Electrical Control of Magnetization in Narrow Zigzag Silicon Carbon

J. Phys. Chem. C 2009, 113, 21213–21217

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Electrical Control of Magnetization in Narrow Zigzag Silicon Carbon Nanoribbons Ping Lou*,†,‡ and Jin Yong Lee*,† Department of Chemistry, Sungkyunkwan UniVersity, Suwon 440-746, Korea, and Department of Physics, Anhui UniVersity, Hefei 230039, Anhui, China ReceiVed: July 12, 2009; ReVised Manuscript ReceiVed: October 13, 2009

A first principles investigation of the electronic properties of narrow silicon carbon nanoribbons (SiC NRs) having zigzag-shaped edges passivated by hydrogen is presented. It is found that the zigzag SiC NRs exhibit interesting behavior. When an external transverse electric field is applied, the zigzag SiC NRs are converted to ferromagnetic metal from magnetic semiconductor. Interestingly, the magnetization direction depends on the field direction; i.e., the field direction is reversed, and the magnetization direction inverses. Thus, the ZSiC NRs may be utilized for spintronic devices by rendering the enhanced magnetization and changing the spin orientation. Introduction Spintronic devices are believed to be smaller, faster, and far more versatile than the conventional electronic devices, which act according to the following simple scheme: (1) information is stored (written) into spins as a particular spin orientation (up or down), i.e., the magnetization, (2) the spins, being attached to mobile electrons, carry the information along a wire, i.e., the spin-polarized electron transport, and (3) the information is read at a terminal. Its key feature is the control and manipulation of the “spin” of the electron, instead of its charge that is the focus of the electronic.1 It is noted that the graphene nanoribbons (NRs) offer a possibility of achieving these purposes.2-7 The graphene NRs are made by cutting the graphene sheets, where the edge carbon atoms are passivated by hydrogen. It was found that the graphene NRs can be either metallic or semiconducting depending on the width and structure of the edges.8-18 Notably, the zigzag graphene NRs (graphene nanoribbons with zigzag edges) are a magnetic semiconductor with a small band gap and have ferromagnetic ordering at each edge, and their spins at each edges are antiparallel.16,19-28 When a very strong transverse electric field is applied, the ZG NRs transform to half-metal,19-22where only one of the spin channels conducts, while the other remains insulating, which suggests possibilities for the control and manipulation of the spinpolarized electron transport by applying electric field. However, there are only a few examples that show a magnetization change under the applied electric field, and it has proven elusive to manipulate the magnetization by applying an electric field.29,30 Here, we report that the zigzag silicon carbon nanoribbons (ZSiC NRs) can be utilized for manipulating the magnetization by applying an electric field. The band structures of the narrow ZSiC NRs were recently studied,31,32 but their spin polarization under the electric field has not been investigated yet. We found that the ZSiC NRs showed a magnetization by a transverse electric field as well as the conversion of spin polarization. Thus, the ZSiC NRs may be utilized for spintronic devices by rendering the enhanced magnetization and changing the spin orientation.

Figure 1. (color online) Geometric structure of the zigzag SiC NR. SiC NR is periodic along the x direction. The 1D unit cell distance and the ribbon width are denoted by d and N, respectively. The large, middle, and small spheres denote Si, C, and H atoms, respectively.

Models and Methods In our model, N-zigzag SiC NRs are flat in the x-y plane, with N-zigzag chains along the x direction. The edges of zigzag SiC NRs are saturated by hydrogen atoms. Periodic boundary condition (PBC) is used to consider zigzag SiC NRs with infinite length, which is shown in Figure 1. Our calculations were carried out with the OPENMX computer code.33 The DFT within the GGA34 for the exchange-correlation energy was adopted. Normconserving Kleinman-Bylander pseudopotentials35 were employed, and the wave functions were expanded by a linear combination of multiple pseudo- atomic orbitals (LCPAO)36,37 with a kinetic energy cutoff of 200 Ry. The basis functions used were C6.0-s2p2d1, Si6.0-s2p2d1, and H4.5-s1p1. The first symbol designates the chemical name, followed by the cutoff radius (in bohr radius) in the confinement scheme, and the last set of symbols defines the primitive orbitals applied. We adopted a supercell geometry (Figure 1) where the length of a vacuum region along the nonperiodic direction (y, zdirections) was 20 Å, and the lattice constant along the periodic direction (x direction) was 3.11 Å. We used 120 × 1 × 1 k-point sampling points in the Brillouin zone integration. The geometries were optimized until the Hellmann-Feynman forces were less than 0.025 eV/Å. The convergence in energy was 3 × 10-7 eV. We have also increased the size of the supercell to make sure that it does not produce any discernible difference on the results. Results and Discussion

* E-mail: [email protected] (J.Y.L); [email protected] (P.L.). † Sungkyunkwan University. ‡ Anhui University.

As shown in Figure 2a, without external electric field, the ZSiC NR is a ferrimagnetic semiconductor with two different

10.1021/jp906558y CCC: $40.75  2009 American Chemical Society Published on Web 11/10/2009

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Figure 2. (color online) Band structures and spatial distribution of the spin differences of 4-ZSiC NR under an external electric field b Eext of strength (a) zero, (b) 0.1 V/Å, and (c) -0.1 V/Å along the y direction. For the band structures, the red solid and blue dash-dotted lines denote the spin-up and spin-down bands, respectively. The Fermi level is set to zero. For the spatial distribution of the spin differences, the red and blue surfaces represent the spin-up and spin-down, which was drawn by the XCrySDen (Crystalline Structures and Densities) program.38 The other marks are same as in Figure 1.

direct band gaps for the spin-up and the spin-down channels near the X point. The magnetic moment per cell of the ZSiC NR is almost zero, 0.00043 µB. When an electric field is applied toward the +y direction (shown in Figure 2b), i.e., from the edge C atoms to the edge Si atoms, the valence band of the spin-down channel and the conduction band of the spin-up channel cross each other, and both bands cross the Fermi level. Thus, the ZSiC NR is converted to the ferromagnetic (FM) metal. Simultaneously, the direction of the local magnetic moment at the edge C atoms is converted to spin-up from spindown, while the direction of the local magnetic moment at the edge Si atoms is unchanged. As a result, the magnetic moment per cell of the ZSiC NR is changed to 0.155 µB, which indicates that the ZSiC NR has been magnetized by a transverse electric field! On the other hand, as shown in Figure 2c, when an electric field is applied along the -y direction, i.e., from the edge Si atoms to the edge C atoms, the valence band of the spin-up channel and the conduction band of the spin-down channel cross each other, and both bands cross the Fermi level. The ZSiC NR is also converted to the FM metal. Simultaneously, the direction of the local magnetic moment at the edge Si atoms is converted to spin-down from spin-up, while the direction of the local magnetic moment at the edge C atoms is unchanged. As a result, the magnetic moment per cell of the ZSiC NR is -0.304 µB, which shows that not only the magnetization direction has been changed, but also the ZSiC NR has been magnetized. These novel phenomena demonstrate the possibility of tuning the directions of the local magnetic moment at the edge C and Si atoms of the ZSiC NRs, as well as of magnetizing the ZSiC NRs, by applying a transverse electric field.

Lou and Lee

Figure 3. (color online) Projected local density of states for the edge C and Si atoms of 4-ZSiC NR, respectively, under an external electric field b Eext of strength (a), (b) zero, (c), (d) 0.1 V/Å, and (e), (f) -0.1 V/Å along the y direction. In figures, the red solid and blue dash-dotted lines denote the up and down spin channels, respectively. The large and small spheres denote C and H atoms, respectively. The arrows of red solid and blue denote the direction of the spin-up and spin-down that are local on the corresponding edge atoms.

The above results can be understood from the projected local density of states for the edge C and Si atoms (Figure 3). As shown in Figure 3a, when the electric field is zero, for the edge Si atoms, the peak of PDOS in the spin-up channel is below the Fermi level, while the peak of PDOS in the spin-down channel is above the Fermi level. As a result, the edge Si atoms have spin-up local magnetic moment. On the other hand, for the edge C atoms, the peak of PDOS in the spin-down channel is below the Fermi level, while the peak of PDOS in the spinup channel is above the Fermi level; thus, the local magnetic moment of the edge C atoms is spin-down. As shown in Figure 3b, when an electric field is applied toward the +y direction, i.e., C f Si, there is no change in the PDOS for the edge Si atoms, and the local magnetic moment of edge Si atoms is unchanged. However, for the edge C atoms, the peak of PDOS in the spin-down channel is above the Fermi level, while the peak of PDOS in the spin-up channel is below the Fermi level. As a result, the local magnetic moment of the edge C atoms is converted to spin-up from spin-down. It is noted that when the field direction is reversed, i.e., C r Si, the opposite case occurs, which is shown in Figure 3c. Figure 4a and b show the band structures of ground state and corresponding spatial distribution of the spin differences of 4-ZSiC NR and 4-ZG NR, respectively. Note that both band structures near the Fermi surface are very different. Thus, it may be interesting to compare the ZG NRs and the ZSiC NRs. First, without external electric field, in the case of ZG NRs the two edge states are degenerate with opposite spin directions (Figure 4b). However, in the case of ZSiC NRs the spin-down and spin-up bands are not degenerate, i.e., a large band gap of 0.46 eV for the spin-down band at the X point and a small band gap of 0.03 eV for the spin-up band near the X point, which are shown in Figure 4a and Table 1. These can be understood as the following. In the case of ZG NRs, the two edges are terminated by the C atoms. Due to the spin-polarization mechanism, the C atoms at the two opposing edges possess spinopposite electrons, in order to lower the on-site Coulomb

Electronic Properties of SiC NRs

J. Phys. Chem. C, Vol. 113, No. 50, 2009 21215 TABLE 2: Voronoi Charges on the Edge Atoms up spin

down spin

sum

diff

1.184 1.195 1.286 1.318

2.503 2.470 2.432 2.503

0.135 0.080 -0.140 -0.133

2.272 2.184 2.280 2.271

4.411 4.439 4.412 4.411

-0.133 0.0711 -0.148 -0.131

Si ferrimagnetic state E ) 0.1 (V/Å) state E ) -0.1 (V/Å) state FM state

1.319 1.275 1.146 1.185

ferrimagnetic state E ) 0.1 (V/Å) state E ) -0.1 (V/Å) state FM state

2.139 2.255 2.132 2.140

C

TABLE 3: Mulliken Charges on the Edge Atoms up spin

down spin

sum

diff

1.676 1.698 1.829 1.837

3.514 3.492 3.485 3.514

0.162 0.096 -0.173 -0.160

2.273 2.212 2.284 2.272

4.408 4.496 4.416 4.408

-0.138 0.072 -0.152 -0.136

Si ferrimagnetic state E ) 0.1 (V/Å) state E ) -0.1 (V/Å) state FM state

1.838 1.794 1.656 1.677

ferrimagnetic state E ) 0.1 (V/Å) state E ) -0.1 (V/Å) state FM state

2.135 2.284 2.132 2.136

C Figure 4. (color online) Band structures of ground state and corresponding spatial distribution of the spin differences ((a) for 4-ZSiC NR and (b) for 4-ZG NR). The other marks are same as in Figure 2.

TABLE 1: Band Gaps of Spin-Up (∆v) and Spin-Down (∆V) Bands and Transverse Dipole Moment Per Cell (Dy) of the Ground State of the Widths (N) for the ZSiC NRs N

3

4

5

6

∆v (meV) ∆V (meV) Dy (D)

52.98 272.16 2.102

33.59 461.31 2.528

11.89 516.63 2.846

5.52 501.97 3.395

interaction U between electrons with opposite spin at the same site. On the other hand, because there is no electron transfer between the two opposing edge C atoms, there is no transverse charge polarization; hence, the two edge states of ZC NR are symmetric, i.e., degenerate. However, in the case of ZSiC NRs, the two edges are terminated by Si and C atoms, respectively. Due to the different electronegativities between Si and C atoms, electron transfers from Si to C atoms. Consequently, Si and C atoms are charged positively and negatively, respectively. As a result, a transverse internal electric field appears across the ribbons, as well as the transverse charge polarization (displayed by the transverse dipole moment per cell (Dy)). The quantity of the transverse internal electric field is measured simply by the transverse dipole moment per cell (Dy) of the ZSiC NRs; i.e., the large Dy means the large transverse internal electric field (refer to Table 1). For 4-ZSiC NR, the calculated Voronoi and Mulliken charges on the edge Si atoms and the edge C atoms are shown in Table 2 and Table 3, respectively, where the ferrimagnetic and ferromagnetic states are under zero external electric field. E ) 0.1 V/Å and E ) -0.1 V/Å states indicate the ground states under the corresponding external transverse electric field, respectively. The analysis of both the Voronoi and Mulliken charges for the edge atoms clearly shows that the edge Si atoms and the edge C atoms tend to possess less electrons and more electrons, respectively. Hence, there is a net transfer of electron from the edge Si atoms to the edge C atoms. For example, in the ferrimagnetic state (the ground state of system under zero external electric field), the net electron transfer calculated by the Voronoi method is 0.411, in agreement with the trends in

Mulliken charges, which show the electron transfer of 0.407. Thus, the transverse charge polarization leads to the break of the symmetry of the two edge states; i.e., the degeneracy of the two edge states is removed due to the corresponding different electrostatic potentials at the two sides of ZSiC NRs. In other words, if there was no net transfer of electron from the edge Si atoms to the edge C atoms, the two edge states of ZSiC NRs also might be degenerate like the case of ZG NRs. Moreover, the corresponding different electrostatic potential increases with the increase of ZSiC NR width (displayed by the Dy increasing with the widths (N) of the ZSiC NRs, refer to Table 1). As a result, as the ZSiC NRs width increases, the small band gap of the spin-up (∆v) decreases, while the large band gap of the spindown (∆V) first increases and then decreases at N ) 6, as noted in Table 1. However, the transverse charge polarization is not enough to make the small band gap of the spin-up (∆v) to be zero; hence, the ground state of the ZSiC NRs is semiconducting instead of half-metallic. It is noted that these behaviors are similar to that of ZC NRs gap under an external transverse electric field,19-21 where as the external transverse electric field increases, the band gap of one spin channel decreases, while the band gap of the other spin channel first increases and then decreases until ZC NR turns to the half-metallicity. When an external transverse electric field is applied, the degeneracy of the two edge states of ZG NRs vanishes, and, instead, the transverse charge polarization appears. Moreover, the transverse charge polarization increases with the electric field strength. When the maximum of the highest occupied valence band of the edge state of one side meets the minimum of the lowest unoccupied conduction band of the edge state of the other side, charge transfer occurs and the corresponding spin channel becomes metallic; hence, the ZG NR becomes half-metallic as reported previously by the Louie group.19 The valence and the conduction bands of only one spin channel meets the Fermi level, and thus the directions of the local magnetic moment at the two edges do not change. In contrast, for the ZSiC NRs, an external transverse electric field makes the directions of the local magnetic moment at the edge C and Si atoms exhibit novel response depending on the direction of the applied electric field

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and does not induce the half-metallicity. This implies that the effect of the electric field in the case of ZSiC NRs is not simple addition nor subtraction between the internal electric field and the external electric field, as can be found in Table 2 and Table 3. For example, when the external transverse electric field E ) 0.1 V/Å, the directions of the external transverse electric field are opposite to the directions of the transverse internal electric field. The external transverse electric field tends to increase the charges of the edge C atoms. Indeed, the charges of the edge C atoms increase to 0.028 in Voronoi charges and 0.089 in Mulliken charges. When the external transverse electric field E ) -0.1 V/Å, the directions of the external transverse electric field are the same as the directions of the transverse internal electric field. The external transverse electric field tends to decrease the charges of the edge C atoms. However, the charges of the edge C atoms still increase to 0.001 in Voronoi charges and 0.008 in Mulliken charges. In addition, the ZSiC NRs can be magnetized by the external transverse electric field, since the ferrimagnetic state semiconductor is converted to FM metal. It is noted that the predicted novel phenomenon is originated from the special band structures of ZSiC NRs and the external transverse electric field. In order to check the special band structures of ZSiC NRs, we carried out additional ab initio hybrid density functional calculations, as implemented in the Quantum-ESPRESSO package39 using the hybrid exchange density functional in the PBE0 form.40 The results show that the special band structures are robust with respect to the different treatments of electronic exchange and correlation even though the hybrid exchange density functional PBE0 gives a considerably modified description of the band gap (Figures S1 and S2). Moreover, from the comparison of the band structures of ZSiC NRs and ZC NRs, it can be concluded that the special band structures of ZSiC NRs arise from the action of the spin polarization mechanism and the transverse charge polarization. However, it should be pointed out that the different treatments of electronic exchange and correlation may lead to the quantitative difference in band structures, especially in band gap, which are similar to the case of ZC NRs.20,21 Hence, the quantity of the critical external transverse electric field that ZSiC NRs convert to FM metal is dependent on the treatments of electronic exchange and correlation, and further study is necessary for more detail. It is noted that in the case of graphene nanoribbons there are many factors that can affect the presence of the ferromagnetism of the edges. For example, Koskinen, Malola, and Ha¨kkinen found that the zigzag edge is metastable and a planar reconstruction spontaneously takes place at room temperature.41 Boukhvalov and Katsnelson found that the magnetic state of edges in graphene nanoribbons may be unstable, with respect to oxidation and water dissociation at the edges.42 Moreover, Yazyev and Katsnelson have shown that the perfect order of the ferromagnetism of the edges is strongly affected by thermal excitations, thus imposing strict limitations on graphene nanoribbons spintronic devices.43 It is expected that some similar factors exist for spintronics devices based on ZSiC NRs. Nevertheless, the magnetic zigzag edges of ZSiC NRs would be a good candidate for novel spintronics devices despite the fact that no true long-range magnetic order is possible in one dimension. In other words, we assumed that the magnetic interaction along the edge lines was FM and neglected the formation of a spin domain wall; i.e., we assumed that the length of the ribbon edges used in devices was smaller than the length of the magnetic order of zigzag edges of ZSiC NRs.

Lou and Lee Conclusions We found that the magnetic properties of the ZSiC NRs are shown to be tunable by an external transverse electric field. Especially, not only the directions of the local magnetic moment at the edge C and Si atoms respond to the transverse electric field, but also the ZSiC NRs can be magnetized by the transverse electric field. These novel phenomena originated from the special band structures of ZSiC NRs. Our findings open up a new route toward electrical control of magnetization, which may lead to some important applications of the ZSiC NRs in spintronics, such as switches and sensors. Acknowledgment. This work was supported by the Korea Science and Engineering Foundation (KOSEF) Grant funded by the Korean Government (MEST) (R11-2007-012-03002-0) (2009). This work was also supported by the Postdoctoral Research Program of Sungkyunkwan University (2008). Supporting Information Available: Band structures of N-ZSiC NRs (N ) 2, 3, 4, 5, and 6). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) |AhZutic´, I.; Fabian, J.; Das Sarma, S. ReV. Mod. Phys. 2004, 76, 323. (2) Kim, W. Y.; Kim, K. S. Nat. Nanotechnol. 2008, 3, 408. (3) Guo, J.; Gunlycke, D.; White, C. T. Appl. Phys. Lett. 2008, 92, 163109. (4) Mun˜oz-Rojas, F.; Ferna´ndez-Rossier, J.; Palacios, J. J. Phys. ReV. Lett. 2009, 102, 136810. (5) Leo´n, A.; Barticevic, Z.; Pacheco, M. Appl. Phys. Lett. 2009, 94, 173111. (6) Zheng, X. H.; Wang, R. N.; Song, L. L.; Dai, Z. X.; Wang, X. L.; Zeng, Z. Appl. Phys. Lett. 2009, 95, 123109. (7) Nguyen, V.; Hung; Do, V. Nam; Bournel, A.; Nguyen, V. L.; Dollfus, P. J. Appl. Phys. 2009, 106, 053710. (8) Castro Neto, A.; Guinea, F.; Peres, N.; Novoselov, K.; Geim, A. ReV. Mod. Phys. 2009, 81, 109. (9) Han, M. Y.; Ozyilmaz, B.; Zhang, Y.; Kim, P. Phys. ReV. Lett. 2007, 98, 206805. (10) Berger, C.; Song, Z.; Li, X.; Wu, X.; Brown, N.; Naud, C.; Mayou, D.; Li, T.; Hass, J.; Marchenkov, A. N.; Conrad, E. H.; First, P. N.; Heer, W. A. d. Science 2006, 312, 1191. (11) Ci, L.; Xu, Z.; Wang, L.; Gao, W.; Ding, F.; Kelly, K.; Yakobson, B. I.; Ajayan, P. Nano Res. 2008, 1, 116. (12) Chen, Z.; Lin, Y.; Rooks, M. J.; Avouris, P. Physica E 2007, 40, 228. (13) Cancado, L. G.; Pimenta, M. A.; Neves, B. R. A.; Medeiros-Ribeiro, G.; Enoki, T.; Kobayashi, Y.; Takai, K.; Fukui, K.; Dresselhaus, M. S.; Saito, R.; Jorio, A. Phys. ReV. Lett. 2004, 93, 047403. (14) Lee, H.; Son, Y. W.; Park, N.; Han, S.; Yu, J. Phys. ReV. B 2005, 72, 174431. (15) Ezawa, M. Phys. ReV. B 2006, 73, 045432. (16) Son, Y. W.; Cohen, M. L.; Louie, S. G. Phys. ReV. Lett. 2006, 97, 216803. (17) Ezawa, M. Phys. ReV. B 2007, 76, 245415. (18) Ezawa, M. Physica E 2008, 40, 1421. (19) Son, Y. W.; Cohen, M. L; Louie, S. G. Nature (London) 2006, 444, 347. (20) Hod, O.; Barone, V.; Peralta, J. E.; Scueria, G. E. Nano Lett. 2007, 7, 2295. (21) Kan, E. J.; Li, Z.; Yang, J.; Hou, J. G. Appl. Phys. Lett. 2007, 91, 243116. (22) Hod, O.; Barone, V.; Scuseria, G. E. Phys. ReV. B 2008, 77, 035411. (23) Fujita, M.; Wakabayashi, K.; Nakada, K.; Kusakabe, K. J. Phys. Soc. Jpn. 1996, 65, 1920. (24) Wakabayashi, K.; Fujita, M.; Ajiki, H.; Sigrist, M. Phys. ReV. B 1999, 59, 8271. (25) Barone, V.; Hod, O.; Scuseria, G. E. Nano Lett. 2006, 6, 2748. (26) Kudin, K. N. ACS Nano 2008, 2, 516. (27) Sawada, K.; Ishii, F.; Saito, M. Appl. Phys. Express 2008, 1, 064004. (28) Sawada, K.; Ishii, F.; Saito, M.; Kawai, T. Nano Lett. 2009, 9, 269. (29) Lottermoser, T.; Lonkai, T.; Amann, U.; Hohlwein, D.; Ihringer, J.; Fiebig, M. Nature (London) 2004, 430, 541.

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