J. Phys. Chem. C 2009, 113, 2273–2276
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Magnetic Properties of Fully Bare and Half-Bare Boron Nitride Nanoribbons Lin Lai,† Jing Lu,*,†,‡ Lu Wang,† Guangfu Luo,† Jing Zhou,† Rui Qin,† Zhengxiang Gao,*,† and Wai Ning Mei‡ Mesoscopic Physics Laboratory, Department of Physics, Peking UniVersity, Beijing 100871, P. R. China, and Department of Physics, UniVersity of Nebraska at Omaha, Omaha, Nebraska 68182-0266 ReceiVed: September 8, 2008; ReVised Manuscript ReceiVed: December 10, 2008
We calculate the electronic structures of the fully bare and half-bare zigzag-edged boron nitride nanoribbons by using density functional theory. We find that the ground states of both the fully bare boron nitride nanoribbons and the boron nitride nanoribbons with a bare N edge and a H-terminated B edge are halfmetallic. The alignment of the spin at the bare B edge is antiferromagnetic, while that at the bare N edge is ferromagnetic in the ground states of both the fully bare and half-bare zigzag-edged boron nitride nanoribbons. The H-terminated B or N edge of the half-bare zigzag-edged boron nitride nanoribbon exhibits no magnetism. Introduction Single-layer materials, especially graphene, have exhibited interesting physical phenomena and potential applications in nanoscale electronics.1,2 If terminated in one direction, these single-layer materials can be further fabricated into a new kind of quasi-one-dimensional structure called nanoribbons. The fabrication of nanoribbons with widths of ∼20 nm can be achieved by the method of lithographic patterning.3 By using chemical approaches, graphene nanoribbons with widths less than 10 nm have been successfully synthesized.4,5 All the narrow graphene nanoribbons are predicted to be semiconductors by using spin-polarized density functional theory (DFT) calculation.6-9 Remarkably, Son et al. predicted that H-terminated zigzag-edged graphene nanoribbons are halfmetals under a very strong external transverse electric field.8 Edge oxidization can reduce the onset electrical field required to induce the half-metallicity in zigzag-edged graphene nanoribbons.10 Yang et al. predicted that some wide graphene ribbons with NO2 at one edge and CH3 at the other edge are half-metals without resorting to an external electrical field.11 Possible halfmetallicity was also proposed recently for H-terminated BCN nanoribbons.12,13 Magnetism has already been suggested to exist at the defect sites of boron nitride sheets and at the open ends of boron nitride nanotubes by using DFT calculations.14-16 However, neither the localized spin-polarized edge states nor half-metallicity were found to exist in H-passivated boron nitride nanoribbons.12 In this Article, we study the electronic structures of the fully bare and half-bare zigzag-edged boron nitride nanoribbons (ZBNNRs) by using DFT calculation. We find that the fully bare ZBNNRs and the ZBNNRs with a bare N edge and a H-terminated B edge are half-metals. This half-metallicity is associated with the localized ferromagnetic edge state at the bare N edge of the ZBNNRs. The bare B edge behaves like a p-type dopant in the ZBNNR with a bare B edge and a H-terminated N edge. The H-terminated B or N edge has no magnetism. * To whom correspondence should be addressed. E-mail:
[email protected] (J.L.);
[email protected] (X.G.). † Peking University. ‡ University of Nebraska at Omaha.
TABLE 1: Relative Energies of the Spin-Unpolarized, Ferromagnetic, And Antiferromagnetic States of the B-8ZBNNR (N-8ZBNNR) in Units of meV per Edge Atoma magnetic moment spin(µB) unpolarized ferromagnetic antiferromagnetic B-8ZBNNR N-8ZBNNR
208 95
14 0
0 32
1.00 0.89
a The magnetic moment on each edge B (N) atom of the ground state of the B-8ZBNNR (N-8ZBNNR) is given in the last column.
Models and Methods In our model, nZBNNRs denote the fully bare ZBNNRs with n zigzag chains along the z-axis (Figure 1). B-nZBNNRs (NnZBNNRs) denote the nZBNNRs with one bare B (N) edge and one H-terminated N (B) edge. Fully H-terminated ZBNNRs are also calculated for comparison. Periodic boundary conditions and the supercell approximation are employed. The lattice constant along the x-axis (parallel to the ribbon plane) is 30 Å, and that along the y-axis (perpendicular to the ribbon plane) is 10 Å. Increasing these distances shows no remarkable changes in the total energy and the electronic structure of the nanoribbon. Spin-unrestricted DFT calculations are performed within the generalized gradient approximation (GGA) of Perdew-BurkeEmzerhof (PBE) form.17 The all-electron double numerical atomic orbital plus polarization basis set implemented in the DMol3 package18 is used. A 1 × 1 × 5 Monkhorst-Pack19 k-points grid is used for the integration of the first Brillouin zone. The convergence thresholds of geometry optimization are 3 × 10-4 eV on the total energy, 0.05 eV/Å on the maximum force on each atom, and 0.01 Å on the displacement of each atom. Results and Discussion The ground state of the fully H-terminated 8ZBNNR is a nonmagnetic insulator with an indirect gap of 4.26 eV, which agrees well with previous DFT calculations.12 Three possible spin configurations exist in the B-8ZBNNR. The ground state of the B-8ZBNNR is antiferromagnetic at the B edge and spinunpolarized at the H-terminated N edge. As shown in Table 1, it is 14 meV per edge atom more stable than the state with a
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Figure 1. Diagram of the fully bare 16ZBNNR. The N and B atoms are denoted by blue and pink balls, respectively.
TABLE 2: Energies per Edge Atom of the Different Spin-Polarized States and the Spin-Unpolarized State Relative to the Ground State, B(+-)/N(++), in the Fully Bare 8ZBNNR
Figure 2. Spin-polarized electronic structures of (a) B-8ZBNNR and (b) N-8ZBNNR in the ground state. The Fermi level is shifted to zero. The band structure is spin degenerated in panel (a).
ferromagnetic B edge and a nonmagnetic H-terminated N edge and 208 meV per edge atom more stable than the completely spin-unpolarized state. In view of the smaller energy difference (14 meV) between the ferromagnetic and antiferromagnetic states compared with the room temperature (26 meV), BZBNNRs may exhibit a paramagnetic behavior at room temperature. The average magnetic moment on the B atoms at the bare B edge is 1.0µB, and it is zero on the N atoms at the
spin configuration
E (meV)
B(++)/N(++) B(++)/N(--) B(+-)/N(+-) B(+-)/N(-+) B(+-)/N(++) B(++)/N(+-) spin-unpolarized state
7 7 7 7 0 13 128
H-terminated N edge. We present the electronic structure of the ground state for the B-8ZBNNR in Figure 2a. It has an indirect band gap of 4.07 eV, a value merely 0.20 eV smaller than that of the fully H-terminated 8ZBNNR. A flat partially filled impurity state appears in the indirect band gap and is about 1.5 eV above the valence band top, suggestive of a p-type insulator. Next, we calculate the magnetic property of the N-8ZBNNR. Three possible spin configurations exist in the N-8ZBNNR. The ground state of the N-8ZBNNR is ferromagnetic at the bare N edge and spin-unpolarized at the H-terminated B edge. As given in Table 1, it is 32 meV per edge atom lower in energy than the state with an antiferromagnetic N edge and spin-unpolarized B edge and 95 meV lower in energy than the completely spin-
Figure 3. Schematic representation of (a) B(+-)/N(++) (ground state), (b) B(++)/N(--), (c) B(+-)/N(+-), (d) B(+-)/N(-+), (e) B(++)/ N(++), and (f) B(++)/N(+-) states of the fully bare 8ZBNNR. The up and down arrows on the edge atoms denote the spin-up and spin-down directions, respectively. The N and B atoms are denoted by blue and pink balls, respectively. The relative total energies are labeled.
Fully Bare and Half-Bare Boron Nitride Nanoribbons
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Figure 4. Electronic structures of (a) B(++)/N(++), (b) B(++)/N(--), (c) B(+-)/N(+-), (d) B(+-)/N(-+), (e) B(+-)/N(++), and (f) B(++)/N(+-) states of both spin-up (red stars) and spin-down (blue circle) directions for the fully bare 8ZBNNR. The inset is the band structure of the B(+-)/N(+-) state with 0.0 e k e 0.15. The Fermi level is shifted to zero.
unpolarized state. The average magnetic moment on the N atom at the bare N edge in the ground state is 0.89µB. We present the ground state electronic structure of the N-8ZBNNR in Figure 2b. The ground state of the N-8ZBNNR has different electronic structures in the spin-up and spin-down directions: it is metallic in the spin-up direction, whereas it is insulating in the spindown direction with a band gap of 4.68 eV. Hence, the N-8ZBNNR is a typical half-metal. It probably can exist at room temperature without resort to an external electrical field in view of the fact that the energy difference (32 meV per edge atom) between the ferromagnetic and antiferromagnetic states is larger than room temperature (26 meV). The fully bare ZBNNRs have more complicated spin alignments than the half-bare B-ZBNNRs and N-ZBNNRs. The fully bare 8ZBNNR has six different spin-polarized states. They are denoted as B(++)/N(++), B(++)/N(--), B(+-)/N(+-), B(+-)/N(-+), B(+-)/N(++), and B(++)/N(+-) in Figure 3, where B and N indicate the B and N atoms at the bare edges, respectively, and the plus (+) and minus (-) in the parentheses represent the spin-up and spin-down directions, respectively. The ground state of the fully bare 8ZBNNR is the B(+-)/ N(++) state, where the spin is antiferromagnetically coupled at the B edge but ferromagnetically coupled at the N edge. As shown in Table 2, this ground state is 7-13 meV per edge atom lower in total energy than other five spin-polarized states and 128 meV per edge atom lower in total energy than the spin-unpolarized state. The smaller energy differences between the ground state and other spin-polarized states compared with the room temperature (26 meV) suggest that the fully bare ZBNNRs will exhibit paramagnetic behavior at room temperature. However, the high spin state, B(++)/N(++), could be stabilized by applying an external magnetic field or doping with transition metals. The energy difference between the B(++)/N(++) and B(++)/N(--) states is less than 1 meV, which implies that the spin coupling between the two spin-polarized edges is negligible. The electronic structures of the six spin-polarized states are presented in Figure 4. The B(+-)N(++), B(++)/N(++) and B(++)/N(--) states are half-metallic, with band gaps of 2.5 eV, 2.1 eV, and 2.2 eV, respectively, for the semiconducting channels of interest. The B(+-)/N(+-) and B(+-)/N(-+) states have a very small band gap (less than 0.01 eV), and the
two spin channels are degenerated. The B(++)/N(+-) state also has also a very small gap (less than 0.01 eV), but the two spin channels are polarized. Finally, we point out the magnetism of bare boron nitride nanoribbons strongly depends on the shape of their edges. We checked the unsaturated boron nitride nanoribbons with armchair edges and find no magnetic behavior. Similarly, magnetism is reported to exist only at the open zigzag end of the boron nitride nanotubes.16 The magnetism also only exists in zigzag-edged graphene nanoribbons, and armchair-edged graphene nanoribbons are nonmagnetic.6,7 Conclusions In summary, we have calculated the electronic properties of the fully bare and half-bare ZBNNRs. The ZBNNRs with a bare B edge and a H-terminated N edge is a p-type insulator, while both the ZBNNR with a bare N edge and a H-terminated B edge and that with two bare N edges turn out to be half-metals. Therefore, the bare N edge is critical to induce half-metallicity. After completion of this paper, we became aware of a recent paper of Barone and Peralta,20 who also found half-metallic behavior in fully bare ZBNNRs by using the PBE functional.17 The half-metallic spin channel opens a gap when using the Heyd-Scuseria-Ernzerhof (HSE) functional.21,22 However, half-metallic behavior can appear when an external electrical field is applied.20 Acknowledgment. This work was supported by the NSFC (Grant Nos. 10774003, 10474123, 10434010, 90606023, and 20731160012), the National 973 Project (Nos. 2002CB613505 and 2007CB936200, MOST of China), and the Nebraska Research Initiative (No. 4132050400) of the U.S.A. We thank Prof. Dan Wilkins for carefully reading this manuscript. References and Notes (1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Science 2004, 306, 666. (2) Novoselov, K. S.; Jiang, D.; Schedin, F.; Booth, T. J.; Khotkevich, V. V.; Morozov, S. V.; Geim, A. K. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 10451.
2276 J. Phys. Chem. C, Vol. 113, No. 6, 2009 (3) Han, M. Y.; Ozyilmaz, B.; Zhang, Y. B.; Kim, P. Phys. ReV. Lett. 2007, 98, 206805. (4) Li, X. L.; Wang, X. R.; Zhang, L.; Lee, S. W.; Dai, H. J. Science 2008, 319, 1229. (5) Wang, X. R.; Ouyang, Y. J.; Li, X. L.; Wang, H. L.; Guo, J.; Dai, H. J. Phys. ReV. Lett. 2008, 100, 206803. (6) Barone, V.; Hod, O.; Scuseria, G. E. Nano Lett. 2006, 6, 2748. (7) Son, Y. W.; Cohen, M. L.; Louie, S. G. Phys. ReV. Lett. 2006, 97, 216803. (8) Son, Y. W.; Cohen, M. L.; Louie, S. G. Nature 2006, 444, 347. (9) Yang, L.; Park, C. H.; Son, Y. W.; Cohen, M. L.; Louie, S. G. Phys. ReV. Lett. 2007, 99, 186801. (10) Hod, O.; Barone, V.; Peralta, J. E.; Scuseria, G. E. Nano Lett. 2007, 7, 2295. (11) Kan, E. J.; Li, Z. Y.; Yang, J. L.; Hou, J. G. J. Am. Chem. Soc. 2008, 130, 4224. (12) Nakamura, J.; Nitta, T.; Natori, A. Phys. ReV. B 2005, 72, 205429.
Lai et al. (13) Kan, E. J.; Wu, X.; Li, Z.; Zeng, X. C.; Yang, J.; Hou, J. G. J. Chem. Phys. 2008, 129, 084712. (14) Liu, R. F.; Cheng, C. Phys. ReV. B 2007, 76, 014405. (15) Si, M. S.; Xue, D. S. Phys. ReV. B 2007, 75, 193409. (16) Hao, S. G.; Zhou, G.; Duan, W. H.; Wu, J.; Gu, B. L. J. Am. Chem. Soc. 2006, 128, 8453. (17) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (18) Delley, B. J. Chem. Phys. 2000, 113, 7756. (19) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (20) Barone, V.; Peralta, J. E. Nano Lett. 2008, 8, 2210. (21) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. J. Chem. Phys. 2003, 118, 8207. (22) Heyd, J.; Scuseria, G. E. J. Chem. Phys. 2004, 121, 1187.
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