ARTICLE pubs.acs.org/JPCC
Edge States and Half-Metallicity in TiO2 Nanoribbons Andre A. Lino,†,‡ Helio Chacham,‡ and Mario S. C. Mazzoni*,‡ †
Departamento de Física, Universidade Federal do Piauí, Campus Ministro Petr^onio Portela-Bairro Ininga, 64049-550, Teresina, Piauí, Brazil ‡ Departamento de Física, ICEX, Universidade Federal de Minas Gerais, CP 702, 30123-970, Belo Horizonte, Minas Gerais, Brazil ABSTRACT: We apply first-principles calculations to investigate the existence and properties of edge states in TiO2 nanoribbons. We show that edge states may be found either in the gap region or defining the bottom of the conduction band. In both cases, the addition of electrons to the ribbons, which is facilitated by the large work function of TiO2 materials, may drive the systems to a half-metallic state, with conduction taking place along the edges and with only one spin component. We also show that a U-negativity phenomenology may show up in some configurations, resulting in the stabilization of the charged edges.
’ INTRODUCTION Magnetism in bulk materials is usually ascribed to elements with electrons in incomplete d- or f-shells. This is the case of some transition metals, such as Fe, Co, and Ni, as well as the rare-earth metal gadolinium. Compounds in which the chemical bonds are not fully formed in the ground state would also be potential candidates to have magnetic states, if it were not for the fact that frustrated bonds usually lead to nonstable compounds. However, the emergence of novel experimental techniques in connection with the rapid development of nanotechnology research has opened new avenues for the scrutiny of the matter and the development of novel materials at the nanoscale. For instance, the synthesis of carbon ribbons with widths below 10 nm has been reported1 and, more recently, a bottom-up scheme2 has been applied to fabricate carbon ribbons as narrow as 1.0 nm. In parallel, several inorganic nanostructures, such as TiO2 nanotubes,3 ZnO nanowires,4 and a great variety of nanoparticles have been synthesized. Concerning TiO2 materials in particular, protocols5,6 to fabricate ultrathin sheets were reported. The experiments were based on the evaporation of Ti on oxygen-covered Ru surfaces5 or Cu substrates6 followed by an annealing procedure. Hydrothermal techniques have also been employed7 using the reaction of TiO2 particles and NaOH solution. In this case, thin ribbons (e5 nm) were observed. Coming along with these experimental advances, theoretical studies have pinpointed the conditions for the observation of novel features originated from the interplay between structural, electronic, and magnetic properties.8 Carbon ribbons are a good example, with predictions of localized edge states,9,10 and half-metallicity when submitted to transverse electric fields.11 Monolayer TiO2 films have also been investigated by first-principles calculations,12 and in this case, it was shown that half-metallicity may be achieved if oxygen vacancies are produced at the edges. Theoretical results on magnetic states in defective carbon nanotubes13 and in inorganic r 2011 American Chemical Society
ribbons, such as GaN,14 ZnO,15 17 and MoS218 have also been reported. In this work, we focus on the study of the electronic properties of few layer TiO2 nanoribbons. We show the existence of edge states, and we show that they may be manipulated to produce half-metallicity. Distinct structural arrangements for the borders are considered, and the edge states may be found as gap levels or defining the bottom of the conduction band. We found that, in the ferromagnetic configuration, electronic doping may stabilize magnetic states with conduction solely with a spin component.
’ METHODS Our methodology is based on first-principles electronic structure calculations within the pseudopotential density functional theory (DFT)19 formalim. The generalized gradient approximation (GGA)20 is used as a parametrization for the exchange-correlation functional. We employed the SIESTA implementation,21,22 which makes use of norm-conserving pseudopotentials23,24 and a basis set composed of pseudoatomic orbitals of finite range.25 The geometries are relaxed until the maximum force component is less than 0.1 eV/ Å. ’ RESULTS AND DISCUSSION Rutile and anatase are the two most common bulk structural phases for TiO2. The former is the most stable, and the latter, less dense, is more favorable in nanostructures.26 In both cases, the Ti atoms are coordinated to six oxygen atoms which, in turn, are bound to three Ti atoms. In particular, the high reactivity of the [001] surface of the anatase phase makes it important for several applications involving catalytic activity. Recently, a synthesis protocol Received: March 2, 2011 Revised: August 5, 2011 Published: August 09, 2011 18047
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Figure 1. (a) Relaxed structure of a TiO2 infinite sheet. Ti and O atoms are indicated by blue and red circles, respectively. (b) Band structure associated with the geometry shown in (a). The inset shows the points of high symmetry in the Brillouin zone.
that leads to the stabilization of [001] facets in TiO2 nanostructures has been reported.27 Therefore, we have chosen anatase ribbons with a [001] surface to begin our study. As a reference for further comparisons, we show in Figure 1, parts a and b, respectively, the geometry and the electronic structure of an infinite sheet associated with our first model. The cut in the anatase structure produces a layer of 8.96 Å in height. At the surface, the Ti atoms lose one coordination. This layer presents an energy gap of 2.41 eV, at the DFT-GGA level of approximation, with the states at the bottom of the conduction band and at the top of the valence band predominantly localized at the 3d orbitails of Ti atoms and at 2p orbitals of O atoms, respectively. A first ribbon was obtained by cutting this layer, generating a structure oriented along the [010] direction, as shown in the relaxed geometry presented in Figure 2a: the width is 50.28 Å, and the edges are terminated by oxygen atoms in such a way as to keep the 6-fold coordination of the Ti edge atoms. Our first-principles calculations indicate that this structure presents a ferromagnetic configuration, degenerate with the antiferromagnetic solution within 0.01 eV, with a net moment of 8 μB predominantly localized at the edge oxygen atoms. More specifically, the edge atoms O1 and O2, indicated by arrows in Figure 2a, carry a net moment of 1.58 μB, while atoms O3 and O4 have a magnetic moment of 0.40 μB. The corresponding band structure is shown in Figure 2b. Each panel corresponds to a spin component. The interesting aspect in this plot is the existence of two sets of spin-polarized (empty) gap states. The first set is higher in energy and almost dispersionless, while the second set forms dispersive bands. These states are predominantly localized at the edges, as it is possible to see in the isosurface electronic density plot in Figure 2d, which describes the particular case of the lower energy set of gap states. An interesting property of TiO2 materials, which is behind several applications, such as catalysis and solar cells, is their high work function. That makes it easy for TiO2 materials to receive electrons from adsorbed molecules or even originated from other mechanisms, such as from attached porphyrin molecules, which, upon illumination, transfer electrons to the material. What would be the effect of the addition of electrons in the band structure described above? To answer this question, we performed additional fully optimized calculations for the ribbon in the charge state 2. The results, shown in Figure 2c, are quite intriguing: the
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Figure 2. (a) Relaxed structure of a TiO2 anatase nanoribbon. Ti and O atoms are indicated by blue and red circles, respectively. (b and c) Band structures of the neutral and negatively charged ( 2 e) systems, respectively. Black and red lines correspond to the two spin components. (d) Isosurface plot of the electronic density corresponding to the first set of gap states.
gap states seem to be stabilized by the additional charge and are found lower in energy, crossing the Fermi level, and leading the system to present half-metallicity. The stabilization of the charged edges resembles the U-negativity model proposed by Anderson in 1975.28 The idea can be understood in terms of a Hubbard model which contains an on site potential term in the Hamiltonian (U∑i nivniV) that depends on a parameter U and on the occupations for each spin component. The parameter U may be written as a sum of two contributions:29 a positive Coulomb interaction, describing the repulsion between electrons (Ue, which exists for two electrons occupying the site), and a negative bond strength term (UR) describing the covalent part of the binding energy, and which increases with the number of electrons. Adding electrons to the dangling bonds at the edges may cause atomic relaxations, increasing the contribution of the second term and leading to the U-negativity. In fact, we observed relatively large variations in the bond lengths associated with the oxygen edge atoms (indicated in Figure 2a) upon charging the system: the Ti O1 and Ti O2 bonds decreased by 0.08 Å, while the Ti O3 and Ti O4 decreased by 0.06 Å, on average. We estimate the U term in the Hubbard model as 0.45 eV. This is the average decrease in the gap state energies upon charging the system, relative to the top of the valence band (see Figure 2b,c). The overall result is the conduction with one spin component along the edges. This half-metallicity is similar to the one found at O-ended polar surfaces of ceramic oxides,30 such as ZrO2 and MgO, which is due to the existence of 2p holes originated by the lack of donor charge. This reasoning may be corroborated by a Mulliken population analysis. In fact, the oxygen atoms labeled O1 and O2 in Figure 2a have on average ∼0.7 and 0.8 less electrons in the 2p orbitals when compared, respectively, to 2p occupation in bulk anatase and to the average occupation of the other oxygen atoms in the ribbon structure (oxygen atoms rather than the eight edge atoms O1, O2, O3, and O4, on both sides). Moreover, upon doping with two electrons, our population analysis shows that the additional charge goes preferably to the edge oxygen atoms: more precisely, the two edges receive 0.964 electron, while the other electron is equally distributed among the other oxygen atoms of the structure. 18048
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Figure 3. (a) A second model for the anatase ribbon. This time the periodicity is along the [100] direction, and the top part is still the [001] surface. (b and c) Band structures of the system shown in (a) in two charge states: neutral and negatively charged ( 2 e), respectively.
Figure 4. (a) A third model for the anatase ribbon, consisting of only one slab with periodicity along the [100] direction. (b and c) Band structures of the system shown in (a) in two charge states: neutral and negatively charged ( 2 e), respectively.
We performed two additional calculations for anatase ribbons to check the generality of these conclusions with respect to the choice of geometric models. The first one is generated with a rotation of the ribbon described above: We kept considering the [001] surface, but we chose the periodicity along the [100] direction. The resulting ribbon, again with a width of 53.20 Å and with edges saturated in a similar way, is shown in Figure 3a. The results reveal the same basic phenomenology: The band structure of the neutral system, shown in Figure 3b, shows a set of dispersive spin-polarized gap states; upon inclusion of two electrons, these bands go down in energy and cross the Fermi level, as shown in Figure 3c. As for a thinner ribbon, consisting of a single TiO2 layer with periodicity along the [010] direction and represented in Figure 4a, the edge states are found defining the bottom of the conduction band and not within the gap region, as is clear in Figure 4b. Again, with two additional electrons, these bands decrease their energies, become spin-polarized, and cross the Fermi level, as shown in Figure 4c. Are these results restricted to anatase structures? To answer this question, we performed similar calculations for the rutile ribbon shown in Figure 5a. The band structure, represented in Figure 5b, is characterized by a gap energy of 2.0 eV (at GGA level) and by the absence of gap states. The inclusion of two electrons moves the Fermi level upward, as indicated in Figure 5c. The extra charge goes to the edges, and the corresponding states form a set of spin-polarized bands at the Fermi region. Another interesting model may be built based on the idea that the edge oxygen atoms may have their dangling bonds saturated
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Figure 5. Model for a rutile nanoribbon with a [001] surface and periodicity along the [100] direction. (b and c) Band structures of the system shown in (a) in two charge states: neutral and negatively charged ( 2 e), respectively.
Figure 6. (a) Model for a nanoribbon similar to that of Figure 2, but with hydrogen atoms (small black circles) saturating the oxygen edge atoms. (b) Band structure of the system shown in (a) for both spin components (left and right panels): the system is half-metallic even in the absence of electron doping.
by hydrogen atoms. We considered this model for the anatase ribbon of Figure 2a. The resulting geometry is shown in Figure 6a, in which four hydrogen atoms were added to make covalent bonds with oxygen atoms O1 and O2 (both sides). The corresponding band structure is shown in Figure 6b. Interestingly, we found that the system is half-metallic even in the absence of electron doping. Actually, the result is consistent with the previous analysis, if we think that in the present case it is the hydrogen atoms which provide, by means of the covalent bonds, the additional electrons to the 2p edge oxygen orbitals. It is important to mention that the physics described in this work concerns relatively thin slabs, and by increasing the thickness it is expected that structural reconstructions may eventually destroy edge states. Also, other surfaces might have been considered, such as the 001 reconstruction described by Lazzeri and Selloni.31 However, the calculations we have performed for rutile, anatase, for 100 and 010 oriented ribbons, and for distinct ribbon thicknesses show that the effects described are not a particularity of a specific choice.
’ CONCLUSIONS In summary, we investigated the existence of edge states in TiO2 nanoribbons and we described the possibility of half-metallicity 18049
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The Journal of Physical Chemistry C upon negatively charging the system. The behavior seems to be robust with the choice of structural model. Adsorption of donor molecules on top of anatase or rutile ribbons may be a practical way to confirm these predictions. For instance, porphyrin molecules may donate electrons to TiO2 upon illumination, which could lead to a half-metallic system triggered by light.
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(28) Anderson, P. W. Phys. Rev. Lett. 1975, 34, 953. (29) Allan, G.; Lannoo, M. Phys. Rev. Lett. 1991, 66, 1209. (30) Gallego, S.; Beltran, J. I.; Cerda, J.; Mu~ noz, M. C. J. Phys.: Condens. Matter 2005, 17, L451. (31) Lazzeri, M.; Selloni, A. Phys. Rev. Lett. 2001, 87, 266105.
’ AUTHOR INFORMATION Corresponding Author
*E-mail: mazzoni@fisica.ufmg.br.
’ ACKNOWLEDGMENT We acknowledge support from the Brazilian agencies CNPq, FAPEMIG, and Instituto do Mil^enio em Nanotecnologia-MCT. ’ REFERENCES (1) Li, X.; Wang, X.; Zhang, L.; Lee, S.; Dai, H. Science 2008, 319, 1229. (2) Cai, J.; Ruffieux, P.; Jaafar, R.; Bieri, M.; Braun, T.; Blankenburg, S.; Muoth, M.; Seitsonen, A. P.; Saleh, M.; Feng, X.; M€ullen, K.; Fasel, R. Nature 2010, 466, 470. (3) Kasuga, T.; Hiramatsu, M.; Hoson, A.; Sekino, T.; Niinhara, K. Langmuir 1998, 14, 3160. (4) Yang, D. S.; Lao, C.; Zewait, A. H. Science 2008, 321, 1660. (5) M€annig, A.; Zhao, Z.; Rosenthal, D.; Christmann, K.; Hoster, H.; Rauscher, H.; Behm, R. J. Surf. Sci. 2005, 576, 29. (6) Maeda, T.; Kobayashi, Y.; Kishi, K. Surf. Sci. 1999, 436, 249. (7) Yuan, Z. Y.; Colomer, J. F.; Su, B. L. Chem. Phys. Lett. 2002, 363, 362. (8) Enyashin, A. N.; Seifert, G. Phys. Status Solidi B 2005, 242, 1361. (9) Nakada, K.; Fujita, M.; Dresselhaus, G.; Dresselhaus, M. S. Phys. Rev. B 1996, 54, 17954. (10) Son, Y.-W.; Cohen, M. L.; Louie, S. G. Phys. Rev. Lett. 2006, 97, 216803. (11) Son, Y.-W.; Cohen, M. L.; Louie, S. G. Nature 2006, 444, 347. (12) He, T.; Pan, F.; Xi, Z.; Zhang, X.; Zhang, H.; Wang, Z.; Zhao, M.; Yan, S.; Xia, Y. J. Phys. Chem. C 2010, 114, 9234. (13) Alexandre, S. S.; Mazzoni, M. S. C.; Chacham, H. Phys. Rev. Lett. 2008, 100, 146801. (14) Tang, Q.; Cui, Y.; Li, Y.; Zhou, Z.; Chen, Z. J. Phys. Chem. C 2011, 115, 1724. (15) Botello-Mendez, A. R.; Martínez-Martínez, M. T; Lopez-Urías, F.; Terrones, M.; Terrones, H. Chem. Phys. Lett. 2007, 448, 258. (16) Botello-Mendez, A. R.; Lopez-Urías, F.; Terrones, M.; Terrones, H. Nano Lett. 2008, 8, 1562. (17) Chen, Q.; Zhu, L.; Wang, J. Appl. Phys. Lett. 2009, 95, 133136. (18) Li, Y.; Zhou, Z.; Zhang, S.; Chen, Z. J. Am. Chem. Soc. 2008, 130, 16739. (19) Kohn, W.; Sham, L. J. Phys. Rev. 1965, 140, A1133. (20) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (21) Ordejon, P.; Artacho, E.; Soler, J. M. Phys. Rev. B 1996, 53, R10441. (22) Soler, J. M.; Artacho, E.; Gale, J. G.; Garcia, A.; Junquera, J.; Ordejon, P.; Sanchez-Portal, D. J. Phys.: Condens. Matter 2002, 14, 2745. (23) Troullier, N.; Martins, J. L. Phys. Rev. B 1991, 43, 1993. (24) Kleinman, L.; Bylander, D. M. Phys. Rev. Lett. 1982, 48, 1425. (25) We employed a double-ζ basis set, and the range of each orbital was determined by an orbital energy confinement of 0.01 Ry. Test calculations in which polarization functions were included were not found to introduce any significant change in our results. (26) Zhang, H.; Banfild, J. F. J. Matter Chem. 1998, 8, 2073. (27) Yang, H. G.; Sun, C. H.; Qiao, S. Z.; Zou, J.; Liu, G.; Smith, S. C.; Cheng, H. M.; Lu, G, Q. Nature 2008, 463, 06964. 18050
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