Influence of vacancy defects and 3d transition metal adatoms on the electronic and magnetic properties of graphene

Abstract

Based on the density functional theory (DFT) method, we investigated the geometry stability, electronic and magnetic properties of vacancy-defected graphene with and without the adsorption of transition metal (TM) adatoms (V, Cr, and Mn). The results indicated that the appearance of vacancy, which broke the π-band, induced a magnetic property due to the unpaired electrons. After adsorbing the TM atoms, the electronic and magnetic properties were interestingly modified by the impurity states and the spin-polarized electrons of TM atoms. Moreover, the projected density of states (PDOS) results suggested that the magnetism of systems was mainly dominated by the 2p orbitals of C atoms around the vacancy and the 3d orbital of the TM adatoms.

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1 Introduction

Graphene, a well known two-dimensional (2D) single sheet of C atoms, has attracted considerable attention, since its first discovery in 2004.^1–8 Due to its unique geometric structure, graphene exhibits excellent physical and chemical properties such as an unusual quantum Hall effect, massless Dirac fermions, and extraordinary carrier mobility of 15 000 cm² V⁻¹ s⁻¹ at room temperature.^9–11 Moreover, graphene is regarded as a promising material for application because of its virtues of long spin diffusion length and spin lifetime and large spin signal.^12,13 Therefore, modifying of electronic structure and magnetism in graphene is a key area for spintronic applications in the near future.^14,15

During the synthesis process of graphene, it usually suffers various defects such as topological defects, adatoms and edges.^16–22 Various defect structures and arrangements induce various electronic and magnetic properties in graphene.^23–27 The vacancy, a familiar topological defect, results from a missing C atom. Previous reports suggested that the appearance of vacancy-defects could produce magnetic moments in graphene^28–30 and increase the sensitivity to adsorb molecules.^16,31,32 Moreover, 3d orbital transition metal atoms are well known due to their magnetic states. Theoretical studies indicate that doping and adsorbing TM atoms can modify the various properties of graphene for nanoelectronic and magnetic applications.^16,33,34 Cretu et al. explored the localization of TMs on graphene by applying electron microscopy and density functional theory.³⁵ It was found that metal atoms have a high affinity for the defect regions in graphene. Krasheninnikov et al.³⁵ investigated the geometry, structure, bonding and magnetic properties of TM atoms adsorbed on defected graphene by the DFT method. Recently, graphite nanoplatelets (GNPs) were studied as potential candidates for heat spreading because of their special thermal conductivity.^36–38 Compared with GNPs, graphene shows advantageous magnetic properties. However, the results suggested that TM-vacancy complexes exhibited excellent magnetic behavior. Previous studies were mainly focused the effect of TM adatoms on perfect graphene, whereas defected graphene deserves to be explored systemically. Therefore, the combination of vacancies and TM atoms based on graphene is an effective step for achieving interesting electronic structures and magnetism to satisfy various applications.

In this study, we study the effect of vacancy defects and 3d TM atoms (V, Cr, and Mn) on the electronic and magnetic behavior. First, we explored the geometry stability of TM adatoms on defected graphene. Second, we calculated the charge transfer, net magnetic moment, band structure, and density of states of modified TM–vacancy systems to deeply analyze the changes of electronic and magnetic properties in graphene.

2 Computational methods and model

All the DFT calculations were performed by the Dmol³ code.³⁹ We used the generalized gradient approximation (GGA) for exchange-correlation functional, as described by Perdew–Burke–Ernzerhof (PBE).⁴⁰ We selected DFT semicore pseudopotential (DSSP) to replace core electrons as a single effective potential.⁴¹ A double numerical plus polarization (DNP) was employed as the basis set. The DNP basis set corresponds to a double-ζ quality basis set with a p-type polarization function added to hydrogen and d-type polarization functions added to heavier atoms, which was comparable with the Gaussian 6-31G (d,p) basis set and exhibited a better accuracy.⁴²

We applied a 5 × 5 × 1 supercell with periodic boundary conditions on the x and y axes to model the infinite graphene sheet. The vacuum space of 20 Å was set in the direction normal to the sheets to avoid the interactions between periodic images. A 5 × 5 × 1 mesh of k-point and a global orbital cutoff of 5.0 Å were set in the spin-unrestricted calculations. All atoms are allowed to relax. Convergence in energy, force, and displacement were set at 2 × 10⁻⁵ Ha, 0.004 Ha Å⁻¹, and 0.005 Å.

We analyzed the adsorption of TM adatom on VG. The adsorption energy was obtained from the expression

E_ads(TM) = E_T[TM/VG] − E_T[VG] − E_T[TM] (1)

where E_T[TM/VG] is the total energy of TM atom adsorbed on VG, E_T[VG] is the total energy of the VG, and E_T[TM] is the total energy of a free TM atom. Furthermore, we calculated the density of states (DOS) of electrons in modified configuration to explore the electronic and magnetic properties. We performed the degree of spin polarization (P) to present the characteristic of spin-polarization as in the following formula:where N_↑(E_F) and N_↓(E_F) represent DOS of spin-up (↑) and spin-down (↓) electron per eV at Fermi level (E_F), respectively.

3 Results and discussion

3.1 Geometry structure

During the creation of vacancy-defected graphene (VG), we first removed a C atom from the optimized perfect graphene (PG), which suggested the bond length of C–C was 1.420 Å agreeing with the experimental value. After relaxation, the geometry structure of VG was performed in Fig. 1a. As can be observed, the C2 and C3 atoms moved towards the missing C atom, and the bond lengths of C1–C2, C2–C3, and C3–C1 were 2.564 Å, 2.096 Å, and 2.564 Å, respectively. For the transition metal (TM) atoms adsorbed on VG, according to the geometry symmetry, we set two types of initial adsorption sites, including the top site of C1 or C2 and the hollow site of the vacancy. After optimization, the results suggested that the hollow site was the most stable. The optimized atomic structure of a Mn adatom adsorbed on the hollow site (Mn/VG) is illustrated in Fig. 1b. It was observed that the C2–C3 bond was elongated, and the calculated results indicated the C2–C3 bond changed from 2.096 Å to 2.637 Å, which was due to the interaction between the C atoms located at vacancy sites and the Mn adatom. Furthermore, the corresponding data describing the geometry structures of VG with adsorbing the V (V/VG), Cr (Cr/VG), and Mn (Mn/VG) adatoms are summarized in Table 1 in detail. Moreover, the results of adsorption energy were also calculated. It was found that the V/VG exhibited the highest stability with the largest E_ads value of −6.393 eV. Previous literature reports studied the TM-atom adsorbed on the PG, and the results suggested that the adsorption energy varied from 0.14 eV to 3.57 eV,⁴³ which is smaller than that in VG. This indicated the presence of vacancy enhanced interaction between the TM adatom and the graphene substrate. Moreover, the results listed in Table 1 and the atomic structure calculated in Fig. 1b suggested that the adsorption of TM adatoms (V, Cr, and Mn) did not induced serious distortion in VG, except for the influences on the lengths of C–C bonds around the vacancy.

Fig. 1 The optimized structures of (a) VG and (b) Mn/VG.

Table 1 Summary of geometry results for VG and the TM/VG adsorption complex. The properties listed are the bond lengths of C1–C2 (d_C1–C2), C2–C3 (d_C2–C3), C3–C1 (d_C3–C1), the bond distance between the TM adatom and C1 (d_TM–C1), C2 (d_TM–C2), C3 (d_TM–C3), the height of the TM adatom above the graphene surface (h), and the adsorption energy (E_ads)

Configuration	dC1–C2 (Å)	dC2–C3 (Å)	dC3–C1 (Å)	dTM–C1 (Å)	dTM–C2 (Å)	dTM–C3 (Å)	h (Å)	Eads (eV)
V/VG	2.655	2.620	2.623	1.882	1.882	1.898	1.612	−6.393
Cr/VG	2.632	2.627	2.626	1.837	1.840	1.842	1.626	−5.192
Mn/VG	2.632	2.637	2.633	1.839	1.830	1.830	1.566	−4.723

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3.2 Electronic and magnetic properties

The electronic and magnetic properties of VG and VG adsorbing TM adatoms were studied by computing the net magnetic moment of the TM adatom and the adsorption complex, the degree of spin polarization in a material at E_F, the band gaps, and the charge transfer of the TM adatom, which are also listed in Table 2. The net charge transfer of the TM adatom was calculated by the Mulliken analysis.⁴⁴ As shown in Table 2, Cr and Mn acted as acceptors during the interaction process with the Q value of −0.137 e and −0.204 e. In general, transition metals present magnetic characteristics due to their unpaired valence electrons. Based on the calculated results for spin-polarization, the magnetic state of TM atom significantly changes after adsorbing onto VG. As seen in Table 2, VG exhibited a net magnetic moment with a value of 1.522 μ_B, whereas the PG was non-magnetic. The magnetic presence of VG results from the breaking of π-bonds in PG due to the missing C atom, which induced unpaired electrons in VG. Furthermore, the magnetic moments of the TM adatom obviously decreases. For example, that for Mn changed from 5 μ_B for the free state to 1.431 μ_B after interacting with VG. Moreover, the Mn/VG configuration was 0.999 μ_B, which decreased by approximately 0.5 μ_B compared with the VG. The changes of magnetic properties on adsorption of the TM adatom were due to the orbital interaction between the VG and TM atoms and this changes the structure of unpaired electrons. As mentioned in Table 2, P represents the degree of spin polarization at the Fermi level (E_F) and VG was 10.9%. The V-adsorption produced 57.2% spin polarization at E_F. However, the P% of Cr/VG decreased to 0.8%. In conclusion, the V/VG was still appreciable enough for spintronic applications.

Table 2 Summary of electronic and magnetic property results for VG and the TM/VG adsorption complex. The properties listed are the magnetic moment of the TM adatom (μ_adatom), the magnetic moment of the adsorption complex (μ_tot), the percentage of spin polarization in the material at E_F (P), the band gap (E_g), and the charge transfer of the TM adatom (Q)

Configuration	μadatom (μB)	μtot (μB)	P (%)	Eg (eV)	Q (e)
VG	—	1.522	10.9	0	—
V/VG	1.147	0.996	57.2	0.104	0.049
Cr/VG	0.007	−0.001	0.8	0.037	−0.137
Mn/VG	1.431	0.999	13.8	0	−0.204

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To deeply understand the contribution of different atomic orbitals in the changes of electronic and magnetic properties, the band structures, total density of states (TDOS), and projected density of states (PDOS) were calculated are shown in Fig. 2–5. For the graphs illustrating the band structures (Fig. 2a–5a), the top and bottom panel represent the majority (spin-up) and the minority (spin-down) states. It is well known that perfect graphene is a zero band gap semiconductor.^45–48 As shown in Fig. 2a, after introducing the vacancy defect, the spin-up and spin-down bands were unsymmetrical with a net magnetic moment of 1.522 μ_B. A state crossed Fermi level, which resulted from the dangling bonds corresponding to the antibonding π states around the vacancy defect. According to the PDOS of C1, C2, and C3 atoms (Fig. 2b), the magnetic properties were mainly contributed by the C1 atom. It was found that the unpaired electrons of the C1 2p orbital present obvious magnetic behavior. In the case of Cr/VG, the asymmetry of both band structures almost disappears, and the π states located at the k-point exhibited a small energy gap of 0.037 eV. From Fig. 3b, it was found that the hybridization occurred between the C atoms (C1, C2, and C3) with two PDOS peaks located at 2.673 eV and 0.855 eV above the Fermi level. In the case of V/VG, the valence band of majority band structure appeared at the Fermi level and was expected to be metallicity, whereas the minority bands present an energy gap of 0.324 eV. Therefore, a half-metallic behavior was observed in the V/VG configuration. As we can see in Fig. 3b, the spin-up channel of the V 3d orbital crossed the Fermi level, whereas few electrons occupied the minority states at E_F. The obvious spin-polarized phenomenon in the V 3d orbital induced the relative higher degree of spin polarization at the E_F in comparison with other systems, which was consistent with the result discussed in 3.3. For the Mn/VG system, two impurity bands in both the band structures were found through the Fermi level. The spin-up and spin-down states mismatched, and the π network satisfied the Kekule pattern at the k point in the minority bands. According to the PDOS graph (Fig. 5b), there is a PDOS peak of a C 2p orbital at E_F and the spin-down channel was empty. In contrast, the spin-down states of the Mn 3d orbital present dominance at E_F. As a result, the degree of spin polarization for the system decreased.

Fig. 2 (a) The band structure and (b) the PDOS of the VG configuration.

Fig. 3 (a) The band structure and (b) the PDOS of the V/VG configuration.

Fig. 4 (a) The band structure and (b) the PDOS of the Cr/VG configuration.

Fig. 5 (a) The band structure and (b) the PDOS of the Mn/VG configuration.

4 Conclusions

In summary, the magnetic and electronic properties of modified graphene, including vacancy-defected graphene (VG) and VG with TM adatoms (V, Cr, and Mn), were investigated by the method of density functional theory (DFT). Moreover, the computation of geometry structure was also performed. It was found that the adsorption systems exhibited relative high stability with the larger adsorption energy than that of perfect graphene. The adsorption of TM atoms induced impurity states around the Fermi level, which were mainly contributed by the 3d orbitals. Furthermore, the enhancement of magnetism and the degree of spin-polarization was proven to be affected by the interaction between the C atoms around the vacancy defect and the TM adatoms. The band structure suggested that the V/VG system exhibited half-metallic, and the C 2p and V 3d orbitals were predicted to be highly spin-polarized. It is expected that our study could provide useful information to explore the future potential of TM atoms decorating defected graphene for the application of spintronic and magnetic devices.

Acknowledgements

This study is supported by the National Natural Science Foundation of China (NSFC, Grant No. 11604080, 11404096, U1404609, 11304080, 11547153) and the Innovation Team of Henan University of Science and Technology (No. 2015XTD001).

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