Electronic and Magnetic Properties of Fluorinated Graphene with

Article pubs.acs.org/JPCC

Electronic and Magnetic Properties of Fluorinated Graphene with Different Coverage of Fluorine H. Y. Liu,† Z. F. Hou,‡ C. H. Hu,§ Y. Yang,∥ and Z. Z. Zhu*,§,⊥ †

School of Science, Jimei University, Xiamen 361021, China Department of Electronic Science, §Department of Physics and Institute of Theoretical Physics and Astrophysics, and ∥State Key Lab for Physical Chemistry of Solid Surfaces, Xiamen University (XMU), Xiamen 361005, China ⊥ Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Xiamen 361005, China ‡

ABSTRACT: We have studied the electronic and magnetic properties of fluorinated graphene with different coverage of fluorine using first-principles calculations based on the density functional theory. The atomic structures, adsorption energies, and electronic structures of fluorinated graphene are investigated. Our results show that the electronic and magnetic properties of fluorinated graphene sheet exhibit strong dependence on the degree of fluorination. A precise adsorption of fluorine enables a tuning of the band gap from 0 to ∼3.13 eV as well as a transformation from nonmagnetic semimetal to nonmagnetic/magnetic metal, or to magnetic/nonmagnetic semiconductor. Therefore, our study suggests that the property of graphene can be modified by absorbing different amounts of fluorine.

1. INTRODUCTION Graphene has been attracting tremendous attention because of its many unusual properties, and it has also been considered as a promising material in the application of future electronics.1−5 However, the use of graphene in electronics applications suffers from a major drawback; that is, graphene is a semimetal with zero band gap.6,7 Thus, it is very important to seek a way to open an energy gap in the band structure of graphene. A possible way to open a band gap is to adsorb suitable atoms on the basal plane of graphene sheet, because the carbon atoms in graphene are sp2 hybridized and each carbon has a pz orbital in the direction perpendicular to the basal plane, forming a conjugated big π bond, which is relatively stable. Therefore, the surface modification on graphene is not easy in chemistry. A discussion on various surface modifications via the adsorption of organic molecules and inorganic species or the deposition of metal nanoparticles has been given.8 In recent years, many atoms in the periodic table have been extensively studied for their adsorption on the graphene.9−11 These studies have predicted that the property of graphene can be altered dramatically, especially for the electronic conductance and magnetism. In particular, recent experimental studies10,12 have shown that full fluorination of graphene sheet can lead to a transition from relatively high conductive semimetal to insulator. The fully fluorinated graphene with each carbon atom adsorbing one fluorine atom is known as fluorographene.12 It is also reported that fluorographene is a high-quality insulator (its resistivity >1012 Ω) with an optical gap of about 3 eV.12 Fluorographene exhibits a Young’s modulus of 100 N/m and has a high thermal stability against temperature up to 400 °C.12 Furthermore, the C4F, with 25% coverage of fluorine atoms © 2012 American Chemical Society

adsorbed on one side of the graphene sheet, has also been synthesized, and its theoretical band gap is about 2.93 eV.13 These simply raise a question of what property a fluorinated graphene can have if different coverage of fluorine adatoms is adsorbed on the graphene surface, especially on the behaviors of conductance and magnetism, which are important for diverse electronics applications. To this end, we perform the firstprinciples calculations to investigate the electronic and magnetic properties of fluorinated graphene sheet with different coverage of fluorine. The remainder of this Article is organized as follows. In section 2, we introduce the computational methods for the calculations of fluorinated graphene (CFx). The computed adsorption energies and the electronic structures of CFx are presented in section 3. Finally, we draw conclusions in section 4.

2. THEORETICAL CALCULATIONS In this work, we have studied the fluorinated graphene (CFx) sheets under various coverage of fluorine (x = 1.0, 0.944, 0.875, 0.5, 0.25, 0.125, 0.056, and 0.031). The supercell is employed to model CFx, and the size of the supercell is listed in Table 1. To avoid the interactions between the adjacent fluorinated graphene sheets, a vacuum space of 16 Å in the z-direction perpendicular to the atomic plane is used in the supercell. CF corresponds to the fully fluorinated graphene, in which each carbon atom adsorbs one fluorine atom. The chair configuration of CF is depicted in Figure 1a and b. CF0.944 and CF0.875 Received: April 5, 2012 Revised: July 25, 2012 Published: August 3, 2012 18193

dx.doi.org/10.1021/jp303279r | J. Phys. Chem. C 2012, 116, 18193−18201

The Journal of Physical Chemistry C

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top sites of two carbon atoms in the 2 × 2 supercell of graphene. All of the density functional theory (DFT) calculations on CFx are performed by using the projector augmented wave (PAW) method,14 as implemented in the Vienna ab initio simulation package (VASP).15,16 The exchange-correlation functional is treated by the generalized gradient approximation (GGA).17 The wave functions are expanded by plane waves with a kinetic energy cutoff of 500 eV. The Brillouin zone integration is approximated by using a special k-point sampling of the Monkhorst−Pack scheme18 with a Γ-centered grid. The convergence of the total energy with respect to both the k-point sampling and the plane-wave cutoff energy is checked, and the above setup is found to provide good accuracy in the present study. The k-mesh size chosen in the k-point sampling for each case of CFx is summarized in Table 1. All of the atomic configurations are fully relaxed until the Hellmann−Feynman forces on all of the atoms are smaller than 0.005 eV/Å. The spin polarization is taken into account for studying the magnetic properties of fluorinated graphene. To understand the bonding nature in fluorinated graphene, we calculate the deformation charge density Δρ(r)⃗ , which is defined as the difference between the total charge density ρ(r)⃗ in the solid and the superposition of independent atomic charge densities placed at the atomic sites of the same solid, that is:

Table 1. Supercell Size and the k-Mesh Size Chosen in the Calculations of Fluorinated Graphene (CFx) Sheetsa CFx

nC/nF

CF CF0.944 CF0.875 CF0.5 CF0.25 CF0.125 CF0.056 CF0.031

2/2 18/17 8/7 2/1 8/2 8/1 18/1 32/1

k-mesh

supercell size 1 3 2 1 2 2 3 4

× × × × × × × ×

1 3 2 1 2 2 3 4

11 5 7 11 7 7 5 3

× × × × × × × ×

11 × 1 5×1 7×1 11 × 1 7×1 7×1 5×1 3×1

nC and nF are the number of carbon and fluorine atoms in the supercell, respectively. a

Figure 1. (a) Top view and (b) side view of fluorographene CF; (c) side view for a half-fluorinated graphene CF0.5. C and F atoms are represented by green and red balls, respectively.

N

correspond to the cases of high-fluorinated graphene, and here they are constructed by removing one fluorine atom from the 3 × 3 and 2 × 2 supercells of CF, respectively. CF0.5 represents the half-fluorinated graphene. For simplicity, an ordered structure of CF0.5 is considered: one-half of carbon atoms in the primitive cell of graphene sheet are fluorinated (see Figure 1c). The CF0.125, CF0.056, and CF0.031 are the low-fluorinated graphene with single F atom adsorbed on the top site of a carbon atom in the 2 × 2, 3 × 3, and 4 × 4 supercells of graphene, respectively. The CF0.25 is also the low-fluorinated graphene, and it is considered by two F atoms adsorbed on the

Δρ( r ⃗) = ρ( r ⃗) −

∑ ρatom ( r ⃗ − R⃗μ)

(1)

μ=1

where R⃗ μ is the atomic position.

3. RESULTS AND DISCUSSION 3.1. Structural Properties and Adsorption Energy of Fluorinated Graphene. To examine the stability of fluorinated graphene, we calculate the averaged adsorption energy per fluorine atom as follows:

Table 2. Lattice Constant (a, in Å) of Supercell for Fluorinated Graphene, the Averaged C−C Bond Lengths (d1,C−C and d2,C−C, in Å), the Averaged C−F Bond Length (dC−F, in Å), the Adsorption Energy (Ead, in eV per fluorine adatom), the Band Gap (Eg, in eV), the Total Magnetic Moment of Supercell (Mt, in μB per cell), and the Spin Polarization Energy (ESP, in eV)a CFx

a

d1,C−C

graphene

1.424 1.42c

CF0.944 CF0.875 CF0.5 CF0.25

2.467 2.47b 2.461d 2.606 2.61e 2.6c 2.48f 7.789 5.173 2.552 4.967

1.524 1.523 1.502 1.508

1.578 1.573

CF0.125 CF0.056 CF0.031

4.947 7.401 9.868

1.481 1.479 1.479

CF

d2,C−C

1.581 1.58e 1.579c

dC−F

Ead

1.383 1.38e 1.371c

3.41

1.401

1.388 1.395 1.492 1.457

3.31 3.16 1.48 2.89

1.414 1.411 1.409

1.536 1.565 1.572

2.21 2.32 2.38

Eg

Mt

ESP

0.0

0.0

0.0

3.13 3.1e 3.2c 3.0f in-gap state in-gap state metallic 2.92 2.93d metallic metallic metallic

0

0.0

0.594 0.595 0.351 0

−0.398 −0.308 −0.005 0.0

0.456 0 0

−0.022 0.0 0.0

a d1,C−C and d2,C−C are the C−C bond lengths for the first and second nearest neighbors of F adatom or F vacancy site, respectively. ESP is defined as the energy difference between the spin-polarized state and the non-spin-polarized state. bGGA results from ref 11. cGGA results from ref 6. dGGA results from ref 13. eGGA results ref 29. fExperimental results from ref 12.

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The Journal of Physical Chemistry C Ead = 1/nF*[Et,G + nFEt,F − Et,FG]

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energy increases and becomes more positive, indicating that the fluorinated graphene becomes energetically favorable with increasing coverage density of fluorine adatoms on both sides of the graphene sheet. 3.2. Low-Fluorinated Graphene. We first examine the behavior of single fluorine adatom on graphene. The 4 × 4, 3 × 3, and 2 × 2 supercells of graphene are employed, resulting in the cases of CF0.031, CF0.056, and CF0.125, respectively. Three typical adsorption sites for a fluorine adatom are studied: (i) a top site, denoted as T-site, where F atom is adsorbed on the top of a C atom; (ii) a bridge site, denoted as B-site, where F adatom is located above the midpoint of a C−C bond; and (iii) a hollow site, denoted as H-site, where F atom is located above the center of a hexagonal ring. In our calculations, it is found that the T-site is the most energetically favorable one for single fluorine adatom. The F adatom at the T site induces a remarkable protrusion of C1 atom; however, the protrusions of C2 atom are negligible. The C−F bond length (1.572 Å) in the calculation of a 4 × 4 supercell agrees well with the result obtained by a 5 × 5 supercell.19 Figure 3a presents the contour plot of the deformation charge density in the (1010̅ ) plane in the case of CF0.056 as an example. It can be seen that F−C1 bond is a polar covalent bond. The same trend is also found for single F adatom in the cases of CF0.031 and CF0.125. Because of the higher electronegativity of fluorine, charge transfers from C1 atom to F adatom, and it is also expected that single fluorine adatom would act as hole doping.20 From the Bader charge analysis,21 the net increase in charge of F adatom is about 0.56 e. The band structures for perfect graphene and CF0.056 are depicted in Figure 3b. For perfect graphene, it is well-known that the Fermi level coincides with the Dirac point. In CF0.056, the Fermi level shifts down into the valence bands of graphene and is about 0.75 eV below the Dirac point, indicating that single F adatom indeed acts as a hole dopant. The impurity state induced by single F adatom appears just below the Fermi level and hybridizes with the bulk π band of graphene. From the density of states (DOSs) of CF0.056 shown in Figure 3c, we can find that the impurity state is mainly localized at the F and C2 atoms. This is consistent with the previous studies22−25 of tightbinding model, which predicts that a single impurity in sublattice A of graphene induces an impurity state mostly localized in sublattice B and vice versa due to the existence of two nonequivalent Dirac points. In the case of CF0.125, single F adatom on graphene induces spin polarization and the resulting magnetic moment is about 0.456 μB per cell. The spin-polarized state of CF0.125 is about 0.022 eV lower than the nonmagnetic one. This energy difference is comparable to the kBT at room temperature (i.e., 0.0258 eV), indicating that the spin-polarized state of CF0.125 could survive at the room temperature. From the distribution of spin density shown in Figure 3d, the magnetic moments are mainly localized at the F and C2 atoms. They are caused by the spin exchange splitting of the quasilocalized defect states. As pointed out by previous studies,22,23,26 ferromagnetic ordering is the only possibility for the magnetism originating from quasilocalized states induced by defects in the same sublattice, and therefore the itinerant magnetism originating from the quasilocalized states induced by single F adatom on graphene is responsible for the fractional magnetic moments and weak Stoner ferromagnetism27 of CF0.125. The indirect coupling occurs through the combination of F adatom pz orbital with the bulk π state of graphene.

(2)

where Et,G and Et,FG represent the total energy of pure and fluorinated graphene, respectively. Et,F is the total energy of an isolated F atom, and nF is the number of F atoms in the supercell. The positive sign of Ead defined in eq (2) indicates that the adsorption of fluorine atoms on graphene would be energetically favorable. The lattice constant, C−C bond length, C−F bond length, adsorption energy, band gap, and magnetic moment of fluorinated graphene are summarized in Table 2. To clearly illustrate the dependence of aforementioned quantities on the fluorine coverage, the results as a function of x in CFx are also depicted in Figure 2. For simplicity, the first and second nearest

Figure 2. The averaged lattice constant (a0 = a/2n, where a is the lattice constant for a n × n supercell as listed in Table 1 for CFx), the averaged length (d1,C−C) of the C−C bonds next to the “F-vacancy” (in CF0.944 and CF0.875) or the F-adatom (in CF0.25, CF0.125, CF0.056, and CF0.031), the averaged length of the C−F bonds (dC−F), and the adsorption energy per fluorine adatom (Ead) as a function of x in CFx.

neighboring C atoms of F adatom or vacancy in CFx are denoted as C1 and C2 throughout this article. From the results shown in Figure 2 and listed in Table 2, one can see that the averaged C−F bond length decreases with increasing degree of fluorination, indicating that the chemical bonding of fluorine on graphene strongly depends on the fluorine coverage. As discussed below, the covalency of the C−F bond in the fluorographene is more significant than that of single F atom adsorbed on the top of a C atom. Alternatively, a previous study19 shows that the chemical bonding of a F atom adsorbed on the top of a C atom in graphene strongly depends on carrier doping. On the contrary to the C−F bond length, the averaged C−C bond length is elongated when the coverage (x) of fluorine adatom in CFx increases. As the coverage of fluorine on graphene increases, the C−C bonding transforms from a sp2 type to a sp3 one, which corresponds to a larger interatomic distance. Therefore, the average lattice constant (a0 = a/2n, where a is the lattice constant of a n × n supercell as listed in Table 1 for each case of CFx) of fluorinated graphene increases with increasing fluorine coverage. The adsorption energy per fluorine adatom Ead as a function of x in CFx is depicted in Figure 2. As x in CFx goes from 0 to 0.5 for the single-sided fluorination of graphene, the F coverage at x = 0.25 has the largest value of the F adsorption energy, and the F coverage at x = 0.5 has the lowest adsorption energy. On the contrary, as x goes from 0.5 to 1, the value of the adsorption 18195



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Figure 3. (a) Contour plot of the deformation charge density in the (101̅0) plane of CF0.056. Electron accumulation (depletion) is represented by orange solid (blue dashed) lines. (b) Band structures of perfect graphene (a 3 × 3 supercell, cyan dashed line) and CF0.056 (black solid line). The contributions from F pz orbital to the wave function are indicated by the size of red open points. (c) Total density of states and partial density of states for CF0.056. (d) Isosurface of spin density for CF0.125 (yellow and blue for the majority and minority spins, respectively). The Fermi level in (b) and (c) is set to zero.

It should be pointed out that CF0.056 and CF0.031 are nonmagnetic due to the absence of the exchange splitting of impurity states. In both cases, the adatom−adatom distance is large enough to prevent adatoms from coupling even through bulk π state of graphene. In other words, the ground state of single F adatom in a n × n supercell of graphene with n ≥ 3 is not spin-polarized due to the large distance of F adatoms, suggesting that the magnetic coupling interaction between F adatoms is short-range. This is not surprising because the

indirect exchange interaction is described by a corresponding range function that decays with the distance between magnetic moment.23,26 We also study the case of two F atoms adsorbed on the top sites of two carbon atoms in graphene. In particular, the case of two F adatoms in the 2 × 2 supercell of graphene corresponds to CF0.25; that is, a quarter of graphene is fluorinated. In the single-sided fluorination of a 2 × 2 supercell, our calculations show that the adsorption of two F atoms on the third nearest 18196



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Figure 4. (a) Top view of the optimized atomic structure of CF0.25, which is formed by two F atoms adsorbed on the third-nearest neighbors (i.e., para sites) on the single side of graphene. C and F atoms are represented by the green and red balls. The periodic boundary of the unit cell of CF0.25 is indicated by the blue dashed line. The π resonance around six equivalent C2 atoms is schematically indicated by circle. (b) Band structure of CF0.25. (c) Total density of states (DOS) of CF0.25 and the partial DOS of F, C1, and C2 atoms in CF0.25. The Fermi level in (b) and (c) is set to the valence band maximum.

neighbor sites (i.e., para sites) is more stable than that of two F atoms on the second nearest neighbor sites (i.e., meta sites) by 0.95 eV. As below, we will mainly discuss the adsorption of two F adatoms on the para sites. The optimized atomic structure of this configuration is depicted in Figure 4a. The C1−C2 bond length is 1.508 Å, and the C1−F bond length is 1.457 Å. The F−C1−C2 angle (i.e., the angle between the C1−C2 σ bond and the z axis) is about 103.336°, and thus the resulting hybridization parameter A19,28 of the s and pz atomic orbitals of C1 atom is 0.335, which is larger than that in the halffluorinated graphene and smaller than that in the fully fluorinated one as discussed below. Therefore, the C1 atoms in CF0.25 are sp3 moderately hybridized. For the configuration of CF0.25 considered here, it can be regarded as π resonances on C2 atoms surrounded by sp3 hybridized C1 atoms (see Figure 4a). The adsorption energy for the configuration of CF0.25

considered here is 2.89 eV, which is the largest one in the cases of single-sided fluorination. This agrees well with the result reported in ref 13. The band structure and DOSs of CF0.25 are presented in Figure 4b and c, respectively. CF0.25 is nonmagnetic and has an indirect band gap of 2.92 eV in the present GGA calculations, in good agreement with the value of 2.93 eV reported in ref 13. The valence band edge consists of the combination of C2-pz and F-(px + py) orbitals. The lowest conduction band is dominated by the pz orbitals of F atoms, and the second lowest one is derived from the pz orbitals of C2 atoms. For the configuration of CF0.25 considered here, the way of arrangement of F atoms on the graphene surface leads to the formation of hexagonal conjugated big π bonds of the unfluorinated C atoms, and such π bonds are well separated by fluorinated C-atoms, which leads to the semiconducting nature of the system. 18197



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Figure 5. (a) Band structure of CF. The contributions from F pz orbital (C px + py orbitals) to the wave function are indicated by the size of red (gray) open points. Partial density of states (DOS) for (b) graphene and (c) fluorographene CF. (d) Contour plot of the deformation charge density in the (101̅0) plane of CF. Electron accumulation (depletion) is represented by orange solid (blue dashed) lines. The Fermi level in (a), (b), and (c) is set to the valence band maximum.

3.3. Fully Fluorinated Graphene. For fully fluorinated graphene (CF), the previous DFT calculations6 predicted that the chair configuration of CF is more stable than the other three, that is, the zigzag, boat, and armchair configurations. Here, we concentrate on the chair configuration of CF (denoted as fluorographene). The optimized atomic structure of fluorographene is depicted in Figure 1a and b. The C−F bond length is about 1.383 Å, the F−C−C angle (i.e., the angle between the C−C σ bond and the z axis) is about 107.95°, and thus the resulting hybridization parameter A19,28 of the s and pz atomic orbitals of C atom is 0.458, which is much closer to that (A = 0.5) of sp3 configuration.28 Therefore, the dominant bonding character in fluorographene is the sp3 type. The band structure and DOSs of fluorographene are presented in Figure 5a and c, respectively. Fluorographene is nonmagnetic and has a wide direct band gap with a transition at Γ-point. As compared to pure graphene (see Figure 5b), the valence bandwidth of fluorographene shrinks significantly.

Because of the sp3 hybridization of C and F atoms and their strong interactions, a large band gap in fluorographene is opened. The valence band edge is contributed by σ states of the C and F atoms, while the conductance band edge mainly originated from the antibonding pz states of the C and F atoms. The obtained band gap of fluorographene in the present GGA calculations is 3.13 eV, which is qualitatively in agreement with the previous reports.6,13,29 Regarding the typical underestimation of band gap by the DFT calculations at the GGA level, the fully fluorinated graphene would be an insulator. Recently, the many-body GW approach has predicted a band gap of 7.5 eV for fluorographene.30 However, the experimental value is about 3.0 eV, as reported in ref 12. The discrepancy between theory and experiment for the band gap of fluorographene may be attributed to defects or the corrugation in the realistic system.6,30 The contour plot of the deformation charge density in the (101̅0) plane of the fluorographene is shown in Figure 5d. We 18198



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Figure 6. (a) Spin-polarized band structure of CF0.5. The contributions from F (C2) pz orbital to the wave function are indicated by the size of red (blue) open points. (b) The spin-polarized partial density of states of CF0.5. (c) Contour plot of the deformation charge density in the (101̅0) plane of CF0.5. Electron accumulation (depletion) is represented by orange solid (blue dashed) lines. The Fermi level in (a) and (b) is set to zero.

μB/atom) and F-pz orbital (0.123 μB/atom). The in-plane buckled C1−C2 bond is covalent (see the deformation charge density plot in Figure 6c). Becasue of the strong coupling between C1-pz and F-pz orbitals, the π conjugation network of C atoms in graphene sheet is slightly destroy, leaving one dangling bond at the C2 atom. Therefore, the magnetism of CF0.5 can be ascribed to the exchange splitting of the dangling C2-pz orbital with a coupling with impurity state induced by F adatom. 3.5. High-Fluorinated Graphene: Single F Vacancy in Fluorographene. For high-fluorinated graphene, it is modeled by removing one fluorine atom from the 3 × 3 and 2 × 2 supercells of fluorographene, corresponding to the cases of CF0.944 and CF0.875, respectively. The DOSs of CF0.944 and CF0.875 are shown in Figure 7a and b. Generally, they look quite similar. In both cases, F-vacancy induces a defect state in the band gap. Such a defect state is localized strongly on C1 atom and shows a weak extension on the nearest neighboring F atoms (i.e., F2 shown in Figure 7c). The defect state induced by F vacancy mainly comes from the dangling pz orbital of the C1 atom. In the case of CF0.944, the defect state-induced F vacancy is much sharper than the one in the case of CF0.875, due to a larger supercell size in the former case that results in a weak interaction between the defect states localized at C1 atoms in periodic images.

can see that the C−F bond exhibits a very polar covalent nature. Electron charges are accumulated in the intermediate region between C atoms, and thus the C−C bond is mainly covalent. 3.4. Half-Fluorinated Graphene. Another typical case of fluorinated graphene is the half-fluorinated one, CF0.5, where only one-half of the carbon atoms in graphene are fluorinated. Here, we consider the configuration of all adsorbed F atoms on the same side of graphene. The optimized atomic structure is presented in Figure 1c. The C1−F bond length is about 1.492 Å, the F−C1−C2 angle is about 101.05°, and thus the resulting hybridization parameter A19,28 of the s and pz atomic orbitals of C1 atom is 0.276. Therefore, the sp3 hybridization of C1 atom in CF0.5 is much weaker than the one in fluorographene. The band structure and DOSs of CF0.5 are presented in Figure 6a and b, respectively. For the configuration of CF0.5 considered here (see Figure 1c), it exhibits magnetic and metallic behavior. The spin-polarization energy of CF0.5, which is defined as the energy difference between the magnetic state and the nonmagnetic one, is only about 5 meV. The bands around the Fermi level are dominated by the pz state of C2 atom (i.e., the carbon is not fluorinated) together with some contribution from the pz state of F atom. The total magnetic moment of CF0.5 is about 0.351 μB per unit cell (see Table 2), whose main contributions come from the C2-pz orbital (0.255 18199



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Figure 7. Spin-polarized density of states of (a) CF0.944 and (b) CF0.875. (c) Isosurface of spin density for CF0.944 (yellow and blue for the majority and minority spins, respectively). The Fermi level in (a) and (b) is set to zero.

coverage of fluorine. It is revealed that the electronic and magnetic properties of graphene can be modified by the absorption of different amounts of fluorine adatoms. Graphene is a nonmagnetic semimetal, which can be transformed into either a nonmagnetic/magnetic semiconductor/insulator with a direct band gap or a nonmagnetic/magnetic metal, depending on the concentration of the adsorbed fluorine adatoms. The present study suggests that the adsorption of fluorine on the surfaces of graphene is a promising approach to modify the properties of graphene, which could lead to more flexible electro-optical applications of graphene in the future.

Moreover, the F-vacancy in the CF0.944 and CF0.875 leads to the appearance of magnetic properties. To reduce the Coulomb repulsion energy, the unsaturated electron of C1 atom associated with the dangling bond is spin-polarized, which leads to an intrinsic magnetic moment on C1 atom and induces a negative spin density on C2 atoms and a positive spin density on F2 atoms (see Figure 7c). In both cases, the total magnetic moment induced by a F vacancy is about 0.59 μB per cell. The local magnetic moments of C1 and F2 atoms are 0.45 μB and 0.05 μB, respectively. The indirect exchange interaction,23 taking into account the role of intrinsic spin−orbit interaction, is responsible for the coupling between magnetic moments of F-vacancy defects. Such an interaction gives rise to an energy gap at the Fermi level (see Figure 7a and b), which makes the usual RKKY model not applicable due to the absence of electrons at the Fermi level. Because of the F-vacancies in the same sublattice, the corresponding indirect exchange interaction is ferromagnetic, with the range function decaying exponentially with the distance between magnetic moments. In addition, the interaction mediates by the virtual transitions of electrons through the gap and the excitations of real electron− hole pairs in the vicinity of the Fermi energy.23

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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

The present work was supported by the National Basic Research Program of China (973 program, Grant No. 2011CB935903), and the Natural Science Foundation of Fujian Province (Grant No. 2008J04018) of China.

4. CONCLUSIONS We have employed the first-principles method within the density functional theory to study the structural, electronic, and magnetic properties of the fluorinated graphenes with different 18200



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