem is not directly applicable to the nitrogen-bearing defect motifs in our study because of the presence of inhomogeneous electron−electron interactions. Nevertheless, magnetic moments for most of the nitrogen-bearing defects in the present study (Figure 1e−h) can be derived from the magnetic moments of the constituting C6, C5N, and C4N rings. Nitrogen forms three σ bonds, the remaining two electrons are paired up in N-doped graphene configuration. Thus, N-doped graphene is nonmagnetic consistent, with previous computations.13 One in-plane dangling electron contributes m = 1.0 μB in defect with the C6 ring. In the C5N ring, two of the nitrogen electrons form σ bonds: One is donated to the π-electron system of the C5N ring, and the remaining two electrons form an in-plane lone electron pair. Thus, in the absence of other factors, the magnetic moment is expected to be zero as long as effects on the electronic structure remain localized. Similarly, C4N has one unpaired electron, which contributes a magnetic moment of m = 1.0 μB. A detailed analysis of the magnetization shows that the magnetic moment is mainly localized on the C atom of the C6 ring with a dangling electron and on the N atom of the C4N ring. The predicted magnetic moments of the Py-N, P-N2, and P-N4 defect motifs can be explained by adding the magnetic moments of the C6, C5N, and C4N fragments that border these defect motifs. The only exception is the P-N3 defect (Figure 1f) with three bordering C5N rings, which is expected to be nonmagnetic. In contrast, our DFT computations predict a magnetic moment of m = 0.46 μB. The analysis of the spin density shows that this finite and noninteger magnetic moment can be attributed to the nitrogen atoms. This finite magnetic moment is likely due to the direct overlap of the nitrogen wave functions. The N−N distance, d = 2.6 Å, is ∼16% shorter than the van der Waals (vdW) bond distance (RvdW ≈ 3.1 Å, ref 49.). SV, Py-N, and P-N2 might be of particular interest for applications that rely on magnetism

defect TM-doped

ΔE (eV)

TM−N (TN) TM−N (B) TM−N (HN) TM−N (H) TM−N3 TM−N2 TM−N4

0.14 − 0.37 0.46 −0.02 −0.45 −1.37 −0.88 −3.54

TM-doped

0.48

TM−N (TN) TM−N (B) TM−N (HN) TM−N (H) TM−N3 TM−N2 TM−N4

0.77 0.75 0.32 −0.03 −0.95 −0.54 −3.09

BE (eV) Co −7.7 −7.6c − − − −1.33 −4.90 −7.92 −7.54 Fe −7.3 −7.0d − − − −0.91 −4.48 −7.56 −7.07

m (μB)

ΔEm (eV)

1.0 1.0c,d − − − 0.49 2.29 1.00 1.00

− − − − − 0.01 0.68 0.22 0.12

0.00 0.0d,e − − − 1.96 3.11 2.50 2.00

− − − − − 0.53 0.26 1.05 0.62

a

TM−N3 is an SV-derived defect; TM−N2 and TM−N4 are DVderived defects. bFor further explanation and computational details, see text. cReference 23. dReference 14. eReference 50.

and magnetic moments for Co- and Fe-doped graphene.14,23,50 Of the possible TM adsorption sites on N-doped graphene: TM−N: TN: on top of N; B: over a C−N bond; HN: above the center of C5N hexagon; H: above the center of carbon hexagon), the TM binds most strongly in the H configuration (Figure 2a and Table 2). Nevertheless, the low binding energies suggest that the TMs are likely mobile at room temperature, which promotes the formation of TM clusters/nanoparticles and a decreasing fraction of isolated dispersed TMs over time.14 However, a material solution that combines advantageous energetics, high magnetic moments, and high magnetic stabilization energies is given by TMs that are associated with N-decorated SV and DV defects. These defect motifs have ∼5− 8 eV lower formation energies (Figure 2b−d, Table 1 and Table 2) than TM-free N-decorated SV and DV, and the binding energies of the TMs are significantly higher (Table 2). Our calculated BEs for TMs on P-N3 and P-N4 defects in graphene are slightly smaller than the previously reported BEs of TMs in topologically similar defects in CNTs.41,51 Nevertheless, we found that TMs bind more strongly in P-N4 8163

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Figure 3. (a) DOS for Co−N3, (b) pDOS for Co−N3, (c) DOS for Co−N2, (d) pDOS for Co−N2, (e) DOS for Co−N4, and (f) pDOS for Co−N4 configurations. C and N pDOS have been averaged over all chemically equivalent atoms, respectively. The arrows denote spin-up (↑) and spin-down (↓) states.

Figure 4. (a) DOS for Fe−N3, (b) pDOS for Fe−N3, (c) DOS for Fe−N2, (d) pDOS for Fe−N2, (e) DOS for Fe−N4, and (f) pDOS for Fe−N4 configurations. C and N pDOS have been averaged over all chemically equivalent atoms, respectively. The arrows denote spin-up (↑) and spin-down (↓) states.

The magnetic moments of graphene configurations with inplane TM−Nx (x = 1, 2, 3, 4) defects vary over a large range (Table 2). The magnetic moments of TM−N3 (m = 2.29 μB for Co−N3 and m = 3.11 μB for Fe−N3) defects in graphene are predicted to be significantly higher than those previously computed for topologically identical defects in a (10, 0) nanotube (m = 1.50 μB for Co−N3 defect and m = 0.00 μB for Fe−N3 defect).41 In contrast, the magnetic moments of Co−/ Fe−N4 defects are similar in graphene and a (10, 0) CNT.41 Thus, as in the CNT, we find that the magnetic moment of a nitrogen-coordinated TM in graphene depends strongly on the defect chemistry and geometry. The differences in the magnetic moments are most likely due to the curvature of the nanotubes. On the inside of small nanotubes, 2pz orbitals are compressed in comparison to those in planar graphene, which increases the electronic kinetic energy and reduces the magnetic moment. We note that the magnetic moments of TM−Nx in-plane defects in graphene can be higher than the corresponding magnetic moments of the elemental solids (for bcc Fe, m = 2.13 μB;52 for hcp Co, m = 1.71 μB53), showing the strong effect of nitrogen atoms on the magnetic state of the TM center. The non-integer magnetic moments can be attributed to the strong interaction between the TM and the coordinating atoms, as in a previous work on nitrogen-free TMs in SV and DV.14 The analysis of the spin density for TM−Nx defect motifs shows

defect than in P-N3 defect. This order of the BEs of TMs in PN3 and P-N4 defects in graphene are in agreement with those reported for CNTs.41 The increased stability in the presence of the defects associated with TMs can be attributed to the reduced electrostatic repulsion between nitrogen lone-pair electrons due to the hybridization between N and TM. Activation barriers for Fe and Co migration have previously been reported for nitrogen-free SV as 3.6 and 3.2 eV, repectively. 14 The same study also showed that the corresponding migration barriers for DV are ∼5 eV. These high activation barriers suggest that in-plane defects in graphene are thermodynamically and kinetically stabilized. The electronic densities of states for TM−Nx defects in graphene (Figures 3 and 4) show that the TM leads to a finite density of states (DOS) at the Fermi level, as confirmed by the site-projected DOS (pDOS). The presence of N 2p peaks at the Fermi level further signifies the hybridization between N and the TM, as expected. This electronic interaction leads to the formation of bonds between N and the TM, resulting in lower defect formation energies (Table 2). We also note that none of the TM−Nx defect motifs investigated here has a band gap in either spin-up or spin-down channel close to the Fermi energy (Figures 3 and 4). Thus, it is unlikely that TM−Nxmodified graphene will find direct application in spintronics. 8164

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Figure 5. Spin density plots for (a) Co−N3, (b) Co−N2, (c) Co−N4, (d) Fe−N3, (e) Fe−N2, and (f) Fe−N4 defects. Gray, carbon; blue, nitrogen; brown, cobalt or iron. The isosurface value of 0.01 e Å−3 was chosen following ref 13.

predict to be planar, is a prime candidate for two-dimensional magnetic applications. For Co−N3 and Fe−N3, we found nonplanar geometries in which Co and Fe are located ∼1.25 and ∼1.33 Å, respectively, above the graphene plane. This height is similar to the height that has been reported for the nitrogen-free analogues.14 Thus, especially atomic layer fm Co−N3, Fe−N3, and Fe−N4 defect motifs show magnetic properties that could find applications in magnetism and nanoelectronics.

that it is highly localized on the TM and the coordinating nitrogen atoms (Figure 5). Therefore, transition metals stabilize nitrogen defects in graphene, and nitrogen atoms play a beneficial role in localizing the magnetic moments on defect motifs. For all defective graphene configurations except Fe−N3, the magnetic stabilization energy is larger for the configurations with the larger magnetic moments (Table 2). To investigate possible afm interactions between defects, we doubled the simulation cell in the y direction (SC 1 × 2 × 1). For Fe-doped graphene (SV), it was previously found that an afm spin arrangement is stabilized by 140 meV relative to the competing fm state.54 In contrast, our results show that nitrogen coordination of the TM can stabilize the fm spin state. For Fe−N2, we found that the afm state is stabilized by ∼57 meV (defect distance ≈ 8.52 Å), which is lower than in the absence of nitrogen. More importantly, our computations predict that the fm spin structures of Co−N3, Fe−N4, and Fe−N3 defect motifs are stabilized by 3, 7, and 26 meV, respectively, as compared to the competing afm spin state. The predicted stabilization energies of the ferromagnetic spin structures are lower than those of direct TM doping in graphene when the TMs occupy the same sublattice.23 However, the same study also showed that, for TM on different sublattices, nonmagnetic or afm spin structures are energetically favorable.23 Fe in nitrogen-free DV was previously predicted to have a high magnetic moment of m ≈ 3.3 μB.14 Our computations of Fe in nitrogen-free DV showed a finite but lower magnetic moment of m = 2.4 μB, consistent with the expectation that the magnetic moment should decrease in the 3d series beyond Mn.14 However, the corresponding SC 1 × 2 × 1 computations for Fe in DV show that the system adopts a nonmagnetic ground state. Thus, our computations predict consistent fm ordering of nitrogen-coordinated TM at least in the case of the high defect densities considered here. XPS measurements support the presence of in-plane TM−Nx defect motifs in self-assembled non-platinum-group-metal carbon-supported electrocatalysts.55,56 Our results corroborate the XPS observations in that the nitrogen replacement of carbon atoms closest to the vacancies is exothermic (Table S1 in Supporting Information). This suggests that the TM−Nx defect motifs considered here can be synthesized similarly to nitrogen-free TM-doped graphene28 but with intermittent exposure of graphene to nitrogen and the TM. Therefore, especially Fe−N4, which we

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CONCLUSIONS In summary, in-plane TM−Nx (x = 0, 1, 2, 3, 4) defects in graphene have been studied using first-principles calculations. Our computations show that the formation of vacancies in graphene is energetically unfavorable, whereas N decoration in vacancies is more favorable. Magnetism of N-decorated in-plane defects in graphene can be rationalized by simple electron counting, and non-integer magnetic moments can be attributed to N−N distances that are smaller than the corresponding van der Waals distance. We found that the stability of in-plane PN2, P-N3, and P-N4 defects in graphene can be significantly increased by saturating dangling bonds with transition metals such as Co or Fe. The hybridization between electronic TM 3d states and N 2p states leads to the formation of covalent bonds between the TM and N and a finite density of states at the Fermi level. However, the localization is not strong enough to open a band gap close to the Fermi energy. Thus, TM−Nx defect motifs in graphene are unlikely to find direct applications as spintronic materials. The magnetic state of TM−Nx defect motifs is found to shift from antiferromagnetic to ferromagnetic with increasing nitrogen content. This observation emphasizes the beneficial role of TM−N x defects for stabilizing ferromagnetism in graphene. Co−N3, Fe−N3, and Fe−N4 defect motifs are predicted to be particularly promising candidates for graphene-based ferromagnets, which could find applications in nanoelectronics and nanomagnetism.

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ASSOCIATED CONTENT

S Supporting Information *

Formation energy of nitrogen decoration in a single vacancy (SV) and a double vacancy (DV) in graphene for pyrrolic N (Py-N), pyridinic N3 (P-N3), pyridinic N2 (P-N2), and pyridinic 8165

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N4 (P-N4) defect configurations. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by the DOE-EPSCoR Implementation Program: Materials for Energy Conversion. S.K. and B.K. gratefully acknowledge computing resources provided by the New Mexico Computing Applications Center (NMCAC). This research was supported in part by the National Science Foundation through TeraGrid resources provided by NCSA and LONI under Grant DMR-100075.

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dx.doi.org/10.1021/jp2121609 | J. Phys. Chem. C 2012, 116, 8161−8166