Electronic and Magnetic Engineering in Zigzag Graphene

Article pubs.acs.org/JPCC

Electronic and Magnetic Engineering in Zigzag Graphene Nanoribbons Having a Topological Line Defect at Different Positions with or without Strain Q. Q. Dai, Y. F. Zhu,* and Q. Jiang* Key Laboratory of Automobile Materials, Ministry of Education, and Department of Materials Science and Engineering, Jilin University, Changchun 130022, China ABSTRACT: Using first-principles calculations, we perform a comprehensive study of the locations of a topological line defect (a line defect consisting of alternating pairs of pentagons and octagons or 585 LD) on the electronic and magnetic properties of zigzag graphene nanoribbon, with 12 zigzag chains (12-ZGNR) with or without tensile strain (ε). When ε = 0, it is found that 585 LD preferably forms near the edge. As 585 LD shifts from the center to the edge, the systems experience transitions from antiferromagnetic (AFM) semiconductors to an AFM half-metal and then to a ferromagnetic (FM) metal. As ε increases, the band gaps of the AFM semiconductors decrease and then the AFM semiconductors change into AFM half-metals. Finally, all the AFM systems turn into FM metals. The critical ε values of these transitions decrease as 585 LD moves to the edge. A similar behavior can also be found in 8- and 16-ZGNRs. However, the AFM half-metal region disappears in 8- and 16-ZGNRs due to different variation tendencies of the critical ε values for the electronic and magnetic phase transitions with the width of ZGNRs. These intriguing electronic and magnetic modulation behaviors make such defective ZGNRs very useful in nanoelectronic and spintronic devices.

1. INTRODUCTION Low-dimensional carbon-based nanomaterials, such as graphene and graphene nanoribbons (GNRs), have attracted considerable attention in recent years due to their extraordinary physics and promising applications in future nanoelectronics.1,2 Nevertheless, various applications of graphene and GNRs require that their electronic properties can be properly modulated at nanoscale. A general method is chemical functionalization or doping, which has been widely investigated using various techniques.3−6 Because the electronic properties of graphene and GNRs originate from their specific structures, the lattice modification at the atomic level is essentially needed to tune their electronic structures.1,2 Indeed, introducing topological defects of nonhexagonal rings in the honeycomb lattice is an effective way to tailor the local properties of graphene-based nanomaterials and to achieve new functionalities for suitable applications. Theoretically, such topological defects are predicted to change not only the electronic structures, 7−14 but also the chemical activity 15,16 and thermal17−19 properties. For example, topological defects in graphene can be used as the centers of chemical activity. Many transition metal atoms can form covalent bonds with the defects, which change the electronic properties of graphene by charge injection from metal atoms and point to a possible application of such composite structures in catalysis.16 The topological defects are usually characterized by pentagonal and heptagonal rings in the hexagonal carbon lattice (for instance, Stone-Wales and 555−777 defects), which © 2013 American Chemical Society

can appear during growth process and be deliberately introduced by ion irradiation.20−22 Furthermore, diffusion, coalescence, and reconstruction of these nonhexagonal rings have been studied by both theoretical and experimental techniques.22−25 In addition to the point defects, the extended line defect (LD) composed of alternating pentagon-heptagon (5−7) structure has also been observed during chemical vapor deposition growth on Cu substrate.25−29 And this 5−7 LD has been confirmed to have enormous influences on the mechanical29−31 and electronic7−10,32,33 properties of graphene-based materials. In particular, when the linear array of 5−7 rings are embedded in GNRs, the hybrid GNRs consisting of both armchair- and zigzag-like segments are formed and predicted to possess unique electronic and transport properties that differ from the pristine zigzag and armchair GNRs.9−11 Just recently, Lahiri et al. discovered that by using Ni(111) surface as a substrate, a new LD can be formed when two graphene sheets with different crystallographic orientations are translated to each other and then coalesce.34 Differing from the previous 5−7 LD, this topological defect consists of a line of alternating pairs of pentagons and octagons (585 LD), which can act as a conducting metallic wire when embedded in the perfect graphene.34 By engineering the topological LD, localized electronic states are introduced at Fermi level (EF) Received: July 11, 2012 Revised: February 13, 2013 Published: February 15, 2013 4791

dx.doi.org/10.1021/jp3068987 | J. Phys. Chem. C 2013, 117, 4791−4799

The Journal of Physical Chemistry C

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Figure 1. (a−f) Optimized structures of N-585-M systems. The gray and white balls denote carbon and hydrogen atoms, respectively. (g) Total energies of the N-585-M systems by choosing the energy of 6-585-6 system as a reference. The solid line serves as a guide to the eye.

ZGNRs) are adopted. Here, we mainly present the calculated results of 12-ZGNR with 585 LD because the other two defective ZGNRs display the similar behaviors. For 12-ZGNR with 585 LD, pentagon pairs and octagon are arranged alternatively along the ribbon axial direction, as shown in Figure 1a−f. Such defective ZGNR can be considered as two ZGNR parts connected by C−C dimer lines. As shown in Figure 1a, when the C−C dimer lines are placed at the middle part of the 12-ZGNR (6 zigzag chains on both sides of C−C dimer lines), 585 LD locates at the center of ZGNR. The position of 585 LD is changed by gradually moving the C−C dimer lines to the left edge of 12-ZGNR. Figure 1f represents the limit case. Here we denote the 12-ZGNR with 585 LD as N-585-M, where N and M are the number of zigzag chains on the left and right sides of the C−C dimer lines, respectively. The dangling bonds at both edges are saturated by hydrogen atoms for all systems. The first-principles DFT calculations are performed using the CASTEP package47 with generalized gradient approximation (GGA) and Perdew−Burke−Ernzerhof (PBE) 48 as the exchange correlation function. Ultrasoft pseudopotentials49 is chosen for the spin-unrestricted computations. The Brillouin zone is sampled by 1 × 6 × 1 (1 × 10 × 1) k-points50 and the energy cutoff of 400 eV is chosen in the geometry optimization (electronic) calculations. The nearest distance between nanoribbons in neighboring cells is greater than 18 Å to ensure no interactions. For geometry optimization, both the cell in the axial direction and the atomic positions are allowed to fully relax until the convergence tolerances of energy, maximum force, and displacement of 1 × 10−5 eV, 3 × 10−2 eV/Å, and 1 × 10−3 Å are reached, respectively. Based on the optimized structures, the tensile ε along the ribbon axis direction is realized by modulating the corresponding lattice parameters. Under different ε, only the atomic positions are relaxed to find the equilibrium states.

and the charge distribution within the defect regions can be created and well controlled.35−38 Especially, when 585 LD is introduced in graphene and carbon nanotubes, these systems exhibit ferromagnetic ordering consisting solely of 3-fold coordinated C atoms without carrier doping or network termination imposed by vacancies or edges.35,36 This suggests such defective carbon nanomaterials as promising candidates for applications in future spintronic nanodevices. However, to our knowledge, there has been hardly any systemic work studying the influence of 585 LD on GNRs in detail. On the other hand, graphene samples grown on substrates are subjected to moderate mechanical strain due to surface corrugation or lattice mismatch.39−41 This mechanical deformation can affect the electronic properties of graphene materials and thus have significant impact on their device applications. Previous theoretical studies have demonstrated that the application of external strain provides a simple and practical method to continuously tune the electronic properties of graphene-based materials.42−46 For example, the band gap of armchair GNRs can change in a zigzag manner under uniaxial strain.42−44 For bilayer graphene, an interlayer electric field can be generated by applying homogeneous strains with different strengths, thereby opening a band gap.45 These suggest a maneuverable approach to fabricate electromechanical devices based on carbon nanomaterials. Accordingly, it is also significant to gain physical insight into the effect of external strain on the electronic structures of GNRs with 585 LD. In this contribution, we employ first-principles density functional theory (DFT) calculations to investigate the effects of the position of 585 LD relative to the edge on the electronic and magnetic properties of zigzag GNRs (ZGNRs). Meanwhile, the influences of the defect location on these properties under tensile strain (ε) have also been considered, which demonstrate a significantly different characteristic from the pristine ZGNRs.

2. COMPUTATIONAL METHODS For ZGNR, the ribbon width (W) is defined by the number of zigzag chains perpendicular to the axial direction. In our simulation, the ZGNRs with W = 8, 12, and 16 (8-, 12-, and 16-

3. RESULTS AND DISCUSSION Previous theoretical studies have demonstrated that the pristine ZGNRs exhibit an antiferromagnetic (AFM) ground state.51,52 4792



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Figure 2. (a−f) Band structures of N-585-M systems. Black and red lines denote spin up and down energy bands, respectively (The color used to distinguish the spin energy band is also applicable to other figures below). The Fermi level (EF) is set to zero, and the first conduction (valence) band above (below) the EF is labeled as C1 (V1). The Eg values for the N-585-M systems are given below their corresponding band structures.

Figure 3. (a) Charge density isosurfaces of bands C1 and V1 for spin up and down states for 5-585-7 system. (b) Total DOS and PDOS of 5-585-7 system. Black, blue and red dotted lines denote the total DOS of the whole system, the PDOS of the defect site and the edge atoms, respectively. The EF is set to zero. (c) Charge density isosurfaces of bands C1 and V1 for spin up and down states for metallic system 1-585-11. The value of the isosurfaces is 0.02 e/Å3.

However, when 585 LD is introduced, the corresponding ground state may be influenced. To find the most stable magnetic configurations, the energies of ferromagnetic (FM) and AFM states for the 6-585-6, 5-585-7, 4-585-8, 3-585-9, 2585-10, and 1-585-11 systems are calculated. The calculated energy differences (ΔE = EFM − EAFM) between FM and AFM states for the six systems are 9.80, 9.37, 6.76, 3.51, 1.83, and −0.26 meV, respectively. This indicates that the position of 585 LD has a great effect on the magnetic configurations of the N585-M systems. As 585 LD moves from the center to the left edge, the systems experience a transition from AFM (for 6-5856, 5-585-7, 4-585-8, 3-585-9, and 2-585-10 systems) to FM (for 1-585-11 system) state.

Based on the calculated ground states, the relative stability of these N-585-M systems is investigated. As shown in Figure 1g, we compare their total energies by choosing the energy of 6585-6 system as a reference. The result shows that as 585 LD shifts away from the center to the left edge of 12-ZGNR, the total energies of these N-585-M systems become more and more negative. Especially, there is a large drop in energy from 3-585-9 to 1-585-11 system, which indicates that 585 LD prefers forming near the edge. Furthermore, as 585 LD moves toward the left edge, the lattice parameters in axial direction increase gradually, which are 4.9088 Å for 6-585-6, 5-585-7, 4585-8, and 3-585-9 systems, 4.9118 Å for 2-585-10 system, and 4.9178 Å for 1-585-11 system, respectively. 4793



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to the reduction of Eg for the semiconducting N-585-M systems. For the metallic system 1-585-11, partial of the electronic states near the EF exhibit distinct characteristics compared with other systems. As shown in Figure 3c, the electronic distribution for the spin down state of C1 is only localized on the right edge of ZGNR, which differs from the corresponding electronic states of the other systems that are contributed by 585 LD. It can also be seen from Figure 2f that this energy band displays an edge state character as that in pristine ZGNR. The electronic distribution for the spin up state of V1 is concentrated on both of the defect site and right edge of ZGNR, which are also different from other systems. For the spin up state of C1, the electron states distribute on the two edges and defect site. For the spin down state of V1, the electron states mainly distribute on the left edge and defect site. As shown in Figure 2f, the two energy bands show a similar trend and cross the EF around the Γ point, which lead to a metallic character of the 1-585-11 system. Previous theoretical studies have shown that when 585 LD is embedded in graphene sheet or armchair carbon nanotubes, the polarized electron spins are strongly localized on the atoms connected to the C−C dimers and ferromagnetically aligned along the extended LD.35,36 However, when 585 LD is introduced in ZGNR, the spin ordering along the defect exhibits different characteristics. As shown in Figure 4a and b,

Due to the existence of edges, the electronic properties of N585-M systems exhibit unusual features differing from the metallic character of graphene with 585 LD.34,35 Figure 2a−f displays the band structures of the six N-585-M systems. It can be seen that the band structures of N-585-M systems vary with the different locations of 585 LD in ZGNR. The energy bands of 6-585-6 system for both spins are degenerate, whereas for other N-585-M systems, the energy bands near the EF split into two subbands (spin up and spin down) and exhibit some deformation. When 585 LD moves gradually to the left edge, the degree of splitting and deformation becomes stronger. As shown in Figure 2a−d, the four systems of 6-585-6, 5-585-7, 4585-8, and 3-585-9 are semiconductors with indirect band gaps (Eg). The conduction band minimum (CBM) for 6-585-6 and 5-585-7 systems locates at gamma (Γ) point, but deviates from Γ point for 4-585-8 and 3-585-9 systems. In contrast, the valence band maximum (VBM) keeps unchanged and always locates at A point. The relevant Eg values of these semiconducting N-585-M systems are given under each diagram. For 6-585-6 system, Eg = 0.16 eV. As 585 LD shifts away from the center, the Eg values for the four semiconductors decrease gradually. Compared with the calculated Eg value of pristine 12ZGNR (0.40 eV), the Eg values for these four semiconducting systems drop due to the 585 LD introduced impurity states near the EF (which will be discussed later). When 585 LD locates near the edge, the electronic properties of the two systems 2-585-10 and 1-585-11 exhibit interesting behaviors. The 2-585-10 system displays a half-metallic character, where the spin up and down states show the semiconducting and metallic behaviors, respectively, as shown in Figure 2e. However, for the 1-585-11 system, there is no Eg opening for both spin up and down states and, thus, it shows a metallic behavior (see Figure 2f). Moreover, the energy bands of this system change dramatically near the EF compared to other N585-M systems. To better understand the electronic states of these systems near the EF, the charge density isosurfaces of the conduction band C1 and valence band V1 for both spins have been analyzed. For the four semiconducting systems and the halfmetallic system 2-585-10, the electronic distributions of bands C1 and V1 for both spins display similar behaviors. Here, we take the system 5-585-7 as an example. As shown in Figure 3a, the spin down state of V1 is contributed by the defect site and right edge, and the spin up state of C1 is only contributed by the defect site, where the Eg of this system is determined by the two subbands. For the spin up state of V1, the electronic states mainly distribute on the left edge and defect site. As 585 LD moves close to the left edge, this band exhibits serious deformation, which indicates that a strong interaction exists between the left edge and defect site. Similar to the spin up state of C1, the electronic distribution for the spin down state of C1 also lies mainly on the atoms connected to the C−C dimers. For perfect ZGNRs, the electronic states near the EF are contributed by the two edges.51,52 When 585 LD is introduced in the ZGNR, the impurity states appear near the EF. The total and partial density of states (PDOS) for 5-585-7 system are plotted in Figure 3b, which also shows that the electronic states near the EF are determined by both the 585 LD and the two edges of ZGNR. It is well-known that the Eg of perfect ZGNR is determined by the two peaks marked by the red dashed lines near the EF. The PDOS shows that the 585 LD introduces impurity states within the Eg of the perfect ZGNR, thus leading

Figure 4. (a−c) Isosurfaces of the spin density distribution (Δρ = ρ↑ − ρ↓) for 6-585-6, 5-585-7, and 1-585-11 systems. Blue and yellow surfaces correspond to the isosurfaces of up (positive) and down (negative) spin density (the spin-polarized color identification scheme is also used in other figures below). The value of the isosurfaces is 0.005 e/Å3.

the two edges of ZGNR are still antiferromagnetically coupled, which is similar to the case of perfect ZGNRs.51−53 The magnetism on the atoms connected to the C−C dimers are antiferromagnetically aligned which can be ignored compared to those on the two edges. Since the ZGNR with 585 LD can be considered as a combination of two ZGNR parts by an array of C−C dimers, the atoms connected with the C−C dimers are antiferromagnetically coupled with their corresponding left and right edges, respectively. The calculated results demonstrate that the four semiconducting systems and the half-metallic system 2-585-10 possess a similar magnetic ordering and their total magnetic moments are zero. However, for the metallic system 1-585-11 displayed in Figure 4c, the magnetic alignment on the two edges of the system become FM ordering, and the magnetism on the left edge (0.08 μB per C atom) is weaker than that on the right edge (0.33 μB per C atom), which makes a total magnetic moment of 0.88 μB for this system. Note that when 585 LD is shifted to the right edge of 12ZGNR, a similar effect of the defect location on the electronic 4794



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Figure 5. (a) Energy difference (ΔE) between FM and AFM states versus tensile ε for the N-585-M systems, where the dashed line denotes the zero energy difference. The solid circles, triangles, stars, squares, inverted triangles, and rhombus represent the ΔE of the systems 6-585-6, 5-585-7, 4-5858, 3-585-9, 2-585-10, and 1-585-11, respectively. (b) Spatial spin density distribution of the 5-585-7 system under the tensile ε of 1.0, 2.0, and 5.0%. The value of the isosurfaces is 0.005 e/Å3. (c) Total magnetic moments for the N-585-M systems. The symbols represent the same systems as in (a).

Figure 5b, at the AFM state (ε = 1.0%), the spin ordering is antiferromagnetically coupled between the two edges, but ferromagnetically coupled along the C atoms connected to the C−C dimers. And the total magnetic moment is little. When ε ≥ 1.9%, the magnetic configuration of this system becomes FM state, in which the magnetic coupling between the two edges changes from antiparallel to parallel. The atoms connected to the C−C dimers are still ferromagnetically aligned, but are antiferromagnetically aligned with their corresponding left and right edges, respectively. Moreover, the spin densities on the two edges and 585 LD increase with increasing ε, which is consistent with the enhanced stability of the FM state as discussed above. The spin ordering of the system 2-585-10 at FM state is similar to that of the 5-585-7 system. For the metallic system 1-585-11, the spin ordering on the defect site transforms from antiferromagnetically to ferromagnetically coupled when ε ≥ 5.0%, while on the two edges remain ferromagnetically coupled. The total magnetic moments of all the N-585-M systems under ε are presented in Figure 5c. The calculated results demonstrate that the magnetism is mainly contributed by the two edges and 585 LD, and the magnetic moments on the two sites increase slowly as ε increases, but the total magnetic moments of these systems change little (0.9−1.1 μB). For pristine ZGNRs, Eg increases monotonously with tensile ε.42−44 However, when 585 LD is introduced, the electronic properties of N-585-M systems under tensile ε display different behaviors. For the two systems 2-585-10 and 1-585-11, there is still no Eg opening within the range of the applied tensile ε. The insensitivity of Eg with respect to ε suggests that the two metallic systems can act as the conducting wires in graphenebased electronics. For the semiconducting systems, the tensile ε

and magnetic properties can be found. Thus, we will neglect that case here. In general, graphene materials corrugate under compressive ε,53,54 which would affect their electronic properties. However, the size of the unit cell that is tractable in DFT calculations is too small to capture any long-range corrugations. Therefore, we next only investigate the influences of tensile ε on the magnetic and electronic properties of these N-585-M systems. Under tensile, ε, pristine ZGNRs always keep the AFM state as in the unstrained case.42−44 However, when 585 LD is introduced, a different magnetic behavior is found. Figure 5a gives the ΔE values of N-585-M systems as a function of ε. For the four semiconducting systems, when ε = 0, ΔE > 0 and their ground states are AFM configurations. As ε increases, ΔE decreases gradually. Then, at the critical ε (εc) of 2.0, 1.9, 1.8, and 1.2%, the AFM−FM transitions take place with ΔE < 0 for the four systems, respectively. And it is clear that the εc for this magnetic transition decreases gradually as 585 LD shifts away from the center. Further increasing tensile ε will lead to the ΔE more negative, which indicates that the FM states for these systems become more stable. For the half-metallic 2-585-10 system in the unstrained case, the ground state favors AFM configuration. When ε ≥ 0.7%, this system changes into the FM state. And the absolute values of ΔE are slightly larger than those of the system 3-585-9 at FM state (see Figure 5a). Note that the metallic system 1-585-11 remains FM configuration under ε = 1.0∼4.0% with ΔE values of −0.7∼−2.5 meV. Further increasing ε does not change the FM ground state even though the initial spin configuration is set as the AFM state. For the four semiconducting systems, the magnetic alignments on the edges and the defect site under ε are similar. Here, we use the system 5-585-7 as an example. As shown in 4795



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Figure 6. Spin polarized band structures of the systems (a) 6-585-6 under ε = 1.0, 1.7, and 1.9%; (b) 5-585-7 under ε = 1.0, 1.7, and 1.8%; (c) 4-5858 under ε = 1.0, 1.5, and 1.7%; and (d) 3-585-9 with ε of 0.4 and 1.0%. The EF is set to zero.

always reduces Eg to zero rapidly, where a transition from semiconductor to half-metal appears. The corresponding εc values for the electronic phase transition are 1.7, 1.7, 1.5, and 0.4% for the 6-585-6, 5-585-7, 4-585-8, and 3-585-9 systems, respectively. Further increasing tensile ε will make these AFM half-metallic systems turn into FM metals quickly. To better understand the effects of tensile ε on the electronic properties of N-585-M systems, spin-polarized band structures are calculated. We first discuss the cases of the four semiconducting systems. At the AFM state, the locations of VBM and CBM of 6-585-6 and 5-585-7 systems are the same as their unstrained cases until the zero gap points, as shown in Figure 6a,b. The band C1, which is completely contributed by 585 LD, is very flat and splits into a small band gap between the spin up and down bands around the Γ point. This is similar to the edge states of pristine ZGNRs51,52 and closely associated with the ferromagnetic ordering along the defect site discussed above.35,36 For the 4-585-8 system, the locations of VBM and CBM under tensile ε of 1.0% remain invariant. The C1 band for both spins is still degenerate around Γ point, which implies that the spin ordering on the defect site is still antiferromagnetically coupled. However, as ε further increases, the CBM moves to the Γ point, the VBM keeps unchanged, and the band C1 exhibits a similar characteristic of the systems 6-585-6 and 5585-7 (Figure 6c). For the 3-585-9 system, the locations of VBM and CBM as well as C1 do not change until the zero gap with ε = 0.4%. As ε reaches 1.0%, the C1 band change is the same as the systems 6-585-6 and 5-585-7, where the magnetic alignment along the defect becomes ferromagnetically coupled.

When the four systems become AFM half-metals, the spin up and down channels show semiconducting and metallic behaviors, respectively, as shown in Figure 6. For the four systems at FM state, the bands near the EF experience stronger spin splitting, as shown in Figure 7a,b. The electronic distributions of the bands near the EF show that the α and β bands are completely contributed by the defect atoms (Figure 7c,d). Around the Γ point, the two bands are very flat and separated by a gap. These characteristics are similar to the edge states of pristine ZGNRs and related with the ferromagnetic ordering along the defect site.35,36 Moreover, the gap between bands α and β around the Γ point broadens with the increased tensile ε, which is associated with the enhanced magnetism on the defect atoms.55 The distribution of energy bands for the system 2-585-10 near the EF under ε is similar to the 5-585-7 system at FM state, which is not further discussed here. For the metallic system 1-585-11, the band structures change little under the applied ε, which only involves rising and falling of the bands near the EF. As 585 LD moves from the center to the edge, the electronic and magnetic transitions of 12-ZGNR versus tensile ε are summarized in Figure 8b. Meanwhile, the cases of 8- and 16ZGNRs are also displayed in Figure 8a and c, respectively. In the unstrained case, as 585 LD shifts from the center to the edge, 8-ZGNR and 16-ZGNR also experience the transitions from semiconducting to half-metallic and then to metallic (Figure 8a,c). However, AFM configuration is always present for 8-ZGNR even if 585 LD is located at the edge (Figure 8a). Under tensile ε, the Eg values of all the semiconducting systems 4796



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metals, where the semiconductor−half-metal transition is absent. To understand this phenomenon, Figure 8d shows εc for the semiconductor−half-metal and AFM−FM transitions as functions of the W of ZGNRs when 585 LD locates at the center. It can be seen that as W increases, εc values decrease nonlinearly. When W lies between 10 and 14, the AFM halfmetal regions are present. However, when the W value is smaller than 10 or larger than 14, εc values for the electronic phase transition are higher than those of the magnetic transition, which make the semiconductor−half-metal transition disappear. Further, increasing the tensile ε to 5.0%, these systems remain the FM metallic, being similar to 12-ZGNR. As discussed above, the position of the 585 LD in ZGNR decides the intriguing electronic and magnetic properties and should be well controlled. It is known that the graphene with 585 LD can be formed by translating two graphene sheets with different arrangements relative to each other along the armchair direction34,56 or be realized by reconstruction from an array of divacancies,14,57 while a ZGNR can be cut from the graphene sheet by scanning tunneling lithography.58,59 Thus, through selecting the cutting location, the position of 585 LD in the ZGNR can be controlled. On the other hand, it is noteworthy that such 585 LD in BN nanoribbon is established by implanting C2 (or N2 or B2) dimers into a double hexagonal between the two ribbon domains.36,38 Because ZGNR has the same structure of BN nanoribbon, this technique could be introduced into ZGNR to design the position of 585 LD in ZGNR.

Figure 7. Spin polarized band structures of the system 5-585-7 under tensile ε (a) 2.0 and (b) 5.0%. The EF is set to zero. Charge density isosurfaces of bands α (c) and β (d) that are labeled in (a). The value of the isosurfaces is 0.02 e/Å3.

4. CONCLUSION In summary, the effects of 585 LD locations on the electronic and magnetic properties of 12-ZGNRs with or without tensile ε

for both 8- and 16-ZGNRs also decrease gradually. However, Eg is always larger than zero before the two ZGNRs become FM

Figure 8. Magnetic and electronic phase transitions for the defective (a) 8-, (b) 12-, and (c) 16-ZGNR vs tensile ε as 585 LD moves from the center to the left edge. (d) The variations of εc values for the semiconductor−half-metal (red circles) and AFM−FM (black squares) transitions with the W of ZGNRs when 585 LD locates at the center. 4797



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are systematically investigated using DFT calculations. The results show that the position of 585 LD affects significantly the electronic and magnetic properties of ZGNRs. Without ε, the 585 LD prefers to form near the edge. As 585 LD moves from the center to the edge, the systems experience transitions from AFM semiconductors to an AFM half-metal and then to a FM metal. The AFM semiconductors have indirect band gaps, which gradually decrease as 585 LD shifts close to the edge. By increasing tensile ε, Eg values of all the AFM semiconducting systems decrease and AFM semiconductors−AFM half-metal− FM metal transitions occur. However, for defective 8- and 16ZGNRs, there do not exist AFM half-metal regions before becoming FM metals because the εc values for the magnetic and electronic phase transitions display nonlinear decreasing trends with increased W of ZGNRs. Our work provides fundamental guidance for finding potential applications of such defective ZGNRs in the spintronic and electromechanical devices.

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AUTHOR INFORMATION

Corresponding Author

*Tel./Fax: 86-431-85095876. E-mail: [email protected]; [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge support by National Key Basic Research, Development Program (Grant No. 2010CB631001), and High Performance Computing Center (Jilin University).

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REFERENCES

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Electronic and Magnetic Engineering in Zigzag Graphene

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