Configuration-dependent electronic and magnetic properties of graphene monolayers and nanoribbons functionalized with aryl groups Xiaoqing Tian, Juan Gu, and Jian-bin Xu Citation: The Journal of Chemical Physics 140, 044712 (2014); doi: 10.1063/1.4862821 View online: http://dx.doi.org/10.1063/1.4862821 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Tunable electronic and magnetic properties of WS2 nanoribbons J. Appl. Phys. 114, 093710 (2013); 10.1063/1.4820470 Electronic and magnetic properties of oxygen patterned graphene superlattice J. Appl. Phys. 112, 114332 (2012); 10.1063/1.4769743 Magnetic and electronic properties of -graphyne nanoribbons J. Chem. Phys. 136, 244702 (2012); 10.1063/1.4730325 Mechanically tunable magnetism on graphene nanoribbon adsorbed SiO2 surface J. Appl. Phys. 111, 074317 (2012); 10.1063/1.3702877 Electronic and magnetic properties of zigzag graphene nanoribbon with one edge saturated Appl. Phys. Lett. 96, 163102 (2010); 10.1063/1.3402762
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THE JOURNAL OF CHEMICAL PHYSICS 140, 044712 (2014)
Configuration-dependent electronic and magnetic properties of graphene monolayers and nanoribbons functionalized with aryl groups Xiaoqing Tian,1,a) Juan Gu,1 and Jian-bin Xu2,b) 1
College of Physics and Technology, Shenzhen University, Shenzhen 518060, Guangdong, People’s Republic of China 2 Department of Electronic Engineering and Materials Science and Technology Research Center, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
(Received 19 August 2013; accepted 7 January 2014; published online 30 January 2014) Graphene monolayers functionalized with aryl groups exhibit configuration-dependent electronic and magnetic properties. The aryl groups were adsorbed in pairs of neighboring atoms in the same sublattice A (different sublattices) of graphene monolayers, denoted as the M2 AA (M2 AB ) configuration. The M2 AA configuration behaved as a ferromagnetic semiconductor. The band gaps for the majority and minority bands were 1.1 eV and 1.2 eV, respectively. The M2 AB configuration behaved as a nonmagnetic semiconductor with a band gap of 0.8 eV. Each aryl group could induce 1 Bohr magneton (μB ) into the molecule-graphene system. Armchair graphene nanoribbons (GNRs) exhibited the same configuration-dependent magnetic properties as the graphene monolayers. The net spin of the functionalized zigzag GNRs was mainly localized on the edges demonstrating an adsorption sitedependent magnetism. For the zigzag GNRs, both the M2 AA and M2 AB configurations possibly had a magnetic moment. Each aryl group could induce 1.5–3.5 μB into the molecule-graphene system. There was a metal-to-insulator transition after adsorption of the aryl groups for the zigzag GNRs. © 2014 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4862821] I. INTRODUCTION
Graphene sheets have drawn intense research interest since they were first synthesized in 2004.1 A pristine graphene sheet is a zero band gap semiconductor and is non-spin polarized, limiting its usefulness in applications. The problems associated with current diluted magnetic semiconductors (DMSs) is that the Curie temperature (Tc ) is generally below room temperature.2, 3 Previous investigations have reported numerous methods to introduce magnetism and a band gap into graphene.4–10 The band gap of a graphene bilayer can be opened by applying a vertical electric field to break the potential equivalence. The upper limit of the band gap is 0.26 eV, as a result of the electric field strength being confined by the limit of 0.1 V/Å for a SiO2 gate dielectric.4 The magnetic properties of graphene can be tuned by transitional metal interactions with single and double vacancies in graphene via orbital hybridization.9 Experimental results verified that defects could introduce above-room-temperature ferromagnetism into the graphene sheets.10 In this letter, we present a chemical modification route to obtain ferromagnetic graphene sheets by introducing sp3 bonds into some of the carbon atoms in graphene’s basal plane. Aryl groups have been frequently used to functionalize graphene sheets. The electronic and magnetic properties of graphene sheets functionalized with aryl groups have been investigated both experimentally and theoretically.11–20 The charge transport properties of epitaxial graphene (EG) on a) Email: [email protected] b) Email: [email protected]
0021-9606/2014/140(4)/044712/9
SiC substrates have been tuned from a near-metallic state to a semiconducting state by modification with aryl groups.14 The graphene nanosheets that were functionalized with aryl groups dispersed readily in polar aprotic solvents, allowing alternative avenues for simple incorporation into different polymer matrices.13, 15 Here we study the interaction mechanism between the aryl groups and graphene to reveal the covalent modification features of graphene, which induced strong ferromagnetism in graphene. Also, the band gap was tuned over a wide range. II. CALCULATION METHODS
We used a state-of-the-art first principles technique to study the electronic and magnetic properties of graphene sheets that were functionalized with aryl groups. Theoretical calculations were carried out using the Quantum ESPRESSO package,21 employing the GGA-PBE exchange correlation functional22 with long-range van der Waals dispersion corrections according to the DFT-D procedure.23 A 40 Ry was used as the plane-wave basis set√cutoff. A single layer of graphene with a super cell size of 3 3 × 5 was used as the substrate to simulate adsorption of the aryl groups at the dimer level. √ A single layer of graphene with a super cell size of 2 3 × 4 with four molecules in each cell was used to simulate the adsorption of the aryl groups with a high coverage of 4.7 × 1014 cm−2 . A 2.6-nm-thick vacuum layer was used to eliminate longitudinal interactions between the super cells. 4 × 4 × 1 and 6 × 5 × 1 Monkhorst-Pack k-point meshes were used for the low and high coverage simulations, respectively. For the GNR calculations, a k-point sampling with 15 k
140, 044712-1
© Author(s) 2014
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points uniformly positioned along the 1D Brillouin zone was employed for both the zigzag and armchair GNRs. III. RESULTS AND DISCUSSION A. The adsorption of aryl groups, inducing magnetism and a band gap in graphene
The optimized structure for methoxyphenyl (–C6 H4 – OCH3 ) group dimer adsorption is shown in Figs. 1(a) and 1(b). The adsorption energy is defined as Ead = −(E − E0 − nEmolecule )/n,
(1)
where E is the total energy of the single layer graphene with various molecules adsorbed; Emolecule is the total energy of the molecules; E0 is the total energy of a pristine single layer of graphene, and n is the number of molecules. The adsorption energies of the M2 AA and M2 AB configurations were 1.48 and 1.44 eV, respectively.24 To study the influence of the molecular modifications, the spin polarized density of states (SPDOS) and net spin density distribution were calculated, as shown in Fig. 2. For the M2 AA configuration, the DOS of the spin up and spin down bands was asymmetric, as shown in Fig. 2(a). Thus they had a net magnetic moment. The total magnetic moment for the M2 AA configuration was 2 Bohr magnetons (μB s). The net spin distribution on the B sublattice of graphene was largely localized near the adsorption sites, as shown in Fig. 2(c). The band gaps for the majority and minority bands were both 0.5 eV. For the M2 AB configuration, the DOS did not show any spin polarization and the band gap for graphene was 0.3 V. Thus, the M2 AA and M2 AB configurations had drastically different electronic and magnetic properties. For the M2 AA configuration, spin-polarized 2pz orbitals were
FIG. 2. Electronic structures of graphene functionalized with methoxyphenyl groups: (a) and (b) are the SPDOS of the M2 AA and M2 AB configurations, respectively. (c) 0.02 e/Å3 net spin density distribution of the M2 AA configuration. For the figures with the SPDOS, the SPDOS with a spin up (down) band was positive (negative). This notation is used throughout this paper.
gained, which are useful for graphene-based spintronics. In addition, the light elements had a weak spin-orbital coupling energy because the coupling was proportional to Z4 , where Z is the atomic index. The weaker spin-orbital coupling of the light elements led to a longer spin relaxation time.25 We expected magnetic graphene to have a longer spin relaxation time than a 3D metallic magnet. For the M2 AA configuration, there were unpaired 2pz orbitals in the sublattice B, which led to spin polarization and a total magnetic moment of 2 μB . To further clarify the molecular doping effects, configurations with a high coverage of dopants were calculated (see Fig. 3). The calculated M2 AA configuration (Fig. 3(a)) was observed in experimental scanning tunneling microscope (STM) results12 . For the M2 AA configuration, the SPDOS exhibited spin polarization, as shown in Fig. 4(a). The band gaps of the majority and minority bands were 1.1 and 1.2 eV, respectively. In the M2 AB configuration, the SPDOS did not exhibit spin polarization (Fig. 4(b)). The band gap was 0.8 eV. When there was a high coverage of molecular dopants, the graphene had a distinct band gap. For the M2 AA configuration there were 4 μB in total, and the magnetic moment was on the B sublattice around the methoxyphenyl groups, as shown in Fig. 4(c). The M2 AA configuration possibly had an antiferromagnetic state. The distributions of the spin density of the antiferromagnetic state are shown in Figs. 4(d) and 4(e). The energy difference between the antiferromagnetic and ferromagnetic states is defined as E = EAF − EF ,
FIG. 1. Optimized structure of methoxyphenyl group adsorption on to the graphene monolayer: (a) The M2 AA configuration. (b) The M2 AB configuration. The figures on the right-hand side show which atoms in the graphene sheet were bonded to the methoxyphenyl groups. The H atoms are white; the C atoms in the methoxyphenyl groups are gray, the C atoms in graphene are blue, and the O atoms are red. This notation is used throughout this paper.
(2)
where EAF is the total energy of the antiferromagnetic state and EF is the total energy of the ferromagnetic state. The E was 0.36 eV for the antiferromagnetic state (see Fig. 4(d)) relative to the ferromagnetic state. The E was 0.65 eV for the antiferromagnetic state (see Fig. 4(e)) relative to the ferromagnetic state. Thus the antiferromagnetic state with its spin
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J. Chem. Phys. 140, 044712 (2014) TABLE I. Charge transfer Q (e) between each –C6 H4 –X (X = OCH3 , Cl, Br, NH2 , Me2 N, NO2 ) and graphene. (“−” denotes graphene loses a charge and “+” denotes graphene withdraws a charge).
Q (e)
FIG. 3. Optimized structure of methoxyphenyl group adsorption on to graphene with a high coverage: (a) The M2 AA configuration. (b) The M2 AB configuration. The figures on the right-hand side show which atoms in the graphene sheet were bonded with the methoxyphenyl groups.
density distribution shown in Fig. 4(d) was more stable than that with the spin density distribution shown in Figure 4(e). Comparing the ferromagnetic state shown in Fig. 4(c) with the antiferromagnetic state shown in Fig. 4(d), E was 45 meV, which was averaged over 8 C atoms. The Tc was 500 K , estimated using mean field theory. The magnetic properties of the other aryl groups –C6 H4 –X (X = Cl, Br, NO2 , NH2 , and Me2 N) with different dipoles were investigated.24 All of the
FIG. 4. Electronic structures of graphene functionalized with methoxyphenyl groups: (a) and (b) are the SPDOS of the M2 AA and M2 AB configurations, respectively. (c)—(e) are the net spin density distributions of the M2 AA configuration. Green corresponds to an isosurface of 0.04 e/Å3 and orange corresponds to an isosurface of −0.04 e/Å3 .
OCH3
Cl
Br
NH2
Me2 N
NO2
−0.01
−0.06
−0.05
0
+0.10
−0.08
functionalized aryl groups behaved as high Tc ferromagnetic semiconductors. The Tc values estimated by mean field theory were 483, 480, 476, and 487 K for graphene functionalized with –C6 H4 –Cl, –C6 H4 –Br, –C6 H4 –Me2 N, and –C6 H4 –NH2 , respectively. For graphene functionalized with –C6 H4 –X in M2 AA configurations, there are four unpaired 2pz orbitals in sublattice B, which lead to the spin polarization and a total magnetic moment of 4 μB . The charge transfer between – C6 H4 –X and graphene is analyzed by Bader method.26 From Table I, each –C6 H4 –Me2 N could donate 0.10 electrons to the conduction band of graphene. Thus the concentration of electron carriers had been increased and the conductivity of graphene was to be improved. Other aryl group will withdraw electrons from graphene, turning graphene into a p type semiconductor. These calculations are consistent with the experimental findings where graphene doped with –C6 H4 –Me2 N shows the charge transport properties of an n type semiconductor. Meanwhile graphene doped with other aryl groups shows the transport properties of a p type semiconductor.16 This also prompts a method to tune the graphene into a n or p type semiconductor with different aryl groups. The optimized structures of graphene functionalized with nitrophenyl (–C6 H4 –NO2 ) in the M2 AA and M2 AB configurations are shown in Figs. 5(a) and 5(b), respectively. The M2 AA configuration was spin polarized (see Figure 6(a)). The band gaps for the majority and minority bands were 1.1 and 1.2 eV,
FIG. 5. Optimized structures of nitrophenyl groups adsorbed on to graphene with a high coverage: (a) The M2 AA configuration. (b) The M2 AB configuration. The figures on the right show which atoms in the graphene bonded to the methoxyphenyl groups.
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FIG. 6. Electronic structures of graphene functionalized with nitrophenyl groups: (a) and (b) are theSPDOS of the M2 AA and M2 AB configurations, respectively. (c)–(e) are the net spin density distributions for the M2 AA configuration. Green corresponds to an isosurface of 0.04 e/Å3 and orange corresponds to an isosurface of −0.04 e/Å3 .
respectively. The M2 AB configuration behaved as a nonmagnetic semiconductor with a band gap of 0.8 eV (Fig. 6(b)). Both the M2 AA and M2 AB configurations had distinct band gaps, which could explain the results presented in Ref. 14
J. Chem. Phys. 140, 044712 (2014)
where the graphene functionalized with nitrophenyl groups displayed semiconducting charge transport properties. This could also explain the experimental results in Ref. 18 where the conductivity of the graphene devices gradually decreased as the number of nitrophenyl groups attached to the graphene was increased. For the M2 AA configuration, there were 4 μB in total and the magnetic moment was on the B sublattice around the methoxyphenyl groups, as shown in Figure 6(c). The M2 AA configuration possibly had an antiferromagnetic state. The spin density of the antiferromagnetic state is shown in Figs. 6(d) and 6(e). The E was 0.35 eV for the ferromagnetic state, relative to the antiferromagnetic state (Fig. 6(d)). The E was 0.63 eV for the ferromagnetic state, relative to the antiferromagnetic state (Fig. 6(e)). The antiferromagnetic state with the spin density distribution shown in Fig. 6(d) was more stable than that with the spin density distribution shown in Fig. 6(e). If the ferromagnetic state in Fig. 6(c) was compared with the antiferromagnetic state in Fig. 6(d), the E was 44 meV, found by averaging over 8 C atoms. The estimated Tc of the graphene functionalized with nitrophenyl groups was 486 K, which explains the results in Ref. 12 where the nitrophenyl doped graphene displayed ferromagnetic properties from 4 K to room temperature. According to our calculations, the SPDOS of graphene monolayers functionalized with aryl groups did not exhibit symmetrical characteristics between the conduction and
FIG. 7. (a) Five adsorption sites near the edge in 9 × 6 armchair GNR. (b) and (c) are the optimized structures of the M2 AA configuration. (d) The 0.04 e/Å3 isosurface of the net spin density distribution for the M2 AA configuration. (e) The band structure and (f) the SPDOS in the clean armchair GNR. (g) Band structure and (h) SPDOS for the M2 AA configuration. The purple curve corresponds to the spin up band and the green curve corresponds to the spin down band.
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J. Chem. Phys. 140, 044712 (2014)
TABLE II. Adsorption energy (Ead ) and magnetic moment (M) of five sites near the 9 × 6 armchair GNR edge.
Ead (eV) M (μB )
1
2
3
4
5
2.22 1.0
1.92 1.0
1.39 1.0
1.65 1.0
1.62 1.0
valence bands near Fermi level. Thus the charge transport properties of graphene monolayers functionalized with aryl groups exhibited asymmetric characteristics. This is consistent with other theoretical results that conductivity asymmetry of electrons and holes carriers were found in graphene devices functionalized with aryl groups.17 To investigate the response of the functionalized graphene to an external electric field, a vertical electric field in the range of −0.3 to 0.3 V/Å was applied to the graphene basal plane. This did not change the total magnetic moment of graphene. Thus, the magnetism of the graphene doped with aryl groups should be stable enough for use in spintronic transistor applications.
B. Tuning the electronic structures and the magnetism of GNRs with aryl groups
Experimentally, graphene either has armchair or zigzagshaped edges, allowing the interactions between the
methoxyphenyl groups and the GNRs to be studied. Functionalization of the armchair GNRs with aryl groups was investigated. The GNR scale was defined the same as in Ref. 27. An armchair GNR with a 9 × 6 scale was investigated with five adsorption configurations near the edges, as shown in Fig. 7(a). The adsorption energy and magnetic moment of the site dependence is outlined in Table II. The site dependence of the adsorption energy can be explained as the aryl groups preferred to bond to the edges of the graphene sheets.28 Configuration 1 had the largest adsorption energy because the atoms near the edge could completely relax into a sp3 bonded structure. The aryl groups were adsorbed at the edges of the GNRs. This is in agreement with the theoretical calculations in Ref. 19. If the adsorption site was far from the edge of the GNR, relaxation of neighboring atoms was restricted and the adsorption energy was low. There was a larger barrier for the diffusion of the methoxyphenyl groups near the edge of the GNRs. Thus configuration 1 was the most stable configuration. The magnetic moments for all five configurations were 1 μB . Similar to the magnetism of the twodimensional graphene, the unpaired 2pz orbital was the source of the magnetic moment. The band structure and DOS of the clean 9 × 6 armchair GNR are shown in Figs. 7(e) and 7(f). The clean 9 × 6 armchair GNR was a nonmagnetic semiconductor with a direct band gap of 0.9 eV. The optimized structure of the M2 AA configuration is shown in Figs. 7(b) and 7(c). Its band structure and DOS are shown in Figs. 7(g) and 7(h).
FIG. 8. (a) Five adsorption sites near the edge in 10 × 6 armchair GNR. (b) and (c) are the optimized structures of the M2 AA configuration. (d) The 0.04 e/Å3 isosurface of the net spin density distribution for the M2 AA configuration. (e) The band structure and (f) the SPDOS in the clean armchair GNR. (g) Band structure and (h) spin polarized DOS for the M2 AA configuration. The purple curve corresponds to the spin up band and the green curve corresponds to the spin down band.
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J. Chem. Phys. 140, 044712 (2014)
TABLE III. Adsorption energy (Ead ) and magnetic moment (M) of five sites near the 10 × 6 armchair GNR edge.
Ead (eV) M (μB )
1
2
3
4
5
2.20 1.0
1.79 1.0
1.35 1.0
1.70 1.0
1.58 1.0
The magnetic moment of the M2 AA configuration was 2 μB . The magnetic moment was mainly distributed on the B sublattice of graphene, as shown in Fig. 7(d). This was similar to the functionalized graphene with a M2 AA configuration. The functionalized armchair GNRs with a M2 AB configuration did not have a magnetic moment. The band gaps of the majority and minority bands for the M2 AA configuration were 0.8 and 0.7 eV, respectively. Five adsorption configurations of armchair GNR with a 10 × 6 scale are investigated as shown in Fig. 8(a). The adsorption energy and magnetic moment of the site dependence is outlined in Table III. The site dependence of adsorption energy could explain the experimental findings that aryl groups prefer to bond to graphene edge.28 The configuration 1 has the largest adsorption energy and it could be explained that the atoms near edge could completely relax into a sp3 bonded structure. The magnetic moment of all 5 configurations is 1 μB . Similar to the magnetism of two-dimensional graphene, the unpaired 2pz orbitals are the source of magnetic moment. The DOS of clean 10 × 6 armchair GNR is shown Fig. 8(e).
Clean 10 × 6 armchair GNR is a nonmagnetic semiconductor with direct band gap of 1.0 eV. The optimized structure of M2 AA configuration is shown in Figs. 8(b) and 8(c). Its band structure and SPDOS are shown in Figs. 8(e) and 8(f), respectively. The magnetic moment of M2 AA configuration is 2 μB . The magnetic moment mainly distributes on the B sublattice of graphene as shown in Fig. 8(d), which is similar to graphene functionalized with aryl groups in M2 AA configurations. Armchair GNRs functionalized with aryl groups in M2 AB configuration did not have a magnetic moment. The band gap of majority and minority bands for M2 AA configuration is 0.7 and 0.8 eV, respectively. Methoxyphenyl groups’ adsorption preference of edge site was also found in 12 × 6 and 7 × 6 GNRs. For these armchair GNRs functionalized with methoxyphenyl groups in the M2 AA configuration, each methoxyphenyl group could induce 1 μB into the molecule-graphene system. Meanwhile there was no magnetic moment in armchair GNRs functionalized with methoxyphenyl groups in the M2 AB configurations. The zigzag GNRs with a 6 × 10 scale were investigated using six adsorption configurations near the edge of the GNRs, as shown in Fig. 9(a). The site dependence of the adsorption energy and the magnetic moment is shown in Table IV. Configuration 1 had the largest adsorption energy because the neighboring atoms near the bond sites completely relaxed into a sp3 bonded structure. Relaxation of the bond configurations towards the center of the GNR was restricted;
FIG. 9. (a) Six adsorption sites near the edge of the 6 × 10 zigzag GNR. (b) and (c) are the optimized structures for two methoxyphenyl groups adsorbed on one edge. (d) The 0.04 e/Å3 isosurface of the net spin density distribution for the structures in (b) and (c). (e) The band structure and (f) the SPDOS for the clean zigzag GNR. (g) Band structure and (h) SPDOS for the optimized structures shown in (b) and (c). The purple curve corresponds to the spin up band and the green curve corresponds to the spin down band.
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TABLE IV. Adsorption energy (Ead ) and magnetic moment (M) of six sites near the 6 × 10 zigzag GNR edge.
Ead (eV) M (μB )
1
2
3
4
5
6
3.59 1.5
1.00 3.5
2.71 2.0
1.41 3.1
2.11 3.0
1.78 3.0
as such, the adsorption energy was lower. The site dependence of the adsorption energy also explains why the aryl groups preferred to bond to the graphene edges.28 Adsorption of the aryl groups occurred at the edges of the GNRs. This is in agreement with theoretical calculations in Ref. 19. The most stable configuration, configuration 1, had the lowest magnetic moment of 1.5 μB , and the second most stable configuration, configuration 3, had a magnetic moment of 2 μB . The most metastable configuration, configuration 2, had the largest magnetic moment of 3.5 μB .19 For the other inner configurations, their total magnetic moments were around 3.0 μB . From Figs. 9(e) and 9(f), the clean 6 × 10 zigzag GNR was spin polarized and showed metallic characteristics. The optimized structure of the M2 AA configuration is shown in Figs. 9(b) and 9(c). The net spin density distribution is shown in Fig. 9(d). This was different from the armchair GNR as the net spin was not distributed on the same edges that the methoxyphenyl groups were absorbed on to but was distributed on the opposite edges. The total magnetic moment for this M2 AA configuration was 2 μB . Based on the
band structure and the DOS shown in Figs. 9(g) and 9(h), respectively, the functionalized zigzag GNR showed magnetic semiconductor characteristics. The band gaps of the majority and minority bands were both 1.0 eV. For the zigzag GNR there was a metal-to-insulator transition with the adsorption of the methoxyphenyl groups. If both of the edges in the zigzag-structured GNR adsorbed one methoxyphenyl group, the magnetism of the zigzag GNR was quenched and the zigzag GNR was a nonmagnetic semiconductor.24 Otherwise, the zigzag GRN had a magnetic moment. This was different from the graphene functionalized with methoxyphenyl groups and the armchair GNR, where the M2 AA configuration had a magnetic moment and the M2 AB configuration did not. For the zigzag GNR, both the M2 AA and M2 AB configurations had a magnetic moment. The zigzag GNRs with a 7 × 10 scale were investigated using seven adsorption configurations near the edge of the GNRs, as shown in Fig. 10(a). The site dependence of the adsorption energy and the magnetic moment is shown in Table V. The edgiest configuration 1 has the largest adsorption energy, due to that neighboring atoms near bond site could completely relax to sp3 bonded structure. The relaxation of bond configurations towards inner of GNR is restricted, so the adsorption energy is lower. The site dependence of adsorption energy could also explain the experimental findings that aryl groups prefer to bond to graphene edge.28 The most stable configuration 1 has the smallest magnetic moment of 1.7 μB , and the second stable configuration 3 has
FIG. 10. (a) Seven adsorption sites near the edge of the 7 × 10 zigzag GNR. (b) and (c) are the optimized structures for two methoxyphenyl groups adsorbed on one edge. (d) The 0.04 e/Å3 isosurface of the net spin density distribution for the structures in (b) and (c). (e) The band structure and (f) the spin polarized DOS for the clean zigzag GNR. (g) Band structure and (h) spin polarized DOS for the optimized structures shown in (b) and (c). The purple curve corresponds to the spin up band and the green curve corresponds to the spin down band.
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J. Chem. Phys. 140, 044712 (2014)
TABLE V. Adsorption energy (Ead ) and magnetic moment (M) of seven sites near 7 × 10 zigzag GNR edge.
Ead (eV) M (μB )
1
2
3
4
5
6
7
3.63 1.7
0.99 3.7
2.68 2.4
1.29 3.6
2.10 3.0
0.99 3.1
1.71 3.0
a magnetic moment of 2.4 μB . The most metastable configuration 2 has the largest magnetic moment of 3.7 μB . Other inner configurations’ total magnetic moment is not less than 2.4 μB . From Figs. 10(e) and 10(f), the clean 6 × 10 zigzag GNR was spin polarized and showed metallic characteristics. The optimized structure of the M2 AA configuration is shown in Figs. 10(b) and 10(c). The net spin density distribution is shown in Fig. 10(d). This was different from the armchair GNR as the net spin was not distributed on the same edges that the methoxyphenyl groups were absorbed on to, but was distributed on the opposite edges. The total magnetic moment for this M2 AA configuration was 2 μB . Based on the band structure and the DOS shown in Figs. 10(g) and 10(h), respectively, the functionalized zigzag GNR showed magnetic semiconductor characteristics. For the zigzag GNR there was a metal-to-insulator transition with the adsorption of the methoxyphenyl groups. For the zigzag GNR, both the M2 AA and M2 AB configurations had a magnetic moment.24 Experiments have realized the fabrication of GNRs with a controlled edge structure.29 It is anticipated that the site-specific magnetic properties of GNRs functionalized with methoxyphenyl groups could be used in spintronic applications. Methoxyphenyl groups’ adsorption preference of edge site was also found in 9 × 10 and 4 × 10 GNRs. For these zigzag GNRs functionalized with single methoxyphenyl group, the maximum magnetic moment for 9 × 10 and 4 × 10 GNRs could reach 3.9 and 3.4 μB, respectively.24 For these zigzag GNRs, both of the M2 AA and M2 AB configurations may have a magnetic moment. IV. CONCLUSIONS
In summary, semiconducting ferromagnetic graphene sheets were attained by the adsorption of aryl groups in the M2 AA configuration. Meanwhile, nonmagnetic semiconducting graphene was achieved by the adsorption of aryl groups in the M2 AB configuration. The concentration of aryl groups was 4.7 × 1014 cm−2 . The band gaps of the majority and minority bands in the M2 AA configuration were 1.1 and 1.2 eV, respectively. In the M2 AB configuration the band gap was 0.8 eV with aryl group concentration of 4.7 × 1014 cm−2 . For the M2 AA configuration, each aryl group could induce 1 μB into the molecule-graphene system. Armchair GNRs exhibited the same configuration-dependent magnetic properties as the graphene monolayers, whereas the zigzag GNRs showed strong site-specific magnetic properties by functionalization with aryl groups. For the zigzag GNR, one aryl group could induce 1.5–3.5 μB into the molecule-graphene system. For the zigzag GNR, both the M2 AA and M2 AB configurations had a magnetic moment. The net spin was mainly distributed on the edges of the zigzag GNRs. There
was a metal-to-insulator transition when the zigzag GNR was functionalized with aryl groups. These results demonstrated that the functionalization of graphene with different aryl groups could induce a band gap and a novel configurationdependent magnetism into graphene monolayers and GNRs. ACKNOWLEDGMENTS
X. Tian gratefully acknowledges financial support from NSFC No. 11304206 and NSFSZU Nos. 827.000001 and 00036108. J. Gu was supported by SZBS No. JC201105170651A. J.-B. Xu was supported by GRF 417910 and N_CUHK405/12. The authors thank the National Supercomputing Center in Shenzhen and the High Performance Computing Center of Shenzhen University for the computational facilities. 1 K.
S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004). 2 A. Richardella, J. M. Tang, M. E. Flatté, and A. Yazdani, Nature (London) 442, 436–439 (2006). 3 W. G. Zhu, Z. Y. Zhang, and E. Kaxiras, Phys. Rev. Lett. 100, 027205 (2008). 4 K. F. Mak, C. H. Lui, J. Shan, and T. F. Heinz, Phys. Rev. Lett. 102, 256405 (2009). 5 P. A. Denis, J. Phys. Chem. C 117, 3895 (2013). 6 J. Petucci, C. LeBlond, M. Karimi, and G. Vidali, J. Chem. Phys. 139, 044706 (2013). 7 E. J. Kan, H. Ren, F. Wu, Z. Y. Li, R. F. Lu, C. Y. Xiao, K. M. Deng, and J. L. Yang, J. Phys. Chem. C 116, 3142 (2012). 8 F. Karlický, R. Zboˇril, and M. Otyepka, J. Chem. Phys. 137, 034709 (2012). 9 A. V. Krasheninnikov, P. O. Lehtinen, A. S. Foster, P. Pyykkö, and R. M. Nieminen, Phys. Rev. Lett. 102, 126807 (2009). 10 Y. Wang, Y. Huang, Y. Song, X. Y. Zhang, Y. F. Ma, J. J. Liang, and Y. S. Chen, Nano Lett. 9, 220 (2009). 11 C. Peng, Y. Z. Xiong, Z. B. Liu, F. Zhang, E. C. Ou, J. T. Qian, Y. Q. Xiong, and W. J. Xu, Appl. Surf. Sci. 280, 914 (2013). 12 S. Niyogi, E. Bekyarova, J. Hong, S. Khizroev, C. Berger, W. de Heer, and R. Haddon, J. Phys. Chem. Lett. 2, 2487 (2011). 13 S. J. Park and R. S. Ruoff, Nat. Nanotech. 4, 217 (2009). 14 E. Bekyarova, M. E. Itkis, P. Ramesh, C. Berger, M. Sprinkle, W. de Heer, and R. C. Haddon, J. Am. Chem. Soc. 131, 1336 (2009). 15 J. R. Lomeda, C. D. Doyle, D. V. Kosynkin, W. F. Hwang, and J. M. Tour, J. Am. Chem. Soc. 130, 16201 (2008). 16 E. Pembroke, G. D. Ruan, A. Sinitskii, and J. M. Tour, Nano Res. 6(2), 138 (2013). 17 D. B. Farmer, R. Golizadeh-Mojarad, V. Perebeinos, Y.-M. Lin, G. S. Tulevski, J. C. Tsang, and P. Avouris, Nano Lett. 9, 388 (2009). 18 A. Sinitskii, A. Dimiev, D. A. Corley, A. A. Fursina, D. V. Kosynkin, and J. M. Tour, ACS Nano 4, 1949 (2010). 19 D.-E. Jiang, B. G. Sumpter, and S. Dai, J. Phys. Chem. B 110, 23628 (2006). 20 P. Z. Tang, P. C. Chen, J. Wu, F. Y. Kang, J. Li, A. Rubio, and W. H. Duan, Nanoscale 5, 7537 (2013). 21 P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann et al., J. Phys.: Condens. Matter 21, 395502 (2009). 22 J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). 23 S. J. Grimme, J. Com. Chem. 27, 1787 (2006). 24 See supplementary material at http://dx.doi.org/10.1063/1.4862821 for structures of all possible M2 AA and M2 AB configurations; corresponding DOS and spin density distribution for M2 AA and M2 AB configurations; spin density distribution for single methoxyphenyl group functionalized 6 × 10 and 7 × 10 zigzag GNRs; and spin density distribution
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for methoxyphenyl group dimer functionalized 6 × 10 and 7 × 10 zigzag GNRs. 25 T. D. Nguyen, G. Hukic-Markosian, F. J. Wang, L. Wojcik, X. G. Li, E. Ehrenfreund, and Z. Vardeny, Nat. Mater. 9, 345 (2010). 26 W. Tang, E. Sanville, and G. Henkelman, J. Phys.: Condens. Matter 21, 084204 (2009).
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THE JOURNAL OF CHEMICAL PHYSICS 140, 044712 (2014)
Configuration-dependent electronic and magnetic properties of graphene monolayers and nanoribbons functionalized with aryl groups Xiaoqing Tian,1,a) Juan Gu,1 and Jian-bin Xu2,b) 1
College of Physics and Technology, Shenzhen University, Shenzhen 518060, Guangdong, People’s Republic of China 2 Department of Electronic Engineering and Materials Science and Technology Research Center, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
(Received 19 August 2013; accepted 7 January 2014; published online 30 January 2014) Graphene monolayers functionalized with aryl groups exhibit configuration-dependent electronic and magnetic properties. The aryl groups were adsorbed in pairs of neighboring atoms in the same sublattice A (different sublattices) of graphene monolayers, denoted as the M2 AA (M2 AB ) configuration. The M2 AA configuration behaved as a ferromagnetic semiconductor. The band gaps for the majority and minority bands were 1.1 eV and 1.2 eV, respectively. The M2 AB configuration behaved as a nonmagnetic semiconductor with a band gap of 0.8 eV. Each aryl group could induce 1 Bohr magneton (μB ) into the molecule-graphene system. Armchair graphene nanoribbons (GNRs) exhibited the same configuration-dependent magnetic properties as the graphene monolayers. The net spin of the functionalized zigzag GNRs was mainly localized on the edges demonstrating an adsorption sitedependent magnetism. For the zigzag GNRs, both the M2 AA and M2 AB configurations possibly had a magnetic moment. Each aryl group could induce 1.5–3.5 μB into the molecule-graphene system. There was a metal-to-insulator transition after adsorption of the aryl groups for the zigzag GNRs. © 2014 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4862821] I. INTRODUCTION
Graphene sheets have drawn intense research interest since they were first synthesized in 2004.1 A pristine graphene sheet is a zero band gap semiconductor and is non-spin polarized, limiting its usefulness in applications. The problems associated with current diluted magnetic semiconductors (DMSs) is that the Curie temperature (Tc ) is generally below room temperature.2, 3 Previous investigations have reported numerous methods to introduce magnetism and a band gap into graphene.4–10 The band gap of a graphene bilayer can be opened by applying a vertical electric field to break the potential equivalence. The upper limit of the band gap is 0.26 eV, as a result of the electric field strength being confined by the limit of 0.1 V/Å for a SiO2 gate dielectric.4 The magnetic properties of graphene can be tuned by transitional metal interactions with single and double vacancies in graphene via orbital hybridization.9 Experimental results verified that defects could introduce above-room-temperature ferromagnetism into the graphene sheets.10 In this letter, we present a chemical modification route to obtain ferromagnetic graphene sheets by introducing sp3 bonds into some of the carbon atoms in graphene’s basal plane. Aryl groups have been frequently used to functionalize graphene sheets. The electronic and magnetic properties of graphene sheets functionalized with aryl groups have been investigated both experimentally and theoretically.11–20 The charge transport properties of epitaxial graphene (EG) on a) Email: [email protected] b) Email: [email protected]
0021-9606/2014/140(4)/044712/9
SiC substrates have been tuned from a near-metallic state to a semiconducting state by modification with aryl groups.14 The graphene nanosheets that were functionalized with aryl groups dispersed readily in polar aprotic solvents, allowing alternative avenues for simple incorporation into different polymer matrices.13, 15 Here we study the interaction mechanism between the aryl groups and graphene to reveal the covalent modification features of graphene, which induced strong ferromagnetism in graphene. Also, the band gap was tuned over a wide range. II. CALCULATION METHODS
We used a state-of-the-art first principles technique to study the electronic and magnetic properties of graphene sheets that were functionalized with aryl groups. Theoretical calculations were carried out using the Quantum ESPRESSO package,21 employing the GGA-PBE exchange correlation functional22 with long-range van der Waals dispersion corrections according to the DFT-D procedure.23 A 40 Ry was used as the plane-wave basis set√cutoff. A single layer of graphene with a super cell size of 3 3 × 5 was used as the substrate to simulate adsorption of the aryl groups at the dimer level. √ A single layer of graphene with a super cell size of 2 3 × 4 with four molecules in each cell was used to simulate the adsorption of the aryl groups with a high coverage of 4.7 × 1014 cm−2 . A 2.6-nm-thick vacuum layer was used to eliminate longitudinal interactions between the super cells. 4 × 4 × 1 and 6 × 5 × 1 Monkhorst-Pack k-point meshes were used for the low and high coverage simulations, respectively. For the GNR calculations, a k-point sampling with 15 k
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© Author(s) 2014
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points uniformly positioned along the 1D Brillouin zone was employed for both the zigzag and armchair GNRs. III. RESULTS AND DISCUSSION A. The adsorption of aryl groups, inducing magnetism and a band gap in graphene
The optimized structure for methoxyphenyl (–C6 H4 – OCH3 ) group dimer adsorption is shown in Figs. 1(a) and 1(b). The adsorption energy is defined as Ead = −(E − E0 − nEmolecule )/n,
(1)
where E is the total energy of the single layer graphene with various molecules adsorbed; Emolecule is the total energy of the molecules; E0 is the total energy of a pristine single layer of graphene, and n is the number of molecules. The adsorption energies of the M2 AA and M2 AB configurations were 1.48 and 1.44 eV, respectively.24 To study the influence of the molecular modifications, the spin polarized density of states (SPDOS) and net spin density distribution were calculated, as shown in Fig. 2. For the M2 AA configuration, the DOS of the spin up and spin down bands was asymmetric, as shown in Fig. 2(a). Thus they had a net magnetic moment. The total magnetic moment for the M2 AA configuration was 2 Bohr magnetons (μB s). The net spin distribution on the B sublattice of graphene was largely localized near the adsorption sites, as shown in Fig. 2(c). The band gaps for the majority and minority bands were both 0.5 eV. For the M2 AB configuration, the DOS did not show any spin polarization and the band gap for graphene was 0.3 V. Thus, the M2 AA and M2 AB configurations had drastically different electronic and magnetic properties. For the M2 AA configuration, spin-polarized 2pz orbitals were
FIG. 2. Electronic structures of graphene functionalized with methoxyphenyl groups: (a) and (b) are the SPDOS of the M2 AA and M2 AB configurations, respectively. (c) 0.02 e/Å3 net spin density distribution of the M2 AA configuration. For the figures with the SPDOS, the SPDOS with a spin up (down) band was positive (negative). This notation is used throughout this paper.
gained, which are useful for graphene-based spintronics. In addition, the light elements had a weak spin-orbital coupling energy because the coupling was proportional to Z4 , where Z is the atomic index. The weaker spin-orbital coupling of the light elements led to a longer spin relaxation time.25 We expected magnetic graphene to have a longer spin relaxation time than a 3D metallic magnet. For the M2 AA configuration, there were unpaired 2pz orbitals in the sublattice B, which led to spin polarization and a total magnetic moment of 2 μB . To further clarify the molecular doping effects, configurations with a high coverage of dopants were calculated (see Fig. 3). The calculated M2 AA configuration (Fig. 3(a)) was observed in experimental scanning tunneling microscope (STM) results12 . For the M2 AA configuration, the SPDOS exhibited spin polarization, as shown in Fig. 4(a). The band gaps of the majority and minority bands were 1.1 and 1.2 eV, respectively. In the M2 AB configuration, the SPDOS did not exhibit spin polarization (Fig. 4(b)). The band gap was 0.8 eV. When there was a high coverage of molecular dopants, the graphene had a distinct band gap. For the M2 AA configuration there were 4 μB in total, and the magnetic moment was on the B sublattice around the methoxyphenyl groups, as shown in Fig. 4(c). The M2 AA configuration possibly had an antiferromagnetic state. The distributions of the spin density of the antiferromagnetic state are shown in Figs. 4(d) and 4(e). The energy difference between the antiferromagnetic and ferromagnetic states is defined as E = EAF − EF ,
FIG. 1. Optimized structure of methoxyphenyl group adsorption on to the graphene monolayer: (a) The M2 AA configuration. (b) The M2 AB configuration. The figures on the right-hand side show which atoms in the graphene sheet were bonded to the methoxyphenyl groups. The H atoms are white; the C atoms in the methoxyphenyl groups are gray, the C atoms in graphene are blue, and the O atoms are red. This notation is used throughout this paper.
(2)
where EAF is the total energy of the antiferromagnetic state and EF is the total energy of the ferromagnetic state. The E was 0.36 eV for the antiferromagnetic state (see Fig. 4(d)) relative to the ferromagnetic state. The E was 0.65 eV for the antiferromagnetic state (see Fig. 4(e)) relative to the ferromagnetic state. Thus the antiferromagnetic state with its spin
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J. Chem. Phys. 140, 044712 (2014) TABLE I. Charge transfer Q (e) between each –C6 H4 –X (X = OCH3 , Cl, Br, NH2 , Me2 N, NO2 ) and graphene. (“−” denotes graphene loses a charge and “+” denotes graphene withdraws a charge).
Q (e)
FIG. 3. Optimized structure of methoxyphenyl group adsorption on to graphene with a high coverage: (a) The M2 AA configuration. (b) The M2 AB configuration. The figures on the right-hand side show which atoms in the graphene sheet were bonded with the methoxyphenyl groups.
density distribution shown in Fig. 4(d) was more stable than that with the spin density distribution shown in Figure 4(e). Comparing the ferromagnetic state shown in Fig. 4(c) with the antiferromagnetic state shown in Fig. 4(d), E was 45 meV, which was averaged over 8 C atoms. The Tc was 500 K , estimated using mean field theory. The magnetic properties of the other aryl groups –C6 H4 –X (X = Cl, Br, NO2 , NH2 , and Me2 N) with different dipoles were investigated.24 All of the
FIG. 4. Electronic structures of graphene functionalized with methoxyphenyl groups: (a) and (b) are the SPDOS of the M2 AA and M2 AB configurations, respectively. (c)—(e) are the net spin density distributions of the M2 AA configuration. Green corresponds to an isosurface of 0.04 e/Å3 and orange corresponds to an isosurface of −0.04 e/Å3 .
OCH3
Cl
Br
NH2
Me2 N
NO2
−0.01
−0.06
−0.05
0
+0.10
−0.08
functionalized aryl groups behaved as high Tc ferromagnetic semiconductors. The Tc values estimated by mean field theory were 483, 480, 476, and 487 K for graphene functionalized with –C6 H4 –Cl, –C6 H4 –Br, –C6 H4 –Me2 N, and –C6 H4 –NH2 , respectively. For graphene functionalized with –C6 H4 –X in M2 AA configurations, there are four unpaired 2pz orbitals in sublattice B, which lead to the spin polarization and a total magnetic moment of 4 μB . The charge transfer between – C6 H4 –X and graphene is analyzed by Bader method.26 From Table I, each –C6 H4 –Me2 N could donate 0.10 electrons to the conduction band of graphene. Thus the concentration of electron carriers had been increased and the conductivity of graphene was to be improved. Other aryl group will withdraw electrons from graphene, turning graphene into a p type semiconductor. These calculations are consistent with the experimental findings where graphene doped with –C6 H4 –Me2 N shows the charge transport properties of an n type semiconductor. Meanwhile graphene doped with other aryl groups shows the transport properties of a p type semiconductor.16 This also prompts a method to tune the graphene into a n or p type semiconductor with different aryl groups. The optimized structures of graphene functionalized with nitrophenyl (–C6 H4 –NO2 ) in the M2 AA and M2 AB configurations are shown in Figs. 5(a) and 5(b), respectively. The M2 AA configuration was spin polarized (see Figure 6(a)). The band gaps for the majority and minority bands were 1.1 and 1.2 eV,
FIG. 5. Optimized structures of nitrophenyl groups adsorbed on to graphene with a high coverage: (a) The M2 AA configuration. (b) The M2 AB configuration. The figures on the right show which atoms in the graphene bonded to the methoxyphenyl groups.
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FIG. 6. Electronic structures of graphene functionalized with nitrophenyl groups: (a) and (b) are theSPDOS of the M2 AA and M2 AB configurations, respectively. (c)–(e) are the net spin density distributions for the M2 AA configuration. Green corresponds to an isosurface of 0.04 e/Å3 and orange corresponds to an isosurface of −0.04 e/Å3 .
respectively. The M2 AB configuration behaved as a nonmagnetic semiconductor with a band gap of 0.8 eV (Fig. 6(b)). Both the M2 AA and M2 AB configurations had distinct band gaps, which could explain the results presented in Ref. 14
J. Chem. Phys. 140, 044712 (2014)
where the graphene functionalized with nitrophenyl groups displayed semiconducting charge transport properties. This could also explain the experimental results in Ref. 18 where the conductivity of the graphene devices gradually decreased as the number of nitrophenyl groups attached to the graphene was increased. For the M2 AA configuration, there were 4 μB in total and the magnetic moment was on the B sublattice around the methoxyphenyl groups, as shown in Figure 6(c). The M2 AA configuration possibly had an antiferromagnetic state. The spin density of the antiferromagnetic state is shown in Figs. 6(d) and 6(e). The E was 0.35 eV for the ferromagnetic state, relative to the antiferromagnetic state (Fig. 6(d)). The E was 0.63 eV for the ferromagnetic state, relative to the antiferromagnetic state (Fig. 6(e)). The antiferromagnetic state with the spin density distribution shown in Fig. 6(d) was more stable than that with the spin density distribution shown in Fig. 6(e). If the ferromagnetic state in Fig. 6(c) was compared with the antiferromagnetic state in Fig. 6(d), the E was 44 meV, found by averaging over 8 C atoms. The estimated Tc of the graphene functionalized with nitrophenyl groups was 486 K, which explains the results in Ref. 12 where the nitrophenyl doped graphene displayed ferromagnetic properties from 4 K to room temperature. According to our calculations, the SPDOS of graphene monolayers functionalized with aryl groups did not exhibit symmetrical characteristics between the conduction and
FIG. 7. (a) Five adsorption sites near the edge in 9 × 6 armchair GNR. (b) and (c) are the optimized structures of the M2 AA configuration. (d) The 0.04 e/Å3 isosurface of the net spin density distribution for the M2 AA configuration. (e) The band structure and (f) the SPDOS in the clean armchair GNR. (g) Band structure and (h) SPDOS for the M2 AA configuration. The purple curve corresponds to the spin up band and the green curve corresponds to the spin down band.
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TABLE II. Adsorption energy (Ead ) and magnetic moment (M) of five sites near the 9 × 6 armchair GNR edge.
Ead (eV) M (μB )
1
2
3
4
5
2.22 1.0
1.92 1.0
1.39 1.0
1.65 1.0
1.62 1.0
valence bands near Fermi level. Thus the charge transport properties of graphene monolayers functionalized with aryl groups exhibited asymmetric characteristics. This is consistent with other theoretical results that conductivity asymmetry of electrons and holes carriers were found in graphene devices functionalized with aryl groups.17 To investigate the response of the functionalized graphene to an external electric field, a vertical electric field in the range of −0.3 to 0.3 V/Å was applied to the graphene basal plane. This did not change the total magnetic moment of graphene. Thus, the magnetism of the graphene doped with aryl groups should be stable enough for use in spintronic transistor applications.
B. Tuning the electronic structures and the magnetism of GNRs with aryl groups
Experimentally, graphene either has armchair or zigzagshaped edges, allowing the interactions between the
methoxyphenyl groups and the GNRs to be studied. Functionalization of the armchair GNRs with aryl groups was investigated. The GNR scale was defined the same as in Ref. 27. An armchair GNR with a 9 × 6 scale was investigated with five adsorption configurations near the edges, as shown in Fig. 7(a). The adsorption energy and magnetic moment of the site dependence is outlined in Table II. The site dependence of the adsorption energy can be explained as the aryl groups preferred to bond to the edges of the graphene sheets.28 Configuration 1 had the largest adsorption energy because the atoms near the edge could completely relax into a sp3 bonded structure. The aryl groups were adsorbed at the edges of the GNRs. This is in agreement with the theoretical calculations in Ref. 19. If the adsorption site was far from the edge of the GNR, relaxation of neighboring atoms was restricted and the adsorption energy was low. There was a larger barrier for the diffusion of the methoxyphenyl groups near the edge of the GNRs. Thus configuration 1 was the most stable configuration. The magnetic moments for all five configurations were 1 μB . Similar to the magnetism of the twodimensional graphene, the unpaired 2pz orbital was the source of the magnetic moment. The band structure and DOS of the clean 9 × 6 armchair GNR are shown in Figs. 7(e) and 7(f). The clean 9 × 6 armchair GNR was a nonmagnetic semiconductor with a direct band gap of 0.9 eV. The optimized structure of the M2 AA configuration is shown in Figs. 7(b) and 7(c). Its band structure and DOS are shown in Figs. 7(g) and 7(h).
FIG. 8. (a) Five adsorption sites near the edge in 10 × 6 armchair GNR. (b) and (c) are the optimized structures of the M2 AA configuration. (d) The 0.04 e/Å3 isosurface of the net spin density distribution for the M2 AA configuration. (e) The band structure and (f) the SPDOS in the clean armchair GNR. (g) Band structure and (h) spin polarized DOS for the M2 AA configuration. The purple curve corresponds to the spin up band and the green curve corresponds to the spin down band.
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TABLE III. Adsorption energy (Ead ) and magnetic moment (M) of five sites near the 10 × 6 armchair GNR edge.
Ead (eV) M (μB )
1
2
3
4
5
2.20 1.0
1.79 1.0
1.35 1.0
1.70 1.0
1.58 1.0
The magnetic moment of the M2 AA configuration was 2 μB . The magnetic moment was mainly distributed on the B sublattice of graphene, as shown in Fig. 7(d). This was similar to the functionalized graphene with a M2 AA configuration. The functionalized armchair GNRs with a M2 AB configuration did not have a magnetic moment. The band gaps of the majority and minority bands for the M2 AA configuration were 0.8 and 0.7 eV, respectively. Five adsorption configurations of armchair GNR with a 10 × 6 scale are investigated as shown in Fig. 8(a). The adsorption energy and magnetic moment of the site dependence is outlined in Table III. The site dependence of adsorption energy could explain the experimental findings that aryl groups prefer to bond to graphene edge.28 The configuration 1 has the largest adsorption energy and it could be explained that the atoms near edge could completely relax into a sp3 bonded structure. The magnetic moment of all 5 configurations is 1 μB . Similar to the magnetism of two-dimensional graphene, the unpaired 2pz orbitals are the source of magnetic moment. The DOS of clean 10 × 6 armchair GNR is shown Fig. 8(e).
Clean 10 × 6 armchair GNR is a nonmagnetic semiconductor with direct band gap of 1.0 eV. The optimized structure of M2 AA configuration is shown in Figs. 8(b) and 8(c). Its band structure and SPDOS are shown in Figs. 8(e) and 8(f), respectively. The magnetic moment of M2 AA configuration is 2 μB . The magnetic moment mainly distributes on the B sublattice of graphene as shown in Fig. 8(d), which is similar to graphene functionalized with aryl groups in M2 AA configurations. Armchair GNRs functionalized with aryl groups in M2 AB configuration did not have a magnetic moment. The band gap of majority and minority bands for M2 AA configuration is 0.7 and 0.8 eV, respectively. Methoxyphenyl groups’ adsorption preference of edge site was also found in 12 × 6 and 7 × 6 GNRs. For these armchair GNRs functionalized with methoxyphenyl groups in the M2 AA configuration, each methoxyphenyl group could induce 1 μB into the molecule-graphene system. Meanwhile there was no magnetic moment in armchair GNRs functionalized with methoxyphenyl groups in the M2 AB configurations. The zigzag GNRs with a 6 × 10 scale were investigated using six adsorption configurations near the edge of the GNRs, as shown in Fig. 9(a). The site dependence of the adsorption energy and the magnetic moment is shown in Table IV. Configuration 1 had the largest adsorption energy because the neighboring atoms near the bond sites completely relaxed into a sp3 bonded structure. Relaxation of the bond configurations towards the center of the GNR was restricted;
FIG. 9. (a) Six adsorption sites near the edge of the 6 × 10 zigzag GNR. (b) and (c) are the optimized structures for two methoxyphenyl groups adsorbed on one edge. (d) The 0.04 e/Å3 isosurface of the net spin density distribution for the structures in (b) and (c). (e) The band structure and (f) the SPDOS for the clean zigzag GNR. (g) Band structure and (h) SPDOS for the optimized structures shown in (b) and (c). The purple curve corresponds to the spin up band and the green curve corresponds to the spin down band.
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TABLE IV. Adsorption energy (Ead ) and magnetic moment (M) of six sites near the 6 × 10 zigzag GNR edge.
Ead (eV) M (μB )
1
2
3
4
5
6
3.59 1.5
1.00 3.5
2.71 2.0
1.41 3.1
2.11 3.0
1.78 3.0
as such, the adsorption energy was lower. The site dependence of the adsorption energy also explains why the aryl groups preferred to bond to the graphene edges.28 Adsorption of the aryl groups occurred at the edges of the GNRs. This is in agreement with theoretical calculations in Ref. 19. The most stable configuration, configuration 1, had the lowest magnetic moment of 1.5 μB , and the second most stable configuration, configuration 3, had a magnetic moment of 2 μB . The most metastable configuration, configuration 2, had the largest magnetic moment of 3.5 μB .19 For the other inner configurations, their total magnetic moments were around 3.0 μB . From Figs. 9(e) and 9(f), the clean 6 × 10 zigzag GNR was spin polarized and showed metallic characteristics. The optimized structure of the M2 AA configuration is shown in Figs. 9(b) and 9(c). The net spin density distribution is shown in Fig. 9(d). This was different from the armchair GNR as the net spin was not distributed on the same edges that the methoxyphenyl groups were absorbed on to but was distributed on the opposite edges. The total magnetic moment for this M2 AA configuration was 2 μB . Based on the
band structure and the DOS shown in Figs. 9(g) and 9(h), respectively, the functionalized zigzag GNR showed magnetic semiconductor characteristics. The band gaps of the majority and minority bands were both 1.0 eV. For the zigzag GNR there was a metal-to-insulator transition with the adsorption of the methoxyphenyl groups. If both of the edges in the zigzag-structured GNR adsorbed one methoxyphenyl group, the magnetism of the zigzag GNR was quenched and the zigzag GNR was a nonmagnetic semiconductor.24 Otherwise, the zigzag GRN had a magnetic moment. This was different from the graphene functionalized with methoxyphenyl groups and the armchair GNR, where the M2 AA configuration had a magnetic moment and the M2 AB configuration did not. For the zigzag GNR, both the M2 AA and M2 AB configurations had a magnetic moment. The zigzag GNRs with a 7 × 10 scale were investigated using seven adsorption configurations near the edge of the GNRs, as shown in Fig. 10(a). The site dependence of the adsorption energy and the magnetic moment is shown in Table V. The edgiest configuration 1 has the largest adsorption energy, due to that neighboring atoms near bond site could completely relax to sp3 bonded structure. The relaxation of bond configurations towards inner of GNR is restricted, so the adsorption energy is lower. The site dependence of adsorption energy could also explain the experimental findings that aryl groups prefer to bond to graphene edge.28 The most stable configuration 1 has the smallest magnetic moment of 1.7 μB , and the second stable configuration 3 has
FIG. 10. (a) Seven adsorption sites near the edge of the 7 × 10 zigzag GNR. (b) and (c) are the optimized structures for two methoxyphenyl groups adsorbed on one edge. (d) The 0.04 e/Å3 isosurface of the net spin density distribution for the structures in (b) and (c). (e) The band structure and (f) the spin polarized DOS for the clean zigzag GNR. (g) Band structure and (h) spin polarized DOS for the optimized structures shown in (b) and (c). The purple curve corresponds to the spin up band and the green curve corresponds to the spin down band.
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TABLE V. Adsorption energy (Ead ) and magnetic moment (M) of seven sites near 7 × 10 zigzag GNR edge.
Ead (eV) M (μB )
1
2
3
4
5
6
7
3.63 1.7
0.99 3.7
2.68 2.4
1.29 3.6
2.10 3.0
0.99 3.1
1.71 3.0
a magnetic moment of 2.4 μB . The most metastable configuration 2 has the largest magnetic moment of 3.7 μB . Other inner configurations’ total magnetic moment is not less than 2.4 μB . From Figs. 10(e) and 10(f), the clean 6 × 10 zigzag GNR was spin polarized and showed metallic characteristics. The optimized structure of the M2 AA configuration is shown in Figs. 10(b) and 10(c). The net spin density distribution is shown in Fig. 10(d). This was different from the armchair GNR as the net spin was not distributed on the same edges that the methoxyphenyl groups were absorbed on to, but was distributed on the opposite edges. The total magnetic moment for this M2 AA configuration was 2 μB . Based on the band structure and the DOS shown in Figs. 10(g) and 10(h), respectively, the functionalized zigzag GNR showed magnetic semiconductor characteristics. For the zigzag GNR there was a metal-to-insulator transition with the adsorption of the methoxyphenyl groups. For the zigzag GNR, both the M2 AA and M2 AB configurations had a magnetic moment.24 Experiments have realized the fabrication of GNRs with a controlled edge structure.29 It is anticipated that the site-specific magnetic properties of GNRs functionalized with methoxyphenyl groups could be used in spintronic applications. Methoxyphenyl groups’ adsorption preference of edge site was also found in 9 × 10 and 4 × 10 GNRs. For these zigzag GNRs functionalized with single methoxyphenyl group, the maximum magnetic moment for 9 × 10 and 4 × 10 GNRs could reach 3.9 and 3.4 μB, respectively.24 For these zigzag GNRs, both of the M2 AA and M2 AB configurations may have a magnetic moment. IV. CONCLUSIONS
In summary, semiconducting ferromagnetic graphene sheets were attained by the adsorption of aryl groups in the M2 AA configuration. Meanwhile, nonmagnetic semiconducting graphene was achieved by the adsorption of aryl groups in the M2 AB configuration. The concentration of aryl groups was 4.7 × 1014 cm−2 . The band gaps of the majority and minority bands in the M2 AA configuration were 1.1 and 1.2 eV, respectively. In the M2 AB configuration the band gap was 0.8 eV with aryl group concentration of 4.7 × 1014 cm−2 . For the M2 AA configuration, each aryl group could induce 1 μB into the molecule-graphene system. Armchair GNRs exhibited the same configuration-dependent magnetic properties as the graphene monolayers, whereas the zigzag GNRs showed strong site-specific magnetic properties by functionalization with aryl groups. For the zigzag GNR, one aryl group could induce 1.5–3.5 μB into the molecule-graphene system. For the zigzag GNR, both the M2 AA and M2 AB configurations had a magnetic moment. The net spin was mainly distributed on the edges of the zigzag GNRs. There
was a metal-to-insulator transition when the zigzag GNR was functionalized with aryl groups. These results demonstrated that the functionalization of graphene with different aryl groups could induce a band gap and a novel configurationdependent magnetism into graphene monolayers and GNRs. ACKNOWLEDGMENTS
X. Tian gratefully acknowledges financial support from NSFC No. 11304206 and NSFSZU Nos. 827.000001 and 00036108. J. Gu was supported by SZBS No. JC201105170651A. J.-B. Xu was supported by GRF 417910 and N_CUHK405/12. The authors thank the National Supercomputing Center in Shenzhen and the High Performance Computing Center of Shenzhen University for the computational facilities. 1 K.
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