Lower Electric Field-Driven Magnetic Phase Transition and Perfect

Letter pubs.acs.org/JPCL

Lower Electric Field-Driven Magnetic Phase Transition and Perfect Spin Filtering in Graphene Nanoribbons by Edge Functionalization M. Reza Rezapour,†,‡ Jeonghun Yun,†,‡ Geunsik Lee,*,‡ and Kwang S. Kim*,†,‡ †

Center for Superfunctional Materials and ‡Department of Chemistry, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulsan 44919, Korea S Supporting Information *

ABSTRACT: Perfect spin filtering is an important issue in spintronics. Although such spin filtering showing giant magnetoresistance was suggested using graphene nanoribbons (GNRs) on both ends of which strong magnetic fields were applied, electric field controlled spin filtering is more interesting due to much easier precise control with much less energy consumption. Here we study the magnetic/nonmagnetic behaviors of zigzag GNRs (zGNRs) under a transverse electric field and by edge functionalization. Employing density functional theory (DFT), we show that the threshold electric field to attain either a half-metallic or nonmagnetic feature is drastically reduced by introducing proper functional groups to the edges of the zGNR. From the current−voltage characteristics of the edgemodified zGNR under an in-plane transverse electric field, we find a remarkable perfect spin filtering feature, which can be utilized for a molecular spintronic device. Alteration of magnetic properties by tuning the transverse electric field would be a promising way to construct magnetic/nonmagnetic switches.

I

n magnetoelectric materials,1 the magnetism can be controlled by an electric field, which consumes low energy compared to applying a magnetic field and possesses great potential in memory applications as well as fundamental interests. However, employing these materials would not be highly useful because their composite systems are not effective while operative only at low temperatures.2 In order for these materials to be useful as devices, electric field control could be a useful option to make them operative at room temperature, as reported for thin films BiFeO3 and (In,Mn)As due to large hole-carrier-mediated ferromagnetic coupling and spin−orbit coupling.3−6 Given that the magnetic−electric coupling mechanism has been extensively studied for bulk materials, it could be better utilized in a nanoscale system due to strong Coulomb interaction. In particular, graphene and graphene analogues,7−10 attracting great attention in view of 2D physics and chemistry,11−17 can show intriguing spin states on their edges.18−22 Graphene nanoribbons (GNRs) having two localized electronic edge states23−28 show semiconducting behavior with a band gap depending on their width.29,30 Owing to the one-dimensional ballistic transport characteristics of GNRs, diverse applications for GNR-based devices have been explored.31−37 It is worth mentioning that roomtemperature ferromagnetism is experimentally observed in GNRs.38 The two localized electronic edge states are ferromagnetically ordered and antiferromagnetically coupled to each other, making zigzag GNRs (zGNRs) a promising material for spintronics applications.39−46 Despite studies on electronic/magnetic properties of zGNRs either under an external electric/magnetic field or with edge functionalization, the mechanism of alteration of electronic/magnetic properties has not been clearly addressed. Besides, no magnetic phase © XXXX American Chemical Society

transition in zGNRs was reported in the presence of an electric field beyond the necessary electric field for half-metallicity. Furthermore, we find that an enormous electric field is required to exhibit half-metallicity in pristine zGNRs, which will destroy the zGNR structure. In addition, the half-metallicity by edge functionalization predicted in previous works was based on nonrealistic structures. Thus, the half-metallicity in pristine zGNRs by either applying an external electric field only or edge functionalization only is purely hypothetical and far from reality. Utilizing DFT, we here elucidate the half-metallic and nonmagnetic properties of pristine and chemically realistic edge-modified zGNRs when an external transverse electric field is applied. We describe the full range of band gap variations of both spin components from spin splitting to half-metallic to nonmagnetic features of zGNRs in a unified picture of the onsite Coulomb interaction and electron accumulation/depletion. We show that the critical electric fields to observe halfmetallicity or nonmagnetic behaviors in zGNRs can be significantly decreased if appropriate functional groups are introduced to the zGNR edges. To this end, we consider different chemical functional groups to find more efficient edge decoration of zGNRs. Besides, in order to avoid instability of the full edge-functionalized zGNRs and facilitate experimental realization of the mentioned phenomena, we investigate the cases with lower coverage fraction of functional groups in the zGNR edges and also with wider zGNRs. The transmission Received: October 20, 2016 Accepted: November 23, 2016 Published: November 23, 2016 5049

DOI: 10.1021/acs.jpclett.6b02437 J. Phys. Chem. Lett. 2016, 7, 5049−5055

Letter

The Journal of Physical Chemistry Letters

Figure 1. (a) Atomic structure of pristine 8-zGNR with monohydrogen passivation under a transverse electric field. C1 and C2 represent two edge carbon atoms. (b) Energy gaps of spin-polarized edge states of pristine 8-zGNR versus a transverse electric field. (c) Alteration of the electron population on C1 and C2 edge carbon atoms. (d,e) Local spin density of states (LDOS) at three different electric fields for C1 and C2 atoms, respectively. For each, the upper (lower) peak represents the spin up (down) states.

Figure 1b, the spin up band gap starts to decrease at E = 0.2 V/ Å. This happens due to a significant electron accumulation in the empty spin state at C2 (or depletion of filled spin state C1), modifying the energy levels according to the mean-field on-site Coulombic interaction Eσ = U⟨n σ̅ ⟩, which is mainly attributable to the calculated energy levels. Here Eσ is the energy of the spin σ state, U represents the Coulomb repulsion between two electrons in one site, and ⟨nσ ⟩/⟨n σ̅ ⟩ is the average number of electrons with spin up/down. According to this interaction, a maximal spin up−down gap is obtained when |nσ − n σ ̅ | has the maximal value, and the gap decreases as it decreases from the maximum, and finally the gap disappears when |nσ − n σ ̅ | = 0. In Figure 1d, it is shown that on atom C1 the spin down (up) band at E = 0.5 V/Å shifts up (down) in energy level as compared to that of E = 0.1 V/Å. A similar behavior can be seen in Figure 1e. In a certain range of the E field, the halfmetallicity is maintained with accumulating/depleting electrons. Beyond the critical value (E = 0.8 V/Å in Figure 1b), both spin states sharing the same band gap have an equal number of electrons, and consequently, the spin splitting disappears (see the Supporting Information for a model calculation). In Figure 2a−f, the band structure modifications of pristine 8-zGNR for different electric fields are represented explicitly. It is shown that under a transverse electric field, edge bands are shifted along the electric field while keeping the initial antiferromagnetic orientation. At zero electric field, as shown in Figure 2a, spin up and down states are degenerate. By increasing the electric field, edge bands are separated due to the presence of the electric field (Figure 2b). As the magnitude of the electric field increases and exceeds the half-metallicity conditions, the spin-down states of two edges have almost the same energy equal to the Fermi level, as shown in Figure 2c (E = 0.5 V/Å), and under further increases of the electric field, the spin configuration changes abruptly prior to the paramagnetic transition. Partially occupied edge states at the Fermi level show spin separation, which results in weak ferromagnetism of the net magnetic moment of 0.03 μB/cell along the edge, as illustrated in Figure 2d,e. This effect originates from the local

profile of the edge-modified zGNRs under varying transverse electric fields elucidates how such graphene systems exhibit perfect spin filtering as promising chemistry-based systems for spintronics. We consider a pristine 8-zGNR where, as shown in Figure 1a, a transverse electric field is applied along its width. Here, following the conventional notation, “8” represents the number of zigzag chains along the width of the nanoribbon. Moreover, all structures studied in this work have an antiferromagnetically ordered ground state initially. Figure 1b illustrates spin up and spin down energy gaps versus the external transverse electric field. By applying an in-plane electric field, the band gap of the spin up increases to a maximum and then starts to decrease (from E = 0.2 V/Å) but remains semiconducting in the full range of the external electric field. At the same time, the spin down shows a decreasing band gap that becomes zero, though the band gap is retained in a certain range of electric field (0.3− 0.6 V/Å). The reason is that the electric field makes the conduction and valence bands of the down spin overlapped in energy and therefore the zGNR becomes a half-metal. Increasing the electric field further (over 0.6 V/Å) removes half-metallicity, and finally, the zGNR becomes nonmagnetic beyond a critical electric field (Ec) of 0.8 V/Å. Here we elucidate the mechanism responsible for these features that cover spin splitting to nonmagnetism in zGNRs. As the electric field increases, the number of electrons at each edge atom (C1/C2 in Figure 1a) decreases/increases, as shown in Figure 1c. A gradual decrease/increase causes a nonmonotonic variation of the gap between spin up and spin down bands near the Fermi level. In Figure 1d, at E = 0.0 V/Å, the spin down band is occupied, while the spin up band is empty, where the spin polarization is reversed for the other edge atom in Figure 1e. At E = 0.1 V/Å, the occupancies of spin down and up bands (Figure 1d,e) are slightly modified, with a change in peak positions and intensities as noted from the electron accumulation or depletion shown in Figure 1c. It is most likely that the two spin bands are simply shifted according to the modified local potential relative to those at the zero electric field, which increases/decreases the spin up/down band gap. Before the spin down band gap is closed, as shown in 5050


Letter


Figure 3. (a−c) 8-zGNR functionalized by O−H/N−O2, N−O2/N− H2, and O−H/C−N groups, respectively. (d) Spin up and spin down energy gaps of pristine and O−H/C−N-functionalized 8-zGNR in terms of the applied electric field. α (β) represents the spin up (down) energy gap for pristine 8-zGNR, while α′ (β′) indicates spin up (down) band gaps for O−H/C−N-functionalized 8-zGNR. (e−h) Band structure of O−H/C−N-functionalized 8-zGNR (two zGNR unit cells) with respect to the applied electric field.

Figure 2. Band structure of pristine 8-zGNR for different values of the applied electric field. The red/blue color represents the spin up/down states (in (a) and (f), the red color is hidden under the blue color).

site coulomb repulsion, the so-called Hubbard U term, between different spins. This behavior subsides after sufficient enhancement of the electric field and leads to perfect separation of two edge bands from the Fermi level, so that edge states become fully occupied/unoccupied and the system becomes paramagnetic (Figure 2f). Toward the experimental realization of half-metallic and nonmagnetic characteristics of zGNRs, we investigate the edgefunctionalized zGNRs. Even though the essential electric fields to observe the mentioned magnetic properties of pristine zGNRs are practically high, they can be significantly lowered provided that the edges of zGNRs are decorated by appropriate functional groups. For this purpose, we calculate necessary transverse electric fields to tune the magnetic properties of different edge-functionalized zGNRs. Figure 3a−c represents three chemically pragmatic edge-modified 8-zGNRs with different chemical functional groups, O−H, C−N, N−H2, and N−O2. We consider three different combinations of functional groups that result in perceptible spin splitting, O− H/C−N, N−O2/N−H2, and O−H/N−O2, where each configuration consists of an electron donating group at one edge and a withdrawing group at the other edge. We note that graphene can be etched along a selective crystallographic orientation (e.g., zigzag) with the scanning probe tip;47 thus, the functionalization scheme is feasible with etching under a specific chemical environment.48,49 Decoration with a given group is considered up to half-coverage for each edge because full decoration is less likely. All structures are optimized. Similar to the pristine zGNR case, we apply the transverse electric field along the width of edge-modified zGNRs. As in Figure 3d, chemical modification of the zGNR edges (O−H/ C−N in this case) drives the band gap region to shift toward the lower electric fields. Consequently, the required electric fields to observe half-metallic and nonmagnetic zGNRs decrease from 0.4 to 0.1 V/Å and 0.8 to 0.55 V/Å, respectively. Table 1 lists the range of the electric field in which halfmetallicity is preserved (ER) and critical electric fields to attain the nonmagnetic feature for pristine and three different functionalized zGNRs. It shows that the O−H/C−N edge decoration would be a proper structure because it offers a wider range of half-metallicity as well as much lower critical electric

Table 1. Calculated Ranges of Electric Field to Preserve Half-Metallicity (ER) and Critical Electric Fields (Ec) to Achieve Nonmagnetic zGNRs in Different Edge Decoration of zGNRs functional group

ER (V/Å)

Ec (V/Å)

pristine zGNR N−O2/N−H2 O−H/N−O2 O−H/C−N

0.4−0.6 0.3−0.5 0.2−0.4 0.1−0.4

0.8 0.75 0.6 0.55

field to obtain half-metallic or nonmagnetic zGNRs. Besides, unlike the pristine case, edge-decorated zGNRs represent spin splitting behavior even at zero external electric field. Later on, we will show that this property is beneficial to perform spin filtering in an advantageous way. For the band structure variation of the C−N/O−Hfunctionalized case, similar behavior is noted. Figure 3e−h summarizes the results of band structure calculation for the functionalized system. In Figure 3e, at zero electric field, edge band shifting is observed due to the presence of the functional groups. Applying an external electric field induces extra edge band shifting, which results in half-metallicity conditions in smaller electric fields compared to the pristine zGNR case. Figure 3f shows the band structure where the half-metallicity condition holds. After that, the electronic structure is significantly modified, similar to the pristine case shown in Figure 2e, where the edge-functionalized case shows high net magnetization of 0.26 μB/cell (two zGNR blocks) at E = 0.5 V/ Å, and the corresponding band structure of Figure 3g shows the ferromagnetic edge behavior at one edge while the other edge is nonmagnetic. Beyond the critical point, in Figure 3h, an almost vanishing magnetic moment at both edges is observed, similar to the pristine zGNR case. It is worth mentioning that switching the position of the functional groups to the opposite edges is equal to reversing the electric field direction. The behavior of the band gap variation 5051


Letter


approaches are rapidly developing.50,51 The other effective factor on Ec is the width of the zGNR. To investigate its efficacy, we calculate Ec for 6, 8, 10, 12, 14, and 16-zGNRs (see the Supporting Information). Our calculations show that the critical values of the electric field for wider edge-modified zGNRs would be lower than those for pristine zGNR52 (for example Ec = 0.4 V/Å for O−H/C−N-modified 16-zGNR). It allows one to utilize wider zGNRs and obtain half-metallicity or nonmagnetic zGNRs in lower electric fields, which is more convenient for practical applications. Finally, we study the transport properties of edge-modified zGNRs in the presence of the transverse electric field. To this end, we apply a 0.1 V bias voltage to O−H/C−N-functionalized 8-zGNR and tune the electric field. The bias voltage can be chosen with respect to the band gap discrepancies of spin components on the full range of the applied electric field to obtain the desired proportion of spin filtering. In higher bias voltages, one would observe both spin currents with remarkable difference in magnitude. Figure 5a schematically represents the utilized two-probe system constructed by O−H/C−Nfunctionalized 8-zGNRs. As shown in this figure, an external electric field is applied to the whole system including the electrodes and the device part. In Figure 5b, the current values in terms of applied electric field are presented. By turning the electric field, the spin down component shows nonzero current, while the transport channel for the other component is closed. By enhancing the electric field, the current for the down spin increases to its maximum and then decreases and becomes zero at a certain electric field. Though the spin up current is 0 for E > 0, the spin down current increases up to E ≈ 0.3 V/Å and suddenly dies out at E > 0.4 V/Å. On the other hand, while the spin down current is 0 for E < −0.2 V/Å, the spin up current increases down to E = −0.5 V/Å and suddenly dies out for E < −0.6 V/Å. Thus, we have only spin down current for 0 < E < 0.4 V/Å but only spin up current for −0.6 V/Å < E < −0.2 V/ Å. When E < −0.6 V/Å or E > 0.4 V/Å, both spin up and down currents die out. This behavior can be understood by noting that increasing the electric field reduces the band gap between the conduction and valence bands of the down spin and causes overlap between them. Overlapping conduction and valence bands means hopping from a localized state of one edge to the other edge, which leads to the shoulder peak at 0.0 < E < 0.2 eV/A, while the main peak at 0.2 < E < 0.5 eV/A is due to the intraedge hopping or intraband transition owing to the slightly dispersive band, as shown in Figure 3f. For spin up, the channel is fully blocked all over the applied electric field range. Also, the peaks of spin current appearing a little below the critical field could be due to the subtle ferromagnetism shown in Figure 4. Figure 5c,d shows the transmission profiles for E = 0.3 and 0.5 V/Å, respectively. As seen from Figure 5c, at E = 0.3 V/Å for a 0.1 V bias voltage, the spin down channel is open, while the spin up channel has no contribution within the given bias window. The situation is different at E = 0.5 V/Å. The spin up and down states share the same band gap, which is wider than the bias window, and therefore, the current is zero for both spin components. To show the preponderance of employing edgefunctionalized zGNR to design a spin-filtered transport device, we calculate the I−E curve of pristine 8-zGNR under the same bias voltage as that utilized to obtain the I−E curve of the O− H/C−N edge-decorated 8-zGNR (Vb = 0.1 V). As shown in Figure 5e, pristine zGNR requires a nonzero external electric field to exhibit spin-filtered current, which is E = 0.1 V/Å in this case and increases by enhancing the bias voltage. Contrary to

in the new configuration is the same with the earlier mentioned one except that the opposite spin direction shows halfmetallicity in this case. We investigate the behavior of the total magnetic moment (M) of both pristine and edge-modified 8-zGNRs. As already discussed based on the band structures represented in Figures 2 and 3, an antiferromagnetic or half-metallic configuration is more favorable before Ec due to different occupations of spin components (by the exchange coupling between spin states localized at opposite edges). Beyond Ec, the paramagnetic configuration is more stable because the two spin states are fully occupied or unoccupied. However, interestingly, our calculation reveals that at electric fields slightly lower than Ec, the system shows the ferromagnetic behavior that we already explained based on the band structures of the systems. These meanings are shown for C−N/O−H-functionalized 8-zGNR in Figure 4. This figure represents the total magnetic moment of

Figure 4. Total magnetic moment (M) of C−N/O−H edgefunctionalized 8-zGNR as a function of the in-plane transverse electric field. Each section represents the corresponding ground state under the specified electric field range. AFM, FM, and PM stand for antiferromagnetic, ferromagnetic, and paramagnetic, respectively.

the system for its ground state in terms of the applied electric field. For small electric fields, the total magnetic moment is almost zero, corresponding to the antiferromagnetic configuration. Then, as one can see, there are significant ferromagnetic moments of 0.37 and 0.14 μB at E = −0.6 and 0.4 V/Å, respectively. Beyond the Ec values, M is zero again and the system becomes paramagnetic. Variation of the magnetic moment of zGNR according to the potential difference between its edges would be promising in the way that it provides feasibility to design a magnetic/nonmagnetic graphene-based device that can switch between two possible states by tuning the transverse electric field. A fully edge-decorated GNR is problematic for certain functional groups (such as NO2) because there is a steric repulsion between nearest-neighbor functional groups that causes a large local strain near the edge of the modified zGNR at high coverage. One way to solve this issue is to reduce the fraction of functional groups on the edges. To see how the required values of the electric field to tune the magnetic properties of zGNR vary in terms of coverage fraction of functional groups, we calculate Ec for zGNRs with different densities of functional groups on the edges (see the Supporting Information). It is shown that partially edge-modified zGNR is more efficient than the pristine one and would still be applicable and adequate for practical demands as bottom-up 5052


Letter


Figure 5. (a) Schematic illustration of the two-probe system constructed by an O−H/C−N-functionalized 8-zGNR. Arrows represent the applied external electric field. (b) Current vs applied electric field (I−E) curve at 0.1 V bias voltage for the O−H/C−N-modified 8-zGNR. The downward triangles (red) represent the down spin current, and the upward ones (blue) denote the up spin current. (c,d) Transmission profiles for E = 0.3 and 0.5 V/Å, respectively. (e) I−E curve of a pristine zGNR at Vb = 0.1 V.

under an in-plane transverse electric field, we have shown that such systems show a perfect spin filtering effect with low electric fields and therefore can be employed as chemically functionalized spintronic devices. Using DFT combined with the nonequilibrium Green’s function (NEGF),53−55 we have reported the spin transport behavior of edge-modified zGNRs under various transverse electric fields. The POSTRANS code56,57 developed from the SIESTA package,58 TRANSIESTA codes,54 and UNISTRANS code (developed by Yun, J.; Lee, G.; Kim, K. S.)59 were employed in order to do DFT and DFT+NEGF calculations. The Ceperley−Alder form as parametrized by Perdew and Zunger in the local density approximation (LDA) was used to treat the exchange−correlation effects.60 The double-ζ polarization basis set, the Troullier−Martins pseudopotential,61 and the 200 Ry cutoff energy for the grid-mesh were employed in the calculations. The transmission is given by

the case of pristine zGNRs, our calculations show that edgefunctionalized zGNRs are capable of performing spin-filtered current at a zero external electric field for various ranges of bias voltage and leading to perfect spin filtering as promising building blocks of future spintronic devices. In summary, we have described the spin splitting, halfmetallicity, and nonmagnetism in pristine and chemically functionalized graphene systems in a unified picture and explain the variation of band gaps of spin components in the entire range of the applied electric field. Here we have shown that the critical electric fields to obtain half-metallic or nonmagnetic zGNRs can be drastically lowered by choosing proper functional groups based on realistic chemical structure such as C−N/O−H pair edge functionalization. However, even such edge functionalization alone does not show half-metallicity in the absence of an external electric field. Thus, to achieve halfmetallicity in zGNRs, we need both edge functionalizion and an external electric field. To demonstrate it, we show that the potential difference between two edges of a zGNR, raised by either an external transverse electric field or edge functionalization of the zGNR, alters its magnetic properties. On the basis of the on-site Coulomb repulsion, we elucidate that the charge transfer between two edges, that is, the electron accumulation/ depletion at both edges, describes the observed spin splitting, band gap variation of spin components, and magnetic phase transition in zGNRs. The possibility of switching a magnetic zGNR to a nonmagnetic one and vice versa using an electric field would open a new horizon to design graphene-based magnetic on/off keys applicable in future nanoelectronics and spintronics. The desired magnetic properties of zGNRs are also accessible in wider zGNRs and zGNRs with a small fraction of functional groups on their edges. Therefore, from study of the electron transport behavior of edge-functionalized zGNRs

T = Tr[ΓLG ΓR G†]

(1) †

where Tr represents the trace, ΓL/R = i[ΣL/R − ΣL/R ], with ΣL/R as the self-energy of the left/right electrode, and G denotes the Green’s function. The Landauer−Büttiker formalism is utilized to calculate the current I(E F , Vb) =

2e h

∫ τ(E , Vb[f (E , μs) − f (E , μd )] dE)

(2)

where μs/d = EF ± Vb/2 and EF is the Fermi energy.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.6b02437. 5053


Letter


■

Hydrogenated Graphene: From Spin-Splitting to Localization Effects. ACS Nano 2011, 5, 3987−3992. (15) Avdoshenko, S. M.; Ioffe, I. N.; Cuniberti, G.; Dunsch, L.; Popov, A. A. Organometallic Complexes of Graphene: Toward Atomic Spintronics Using a Graphene Web. ACS Nano 2011, 5, 9939−9949. (16) Wang, B.; Li, J.; Yu, Y.; Wei, Y.; Wang, J.; Guo, H. Giant tunnel magneto-resistance in graphene based molecular tunneling junction. Nanoscale 2016, 8, 3432−3438. (17) Avdoshenko, S. M.; Nozaki, D.; Gomes da Rocha, C.; González, J. W.; Lee, M. H.; Gutierrez, R.; Cuniberti, G. Dynamic and Electronic Transport Properties of DNA Translocation through Graphene Nanopores. Nano Lett. 2013, 13, 1969−1976. (18) Hyun, C.; Yun, J.; Cho, W. J.; Myung, C. W.; Park, J.; Lee, G.; Lee, Z.; Kim, K.; Kim, K. S. Graphene Edges and Beyond: Temperature Driven Structures and Electromagnetic Properties. ACS Nano 2015, 9, 4669−4674. (19) Wu, T. T.; Wang, X. F.; Zhai, M. X.; Liu, H.; Zhou, L.; Jiang, Y. J. Negative Differential Spin Conductance in Doped Zigzag Graphene Nanoribbons. Appl. Phys. Lett. 2012, 100, 052112. (20) Yang, X. F.; Zhou, W. Q.; Hong, X. K.; Liu, Y. S.; Wang, X. F.; Feng, J. F. Half-Metallic Properties, Single-Spin Negative Differential Resistance, and Large Single-Spin Seebeck effects Induced by chemical Doping in Zigzag-Edged Graphene Nanoribbons. J. Chem. Phys. 2015, 142, 024706. (21) Zheng, X. H.; Rungger, I.; Zeng, Z.; Sanvito, S. Effects Induced by Single and Multiple Dopants on the Transport Properties in Zigzagedged Graphene Nanoribbons. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 235426. (22) Munárriz, J.; Gaul, C.; Malyshev, A. V.; Orellana, P. A.; Müller, C. A.; Domínguez-Adame, F. Strong Spin-Dependent Negative Differential Resistance in Composite Graphene Superlattices. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 155423. (23) Kusakabe, K.; Maruyama, M. Magnetic Nanographite. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 67, 092406. (24) Yamashiro, A.; Shimoi, Y.; Harigaya, K.; Wakabayashi, K. Spinand Charge-Polarized States in Nanographene Ribbons with Zigzag Edges. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 68, 193410. (25) Lee, H.; Son, Y.; Park, N.; Han, S.; Yu, J. Magnetic Ordering at the Edges of Graphitic Fragments: Magnetic Tail Interactions between the Edge-Localized States. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 72, 174431. (26) Pisani, L.; Chan, J. A.; Montanari, B.; Harrison, N. M. Electronic Structure and Magnetic Properties of Graphitic Ribbons. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 75, 064418. (27) Barone, V.; Hod, O.; Scuseria, G. E. Electronic Structure and Stability of Semiconducting Graphene Nanoribbons. Nano Lett. 2006, 6, 2748. (28) Kim, W. Y.; Kim, K. S. Prediction of Very Large Values of Magnetoresistance in a Graphene Nanoribbon Device. Nat. Nanotechnol. 2008, 3, 408−412. (29) Yang, L.; Park, C. H.; Son, Y. W.; Cohen, M. L.; Louie, S. G. Quasiparticle Energies and Band Gaps in Graphene Nanoribbons. Phys. Rev. Lett. 2007, 99, 186801−186804. (30) Li, X. L.; Wang, X.; Zhang, L.; Lee, S.; Dai, H. Chemically Derived, Ultrasmooth Graphene Nanoribbon Semiconductors. Science 2008, 319, 1229−1232. (31) Pan, Z. H.; Liu, N.; Fu, L.; Liu, Z. F. Wrinkle Engineering: A New Approach to Massive Graphene Nanoribbon Arrays. J. Am. Chem. Soc. 2011, 133, 17578−17581. (32) Shin, Y. S.; Son, J. Y.; Jo, M. H.; Shin, Y. H.; Jang, H. M. HighMobility Graphene Nanoribbons Prepared Using Polystyrene Dip-Pen Nanolithography. J. Am. Chem. Soc. 2011, 133, 5623−5625. (33) Min, S. K.; Kim, W. Y.; Cho, Y.; Kim, K. S. Fast DNA Sequencing with a Graphene-Based Nanochannel Device. Nat. Nanotechnol. 2011, 6, 162−165. (34) Rezapour, M. R.; Rajan, A. C.; Kim, K. S. Molecular Sensing Using Armchair Graphene Nanoribbon. J. Comput. Chem. 2014, 35, 1916−1920.

Details of the Hamiltonian for the Hubbard model, local density of states and band structures, number of spin up and down electrons at each carbon atom, total number of electrons at each carbon atom, and variations of the critical electric field (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (G.L.) *E-mail: [email protected] (K.S.K.). ORCID

Kwang S. Kim: 0000-0002-6929-5359 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by National Research Foundation of Korea (National Honor Scientist Program: 2010-0020414) and KISTI (KSC-2014-C3-059, KSC-2014-C3-061).

■

REFERENCES

(1) Eerenstein, W.; Mathur, N. D.; Scott, J. F. Multiferroic and Magnetoelectric Materials. Nature 2006, 442, 759−765. (2) Matsukura, F.; Tokura, Y.; Ohno, H. Control of Magnetism by Electric Fields. Nat. Nanotechnol. 2015, 10, 209−220. (3) Heron, J. T.; Bosse, J. L.; He, Q.; Gao, Y.; Trassin, M.; Ye, L.; Clarkson, J. D.; Wang, C.; Liu, J.; Salahuddin, S.; et al. Deterministic Switching of Ferromagnetism at Room Temperature Using an Electric Field. Nature 2014, 516, 370−373. (4) Wang, J.; Neaton, J. B.; Zheng, H.; Nagarajan, V.; Ogale, S. B.; Liu, B.; Viehland, D.; Vaithyanathan, V.; Schlom, D. G.; Waghmare, U. V.; et al. Epitaxial BiFeO3 Multiferroic Thin Film Heterostructures. Science 2003, 299, 1719−1722. (5) Dietl, T.; Ohno, H.; Matsukura, F.; Cibert, J.; Ferrand, D. Zener Model Description of Ferromagnetism in Zinc-Blende Magnetic Semiconductors. Science 2000, 287, 1019−1022. (6) Cheong, S.-W.; Mostovoy, M. Multiferroics: A Magnetic Twist for Ferroelectricity. Nat. Mater. 2007, 6, 13−20. (7) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Electric Field Effect in Atomically Thin Carbon Films. Science 2004, 306, 666. (8) Bolotin, K. I.; Sikes, K. J.; Hone, J.; Stormer, H. L.; Kim, P. Temperature-Dependent Transport in Suspended Graphene. Phys. Rev. Lett. 2008, 101, 096802. (9) Kim, K. S.; Zhao, Y.; Jang, H.; Lee, S. Y.; Kim, J. M.; Kim, K. S.; Ahn, J.-H.; Kim, P.; Choi, J.-Y.; Hong, B. H. Large-Scale Pattern Growth of Graphene Films for Stretchable Transparent Electrodes. Nature 2009, 457, 706. (10) Georgakilas, V.; Otyepka, M.; Bourlinos, A. B.; Chandra, V.; Kim, N.; Kemp, K. C.; Hobza, P.; Zboril, R.; Kim, K. S. Functionalization of Graphene: Covalent and Noncovalent Approaches, Derivatives and Applications. Chem. Rev. 2012, 112, 6156. (11) Feliciano, G. T.; Sanz-Navarro, C.; Coutinho-Neto, M. D.; Ordejón, P.; Scheicher, R. H.; Rocha, A. R. Capacitive DNA Detection Driven by Electronic Charge Fluctuations in a Graphene Nanopore. Phys. Rev. Appl. 2015, 3, 034003. (12) Kim, S.-W.; Kim, H.-J.; Choi, J.-H.; Scheicher, R. H.; Cho, J.-H. Contrasting Interedge Superexchange Interactions of Graphene Nanoribbons Embedded in h-BN and Graphane. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92, 035443. (13) Muñoz-Rojas, F.; Fernández-Rossier, J.; Palacios, J. J. Giant Magnetoresistance in Ultrasmall Graphene Based Devices. Phys. Rev. Lett. 2009, 102, 136810. (14) Leconte, N.; Soriano, D.; Roche, S.; Ordejon, P.; Charlier, J. C.; Palacios, J. J. Magnetism-Dependent Transport Phenomena in 5054


Letter


(55) Datta, S. Electronic Transport in Mesoscopic Systems; Cambridge University Press: Cambridge, United Kingdom, 1997. (56) Kim, W. Y.; Kim, K. S. Carbon Nanotube, Graphene, Nanowire, and Molecule-Based Electron and Spin Transport Phenomena Using the Nonequilibrium Green’s Function Method at the Level of First Principles Theory. J. Comput. Chem. 2008, 29, 1073. (57) Kim, W. Y.; Kim, K. S. Tuning Molecular Orbitals in Molecular Electronics and Spintronics. Acc. Chem. Res. 2010, 43, 111. (58) Soler, J. M.; Artacho, E.; Gale, J. D.; García, A.; Junquera, J.; Ordejón, P.; Sánchez-Portal, D. The SIESTA Method for ab Initio Order-N materials Simulation. J. Phys.: Condens. Matter 2002, 14, 2745. (59) Yun, J.; Lee, G.; Kim, K. S. Electron Transport in Graphene Nanoribbon Field-Effect Transistor under Bias and Gate Voltages: IsoChemical Potential Approach. J. Phys. Chem. Lett. 2016, 7, 2478. (60) Perdew, J. P.; Zunger, A. Self-Interaction Correction to DensityFunctional Approximations for Many-Electron Systems. Phys. Rev. B: Condens. Matter Mater. Phys. 1981, 23, 5048. (61) Troullier, N.; Martins, J. L. Efficient Pseudopotentials for PlaneWave Calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 1991, 43, 1993−2006.

(35) Prasongkit, J.; Grigoriev, A.; Pathak, B.; Ahuja, R.; Scheicher, R. H. Transverse Conductance of DNA Nucleotides in a Graphene Nanogap from First Principles. Nano Lett. 2011, 11, 1941−1945. (36) Saha, K. K.; Drndić, M.; Nikolić, B. K. DNA Base-Specific Modulation of μA Transverse Edge Currents Through a Metallic Graphene Nanoribbon with a Nanopore. Nano Lett. 2012, 12, 50−55. (37) Areshkin, D. A.; Nikolić, B. K. I-V Curve Signatures of Nonequilibrium-Driven Band Gap Collapse in Magnetically Ordered Zigzag Graphene Nanoribbon Two-Terminal Devices. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79, 205430. (38) Magda, G. Z.; Jin, X.; Hagymasi, I.; Vancso, P.; Osvath, Z.; Nemes-Incze, P.; Hwang, C.; Biro, L. P.; Tapaszto, L. RoomTemperature Magnetic Order on Zigzag edges of Narrow Graphene Nanoribbons. Nature 2014, 514, 608−611. (39) Kim, W. Y.; Choi, Y. C.; Kim, K. S. Understanding Structures and Electronic/Spintronic Properties of Single Molecules, Nanowires, Nanotubes, and Nanoribbons Toward the Design of Nano devices. J. Mater. Chem. 2008, 18, 4510−4521. (40) Deng, X.; Zhang, Z.; Tang, G.; Fan, Z.; Zhu, H.; Yang, C. Edge Contact Dependent Spin Transport for n-type Doping ZigzagGraphene with Asymmetric Edge Hydrogenation. Sci. Rep. 2014, 4, 4038. (41) Saraiva-Souza, A.; Smeu, M.; Terrones, H.; Souza Filho, A. G.; Ratner, M. Spin Transport of Polyacetylene Chains Bridging Zigzag Graphene Nanoribbon Electrodes: A Nonequilibrium Treatment of Structural Control and Spin Filtering. J. Phys. Chem. C 2013, 117, 21178−21185. (42) Munoz-Rojas, F.; Fernandez-Rossier, J.; Palacios, J. J. Giant Magnetoresistance in Ultrasmall Graphene Based Devices. Phys. Rev. Lett. 2009, 102, 136810. (43) Son, Y.-W.; Cohen, M. L.; Louie, S. G. Half-Metallic Graphene Nanoribbons. Nature 2006, 444, 347. (44) Kan, E. J.; Li, Z.; Yang, J.; Hou, J. G. Half-Metallicity in EdgeModified Zigzag Graphene Nanoribbons. J. Am. Chem. Soc. 2008, 130, 4224−4225. (45) Hod, O.; Barone, V.; Scuseria, G. E. Half-Metallic Graphene Nanodots: A Comprehensive First-Principles Theoretical Study. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 035411. (46) Hod, O.; Barone, V.; Peralta, J. E.; Scuseria, G. E. Enhanced Half-Metallicity in Edge-Oxidized Zigzag Graphene Nanoribbons. Nano Lett. 2007, 7, 2295−2299. (47) Nemes-Incze, P.; Magda, G.; Kamaras, K.; Biro, P. L. Crystallographically Selective Nano patterning of Graphene on SiO2. Nano Res. 2010, 3, 110−116. (48) Jeon, I. Y.; Choi, H. J.; Jung, S. M.; Seo, J. M.; Kim, M. J.; Dai, L.; Baek, J. B. Large-Scale Production of Edge-Selectively Functionalized Graphene Nanoplatelets via Ball Milling and Their Use as Metal-Free Electrocatalysts for Oxygen Reduction Reaction. J. Am. Chem. Soc. 2013, 135, 1386−1393. (49) Jeon, I. Y.; Bae, S. Y.; Seo, J. M.; Baek, J. B. Scalable Production of Edge-Functionalized Graphene Nanoplatelets via Mechanochemical Ball-Milling. Adv. Funct. Mater. 2015, 25, 6961−6975. (50) Cai, J.; Ruffieux, P.; Jaafar, R.; Bieri, M.; Braun, T.; Blankenburg, S.; Muoth, M.; Seitsonen, A. P.; Saleh, M.; Feng, X.; et al. Atomically Precise Bottom-Up Fabrication of Graphene Nanoribbons. Nature 2010, 466, 470−473. (51) Park, Y. S.; Dibble, D. J.; Kim, J.; Lopez, R. C.; Vargas, E.; Gorodetsky, A. A. Synthesis of Nitrogen-Containing Rubicene and Tetrabenzopentacene Derivatives. Angew. Chem., Int. Ed. 2016, 55, 3352−3355. (52) Kan, E. J.; Li, Z.; Yang, J.; Hou, J. G. Will Zigzag Graphene Nanoribbon Turn to Half Metal under Electric Field? Appl. Phys. Lett. 2007, 91, 243116. (53) Taylor, J.; Guo, H.; Wang, J. Ab Initio Modeling of Quantum Transport Properties of Molecular Electronic Devices. Phys. Rev. B: Condens. Matter Mater. Phys. 2001, 63, 245407. (54) Brandbyge, M.; Mozos, J.-L.; Ordejón, P.; Taylor, J.; Stokbro, K. Density-Functional Method for Nonequilibrium Electron Transport. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 65, 165401. 5055


Lower Electric Field-Driven Magnetic Phase Transition and Perfect

Recommend Documents