A Ferromagnetic Pure Carbon Structure Composed of Graphene and

Article pubs.acs.org/JPCC

A Ferromagnetic Pure Carbon Structure Composed of Graphene and Nanotubes: First-Principles Calculations Ronaldo J. C. Batista,*,† Sabrina S. Carara,‡ Taise M. Manhabosco,† and Hélio Chacham§ †

Departamento de Física, Universidade Federal de Ouro Preto, Campus Morro do Cruzeiro, 35400-000, Ouro Preto, MG, Brazil Instituto de Física, Universidade Federal de Mato Grosso, 78060-900, Cuiabá, Montana, Brazil § Departamento de Física, ICEX, Universidade Federal de Minas Gerais, CP 702, 30123-970, Belo Horizonte, MG, Brazil ‡

ABSTRACT: A hybrid structure that presents phases of three extended allotropes of carbon, nanotube, graphene, and diamond, is proposed in this work. According to our firstprinciples calculations, such structure can be made energetically stable through the application of pressures of the order of 100 kbar to alternate graphene−nanotube layers, which were recently synthesized in large-area films. The existence of sp3 dangling bonds in the hybrid structure gives rise to an exceptionally large density of states near the Fermi level, leading to a ferromagnetic ground state.

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tures17,18 or hydrogen chemisorption,16 for instance. Wang et al.17 have demonstrated the occurrence of ferromagnetism in bulk graphene materials prepared from soluble functionalized graphene sheets. Authors believe that the origin of magnetism comes from the long-range coupling of spin units existing as defects in graphene sheets. Tada et al.16 produced graphene with honeycomblike arrays of hexagonal nanopores, which are hydrogen-terminated with low-defect pore edges. The produced graphene presents large-magnitude ferromagnetism that is derived from electron spins localizing at the zigzag nanopore edges. In this work, we propose a hybrid a ferromagnetic structure that presents phases of three extended forms of carbon: nanotube, graphene, and diamond. According to our firstprinciples calculations, this type of structure can be made energetically stable through the application of pressures of the order of 100 kbar to alternate graphene−nanotube layers, such as those recently synthesized in large-area films.15 Interestingly, the proposed structure, despite being made only by carbon atoms, has a ferromagnetic ground state. The ferromagnetism appears due to the presence of a sp3 dangling bond in the hybrid structure, which leads to an exceptionally large density of states near the Fermi level. Our first-principles methodology is based on the Density Functional Theory (DFT) as implemented in the SIESTA program.22 We used the Generalized Gradient Approximation (GGA) as parametrized in the Perdew−Burke−Ernzerhof scheme (PBE)23 for the exchange-correlation functional. The ionic core potentials were represented by norm-conserving

he allotropes of carbon present properties that have attracted attention for centuries. In the last decades, in particular, the discovery of new allotropes of carbon (fullerenes, nanotubes, and graphene)1−3 gave rise to an intense research work, which demonstrates that such new forms of carbon present several novel properties of great scientific4,5 and technological appeal.6 Once produced, the interaction between these new allotropes of carbon and other organic/inorganic materials has been also investigated because it may change the allotrope properties or introduce new ones. For instance, it has been shown very recently by means of both theory and experiment that the simple physical contact between semiconductor carbon nanotubes (SCNT) and diamond surfaces changes the electrical behavior of the nanotubes from semiconductor to metallic.7 In more extreme cases, at high pressure, for instance, an allotrope can be transformed into another: for instance, graphite transforms into diamond at high pressure, and the opposite can happen at high shear-stress.8 Hybrid structures composed of two or more allotropes of carbon may be of great technological interest. For instance, hybrid structures that combine the 1D structure of a carbon nanotube (CNT) with the 2D structure of graphene have been a topic of recent studies9−14 in which applications such as supercapacitors,9 transparent conductors,10 electrocatalytic materials,12 and gas sensors14 have been addressed. In particular, it is worth mentioning the recent work of TristánLópez et al. in which alternate graphene−nanotube layers have been synthesized in large-area films.15 Such films could be used as electron field emitters, as well as in other applications such as supercapacitors or polymer composites.15 Regarding magnetic properties, it has been demonstrated that carbon nanostructures may present ferromagnetism,16−21 which further increases their potential for technological applications. The ferromagnetism could arise from defects in the carbon nanostruc© 2014 American Chemical Society

Received: November 27, 2013 Revised: March 24, 2014 Published: March 26, 2014 8143

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lattice parameter (4.32 Å) is very close to the five-layer graphene lattice parameter (4.36 Å). (The energy cost to stretch the tube to make it commensurate with graphene is small in comparison to the difference in total energy between the hybrid structure and its high-pressure counterpart.) Along the x-axis, the cell is large enough to avoid interactions between successive periodic tube images. The carbon atoms of the graphene layers below the nanotube make sp3 bonds forming a localized diamond-like structure (diamond-like phase). The sp3 character of C−C bonds decreases inasmuch as the distance from the tube increases. Thus, in the bottom layers, less carbon atoms make sp3 bonds in comparison to the top layers. In each graphene layer, atoms that are not below the nanotube make plane sp2 bonds, forming the graphene phase. It is worth discussing in detail the nanotube/diamond phase contact geometry because it determines the electronic structure near the Fermi level giving raise to the observed ferromagnetism. As we will show in the next paragraphs, a high value of uniaxial pressure can convert the few layer graphene below the CNT into a thin film of diamond oriented in the (111) direction. The (111) diamond surface is a hexagonal lattice with lattice parameter close to that of a graphene sheet. Nevertheless, due to the sp3 nature of the bonds, one-half of the atoms at surface present a dangling bond (the other one-half are bound to the next atomic plane). Thus, some atoms of the diamond surface in contact with the tube make sp3 bonds with tube atoms, which changes the tube cylindrical symmetry, as is shown in the left panel of Figure 1. The part of the tube in contact with the surface becomes flat, and the similarity between tube and surface lattice parameters allows it to bind the (111) diamond-like phase as shown in Figure 2. One could expect that the flat part of the tube becomes an additional (111) plane in which one-half of the atoms (3 in 6 in an unit cell) make sp3 bonds with the diamond-like region below it. However, due the curvature (the tube indents the few layer graphene with applied pressure), 5/6 atoms of the flat part of the tube make sp3 bonds with the diamond-like phase as can be seen in Figure 1 (where it is possible to see five bonds between tube and diamond-like phase) and Figure 2. The carbon atom of the flat part of the tube that does not bind the diamond-like region (the green atoms in Figure 2) makes three covalent bonds. On the other hand, its first neighbors atoms (the blue atoms in Figure 2) make four covalent bonds. Because of such a chemical environment, the green carbon atom is sp3 hybridized; because it makes three bonds only, it presents a dangling bond. As we shall see, such a dangling bond has a strong effect on the electronic structure near the Fermi level, and it is the physical origin of the observed ferromagnetism. At zero pressure, the hybrid structure is energetically less stable than the carbon nanotube atop the five-layered graphene. The total energy per atom of the hybrid structure is 0.16 eV/ atom higher than the total energy per atom of the carbon nanotube deposited on five-layered graphene. Because of the presence of a diamond phase, the hybrid structure is more compact than the nanotube−graphene structure as can be seen in Figure 1. The lower volume of the hybrid structure suggests that it could be more stable under pressure than its counterpart. Indeed, we found that for values of pressure of about 100 kbar, the hybrid structure is the most stable. To investigate the stability of the structures shown in Figure 1, we systematically decreased the Z and Z′ distances in steps of 1 Å. In each step, the Z and Z′ distances were the only parameters kept fixed, while the other cell components the atoms coordinates were

scalar relativistic Troullier−Martins24 pseudopotentials in Kleinman−Bylander nonlocal form.25 The fineness of the real-space grid integration was defined by a minimal energy cutoff of 150 Ry.26 A 6 × 1 × 5 graphene unit cell was employed to represent the five-graphene layer. To sample the respective reciprocal Brilloin zone, a 2 × 6 × 1 Monkhorst− Pack grid was used. The geometries were fully optimized using the conjugate gradient algorithm27 until all of the force components were smaller than 0.05 eV/Å. The Kohn−Sham (KS) eigenfunctions were expanded as linear combination of pseudo atomic orbitals of finite range consisting of double-ζ radial functions per angular momentum (DZ). The range of each atomic orbital was determined by a common confinement energy-shift of δE = 0.01 Ry.28 The orbital confinement tends to shift the energy eigenvalues upward;29 however, it does not change the relative positions of the eigenvalues. Figure 1 shows the geometries of two studied systems: (i) (10,0) carbon nanotubes intercalated with five-layer graphene; and (ii) a hybrid structure in which the (10,0) nanotube makes sp3 bonds with five-layer graphene. The figure also shows the periodic images along the axis perpendicular to the graphene layers (z-axis). Along the tube axis (y-axis), the (10,0) nanotube

Figure 1. Left panel: Unit cell and a periodic image of a five-layer graphene intercalated with a semiconductor (10,0) carbon nanotube. This structure is the most stable at low pressures. Right panel: Unit cell and periodic image of the hybrid nanotube−graphene−diamond structure, most stable at high pressures. The rectangle indicates the nanotube/diamond phase contact geometry detailed in Figure 2. 8144

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function of the applied pressure. It is possible to see that the hybrid structure becomes the most stable for values of pressure of about 100 kbar. Such a value is significantly smaller than the value required to convert five-layered graphe into (111) diamond by means of application of unixial pressure obtained by Kvashnin et al., 150 kbar.30 Such a result shows that the presence of the tube facilitates the sp2 to sp3 conversion. Besides, the presence of tube stabilizes the sp3 phase, which is not stable for systems with less than 6 atomic layers.30 It is important to mention that our theoretical approach produces results in excellent agreement with those of Kvashnin et al.,30 who investigated the phase diagram of quasi-two-dimensional carbon in quasiharmonic approximation within the DFT/plane wave framework. In Figure 3 are also shown the enthalpies of graphite and diamond as a function of applied pressure where it is possible to see that diamond becomes more stable than graphite for pressures above 28 kbar; the value obtained by Kvashnin et al. is 24 kbar. Such values are also consistent with that obtained by Jiang et al.31 who obtained a value of roughly 70 kbar to convert graphite into diamond by application of hydrostatic pressure. The proposed hybrid structure presents an electronic structure that sharply differs from those of graphene and a (10,0) carbon nanotube. As can be seen in Figure 4a and b, the

Figure 2. Nanotube/diamond phase contact geometry (the other atoms of the hybrid structure were removed and two periodical images along the tube axis were added for clarity reasons). Upper panel: Front view. Lower panel: Upper view. The green atom presents a sp3 dangling bond, while its first neighbors (blue atoms) are 4-fold coordinated.

allowed to relax. Such a procedure simulates the effect of uniaxial pressure along the z-axis. Because the temperature is zero, the relative stability of the structures at a certain value of pressure is determined by their enthalpy: H = E0(Z) + PV, where E0(Z) is the total energy from the DFT calculations for different values of Z, P (the solid pressure) is minus the derivative of total energy with respect to volume, and V is the volume of fully relaxed cells. Figure 3 shows the enthalpy as a

Figure 4. (a) Density of electron states near the Fermi level of a (10,0) carbon nanotube. (b) Density of states of the (10,0) carbon nanotube alternated with few-layer graphene, projected on the nanotube atoms. (c) Density of states of the hybrid structure proposed in this work, projected on nanotube atoms.

simple deposition of the nanotube onto few-layered graphene does not affect its electronic structure. However, the presence of sp3 bonds in the tube/film contact region of the hybrid structure eliminates the cyclic boundary condition originally imposed on tube perpendicular wave vectors, and as a result the Van Hove singularities tend to disappear (Figure 4). The hybrid structure presents a peak in the density of states at Fermi level. To understand the physical origin of such a peak,

Figure 3. Enthalpy (H = E0(Z) + PV, where E0(Z) is the total energy from the DFT calculations, P is the solid pressure, and V is the fully relaxed cell volume) as a function of applied pressure. For values of pressure of about 100 kbar, the proposed hybrid structure is the most stable. 8145

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Figure 5. (a) Density of electron states near the Fermi level projected on atoms of the nanotube. (b) Density of states projeted on atoms in contact with diamond/few-layered film; see Figure 2. The green and blue lines represent, respectively, a green carbon atom and its neighboring blue atoms in Figure 2. In both panels, the vertical line indicates the Fermi level.

than the others (0.008 μBohr on average), which shows that the magnetic moment is essentially localized at the dangling bond. Because there is only one dangling bond per unit cell (see Figure 2), we perform a calculation using a supercell that contains two dangling bonds (twice as large along the tube axis) to check if the system is ferromagnetic or antiferromagnetic. The calculation using a double cell results in a total magnetic moment of 4 μBohr, which shows the ferromagnetic character of the hybrid structure. In summary, we propose in this work a hybrid structure that presents phases of the three extended allotropes of carbon: nanotube, graphene, and diamond. Because of the presence of sp3 bonds in the hybrid structure, it is energetically more stable than its counterpart (the nanotube deposited on few-layred graphene) at values of pressure of the order of 100 kbar. Because of the presence of a sp3 dangling bond, the hybrid structure presents an electronic structure that sharply differs from those of graphene, (10,0) nanotube, and diamond. The exceptionally large density of states near the Fermi level leads to ferromagnetism with the magnetic moment, with magnetic moments partially localized at the sp3 dangling bond.

we calculated the density of states of nanotube projected on atoms at the tube/film contact region. As can be seen in Figure 5a, the observed peak is essentially due to atoms at the contact region. Figure 5b shows that one atom of the contact region (the green atom of Figure 2) contributes to most of the peak, which strongly indicates that such a localized state is due to the dangling bond. As we mentioned before, such an atom makes three sp3 bonds leaving a sp3 dangling bond, which is consistent with the observed peak. Despite the fact that structures made of pure carbon rarely present magnetism,32 the exceptionally large density of states near the Fermi level shown in Figure 4c is characteristic of ferromagnetic materials, and therefore suggests the possibility of a ferromagnetic order. As can be seen in the left panel of Figure 6, which shows the band structure of the hybrid

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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 We acknowledge the support from the Brazilian agencies CNPQ and FAPEMIG, and from the project “INCT de nanomateriais de carbono”.

Figure 6. Band structure of the proposed hybrid structure. Left panel: Non spin polarized bands. Middle panel: Minority spin. Right panel: Majority spin. The arrows indicate the narrow bands that split spontaneously and the resulting spin polarized bands.

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structure, there are two narrow bands at the Fermi level that correspond to the observed peak in the density of states. If spin polarization is taken into account in the calculations, those bands split spontaneously into four bands (see right panels of Figure 6), two above and two below the Fermi level. Each spin channel presents a narrow band above the Fermi level, but both occupied bands are in the majority spin channel, which lead to a total magnetic moment per unit cell of 2 μBohr. A Mulliken population analysis shows that one atom (the green atom of Figure 2) presents a magnetic moment (0.8 μBohr) much higher

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