Graphene Spin-Valve Device Grown Epitaxially on the Ni(111

Mar 10, 2011 - INTRODUCTION. Graphene1-3 has shown promising applications in nanoelec- tronics and spintronics4-10 due to its high carrier mobility an...
0 downloads 0 Views 4MB Size
Download PDF
ARTICLE pubs.acs.org/JPCC

Graphene Spin-Valve Device Grown Epitaxially on the Ni(111) Substrate: A First Principles Study Yeonchoo Cho,† Young Cheol Choi,†,‡ and Kwang S. Kim* Center for Superfunctional Materials, Department of Chemistry, Pohang University of Science and Technology, San 31, Hyojadong, Namgu, Pohang 790-784, Korea ABSTRACT: Graphene is a promising material for spintronics due to its outstanding spin transport property. Its maximally exposed 2pz orbitals allow tuning of electronic structure toward better functionality in device applications. Because the positions of carbon atoms are commensurate with those of Ni atoms on the substrate, we design a graphene spin-valve device based on the epitaxial graphene grown on the Ni (111) surface. We explored its transport properties with non equilibrium Green function theory combined with density functional theory. We show that the device has magnetoresistance (∼110%) due to the strong spin-dependent interaction between the Ni surface and the epitaxial graphene sheet.

r 2011 American Chemical Society

between the epitaxial graphene and the Ni(111) surface, the 2pz orbitals overlap with the Ni orbitals, resulting in drastic changes in the shapes of 2pz energy bands.29,30 In addition, the Fermi surface projected onto the close-packed plane of fcc-Ni shows that minority-spin states exist close to the K point, while no majority-spin state resides there. It is thus deduced that the minority-spin states of the graphene would be influenced more than the majority-spin states. These spin-dependent changes in bands near the Fermi energy (Ef) will result in a spin-dependent transport phenomenon, which is essential for spintronic devices. Therefore, it is highly desirable to investigate the detailed transport properties of a spin-valve device, based on the graphene epitaxially grown on the Ni(111) surface (hereafter, we abbreviate this device as Ni|Gr Gr Gr|Ni; refer to Figure 1b). We demonstrate how the Ni substrate modifies the 2pz bands of graphene and the transport properties by non equilibrium Green function (NEGF) theory combined with density functional theory.31-33 ) )

1. INTRODUCTION Graphene1-3 has shown promising applications in nanoelectronics and spintronics4-10 due to its high carrier mobility and long spin relaxation length11-13 as well as practical device applications such as touch panels, memory devices, sensors, water purifiers, and measuring instruments.14-18 The carbon atoms comprising graphene can be classified into two sublattices, which are symmetric and equivalent to each other. Such symmetry leads to the degeneracy at the Dirac point with a zero energy gap; in detail, 2pz orbitals of graphene carbons exhibit linear dispersion near the corners of the first Brillouin zone, resulting in high mobility. However, 2pz orbitals are apt to be influenced by surface modifications because of their spatial openness. Thus, the transport properties can be sensitively tuned by a substrate or adsorbed species.19-23 Although carbon nanotubes show a great prospect in electronic/spintronic applications,19,24,25 graphene is especially advantageous to them regarding sensitivity to substrate due to its planar geometry. For example, a graphene sheet grown on a SiC substrate is a semiconductor with a small band gap. A SiC substrate breaks the sublattice symmetry by affecting the two sublattices differently.21 Theoretical study shows that the graphene grows commensurately on the Ni(111) surface.26 Along with this theoretical understanding, a large patterned graphene was successfully synthesized with the chemical vapor deposition method.27 The carbon overlayer of the fabricated graphene sheet was proven to be well-ordered with 3m symmetry on the Ni(111) surface.28 Among three possible 3m symmetry structures, only considered here is the most stable structure, where C1 sits on the surface Ni atom and C2 is located at the hollow site, as shown in Figure 1a. This geometry leads to sublattice symmetry breaking and gap opening at the Dirac point. Because of the strong interaction

2. COMPUTATIONAL DETAILS We carried out density functional calculations (generalized gradient approximation) with numerical atomic orbital basis and Troullier-Martin-type pseudopotentials using the SIESTA program package.34 The single-ζ-polarization basis set and relatively large cutoff energy (400 Ry) for the grid-mesh were used for all the calculations. 101 k-points were sampled along the plane directions according to the Monkhorst-Pack scheme. Here, we considered the most stable structure only, where one of two Received: December 3, 2010 Revised: January 25, 2011 Published: March 10, 2011 6019

dx.doi.org/10.1021/jp111504q | J. Phys. Chem. C 2011, 115, 6019–6023

The Journal of Physical Chemistry C

) )

) )

) )

) )

sublattices is on top of the surface Ni atom and the other is on top of the hollow site (Figure 1a). All the density of states (DOS) and the band structures were calculated for the hexagonal unit cell where the lattice constant was 2.46 Å, the experimental value for graphite.35 The lattice mismatch was estimated to be only 1.3% at the Ni(111)-graphene interface. The NEGF method was used to model coherent electron transport or compute transmission probabilities. The basis set and the cutoff energy in NEGF calculations were the same as those in band structure calculations. 35 k-points were sampled along the direction perpendicular to electron transport. Transport functions were computed and summed over all the sampled k-points (in this way, we modeled a graphene slab, not a nanoribbon). To study the Ni electrode (or substrate) effect on the graphene, the distance between the Ni(111) surface and graphene was fixed to 2.05 Å for all of the cases, which was the equilibrium distance when 13 Ni layers were sandwiched between two graphene layers.29 For the graphene on multilayers of Ni, the Ni slabs were spaced by 2.0 Å.15 All the transmission calculations were done at the fixed geometry obtained by removing the Ni atoms in the middle area of the several unit cells to form electrodes at both ends (Figure 1b). When a bias voltage V was applied, we assumed that the voltage drop occurred within the extendedmolecule region (Figure 1b) and the chemical potential of the left electrode was shifted by V/2 and the right electrode by -V/2.

3. RESULTS AND DISCUSSION Influences of the Ni substrate can be shown from the band structures and the DOS projected on the carbon 2pz orbitals (PDOS-2pz). We computed those properties for the hexagonal unit cell of the graphene on the Ni(111) surface (to be abbreviated as Ni|Gr) with the number of Ni layers varying from 1 to 13 (Figure 2). The interfacial interaction made the band structure of Ni|Gr notably different from the free-standing graphene. For the majority spin, we can recognize a small gap opening of the carbon 2pz bands at the K point slightly below Ef. The gap size increases as the number of Ni layers increases from one to two, accompanying a shift of the gap midpoint from -0.9 to -0.75 eV. Additional Ni layers hardly shift it after more than two Ni layers are stacked. For the minority spin, the band structure is modified too highly to recognize the carbon 2pz bands near Ef, which means that the minority spin is more influenced by the interaction with the Ni surface atoms. As a consequence, the PDOS-2pz of the system is different from that of the free-standing graphene. For the majority spin, the PDOS2pz has one peak around Ef whose location does not change much over all the cases. The characteristic minimum point below Ef appears in all of the cases, which corresponds to the gap opening region in its band structure. It moves toward Ef by ∼0.25 eV as the number of layers increases from one to two. More Ni layers negligibly contribute to such shift. For the minority spin, the PDOS-2pz has a large zero DOS gap (ZDG) for all of the cases. It ranges from -0.65 to 0.08 eV for the case of one Ni layer. It is noted that the ZDG shifts to a lower energy region with an increased gap size (ranging from -1.0 to 0.0 eV) as the number of Ni layer increases from one to two. It does not shift much and its size is nearly unchanged as the number of Ni layers increases from 2 to 13. From this analysis, we note that less than three layers from the Ni(111) surface play a crucial role in modifying the properties of graphene. This type of surface-induced interactions can be a working mechanism of a spintronic device. Here, we propose the Ni| Gr Gr Gr|Ni device as shown in Figure 1b. We consider cases where electrodes parts have one or two layers of Ni and the length of pure graphene region is 0.85 nm. Comparison between transmission and PDOS-2pz is given in Figure 3. The zero transmission gap (ZTG) region coincides with the minimum DOS region or ZDG region for all the cases except for the minority spin of one Ni layer system, where the ZTG region below Ef is down shifted and 0.15 eV larger in size as compared to ZDG. Hence, we conclude that the transmission value for the Ni| Gr Gr Gr|Ni device can be predicted by evaluating the PDOS2pz in the electrode part, which is easier to compute than the transmission function of the whole device. That is, the PDOS-2pz in electrode part is an important factor for determining the transmission of the Ni|Gr Gr Gr|Ni device. A corollary is that the transmission function of the Ni|Gr Gr Gr|Ni device with 13 Ni layers would not change much from that with 2 Ni layers because PDOS-2pz is similar in those two cases. We have shown a close relation between the PDOS-2pz of the Ni|Gr system having one or two Ni layers and the transmission functions of the Ni|Gr Gr Gr|Ni device. A simple argument can justify these computational results. For the pure graphene region, carbon 2pz states would continuously exist near Ef similar to the free-standing graphene. Thus, for simplicity, we think that electric currents can flow through these 2pz channels at any energy level, only if 2pz states exist in the electrode region at that energy level, ) )

) )

Figure 1. Geometries of an epitaxial graphene on a Ni(111) surface and a spin-valve device. (a) The most stable structure for the grapheneNi(111) interface. The top view shows duplicated four adjacent hexagonal unit cells, where the Ni atoms are represented by big baby blue spheres and are darker as their distance from the interface increases. The carbon atoms are represented by small gray spheres. Side view shows the plane cut along a straight line on the top view. The two nonequivalent carbon atoms C1 and C2 are indicated. (b) The top view of the Ni|Gr Gr Gr|Ni device with a single layer of Ni(111) surface. A small sphere and a large sphere indicate a carbon atom and a nickel atom, respectively. An extended molecule part includes two lines of nickel.

ARTICLE

6020

dx.doi.org/10.1021/jp111504q |J. Phys. Chem. C 2011, 115, 6019–6023

The Journal of Physical Chemistry C

ARTICLE

Figure 2. Curves in each row were obtained from the hexagonal unit cell for the model of graphene on the Ni(111) surface with 1, 2, 3, and 13 layers of Ni, respectively, from top to bottom. The first column shows band structure for the majority spin, and the second column shows it for the minority spin. The third column shows PDOS-2pz for both majority (dotted line) and minority (dashed line) spins.

although we should consider the DOS of the free-standing graphene, which linearly increases as the energy level goes far from Ef. That is, the electric current channels are mostly determined by the carbon 2pz orbitals of the electrode parts, which are severely influenced by the Ni(111) surface. One of the reasons this argument works is that other orbitals do not contribute to the currents. The Ni orbitals scarcely couple to carbon 2pz orbitals of the pure graphene region, and the energy levels of other carbon orbitals like 2px, 2py, and 2s are far from Ef. As a result, not only the carbon 2pz orbitals of the central free-standing graphene are crucial for the transport properties of the proposed device, but also the PDOS-2pz of the Ni|Gr system (which belongs to the electrode part) and the transmission functions of the device are closely related. We also note that close coupling between the substrate and the graphene sheet is a decisive factor, so the maximal band structure tuning will be achieved if a substrate gets closest to the sheet with perfect lattice match.

Disparate influences of the substrate on spins can be exploited in spin-valve applications. To explore such a possibility, we compare transmissions of the device whose electrodes are in parallel and antiparallel spin configurations, respectively (Figure 4). In the case where electrodes are in the parallel spin configuration (P-SC), the transmission function of the device shows ZTG for both majority and minority spins, where the ZTG spans from -0.98 to -0.80 eV for the majority spin and from -1.03 to -0.19 eV for the minority spin. On the other hand, when electrodes are in the antiparallel spin configuration (AP-SC), the transmission functions of both spins are similar to each other, and their ZTG regions are larger than the case of P-SC. To understand this, we note that the current channel at a certain energy level is open when the energy states at both electrodes couple to the energy states of the pure graphene region. (refer to the previous paragraph.) In the case of P-SC, both electrodes have the same electronic structure. Therefore, if 6021

dx.doi.org/10.1021/jp111504q |J. Phys. Chem. C 2011, 115, 6019–6023

The Journal of Physical Chemistry C

4. CONCLUSION We have shown that the band structure of a graphene can be largely tuned by a substrate, especially the Ni(111) surface, and such tuning can be exploited in designing a practical spin valve device. First, we explored the influence of the Ni(111) substrate on the graphene band structure. The first two layers distort it a lot, while more additional layers result in a minor contribution. In the case of the Ni(111) substrate, the effect is spin-dependent. This property is used to design a spin valve device. Quantum transport calculations show that the magnetoresistance of the device is large enough to be applied to a spin valve device and such characteristics are robust in extensive length scales. The density of states projected on graphene 2pz orbitals turns out to be a key measure for substrate effects and is shown to be a major factor determining transport properties. Our device design shows

) )

Figure 3. Transmission function (solid line, in the case of the parallel spin configuration for electrodes) and PDOS-2pz (dashed line) for the free-standing graphene (a), and those for the system of graphene on one Ni layer (“b” for majority spin and “c” for minority spin) and two Ni layers (“d” for majority spin and “e” for minority spin).

We evaluated the magnetoresistance (MR) value for the Ni| Gr Gr Gr|Ni device having one Ni layer, where MR is defined as MR  (RAP - RP)/RP  (GP - GAP)/GAP (R and G represent resistance and conductance, respectively). For the calculation of currents, the bias voltage (Vb) was applied up to 0.20 V with the intervals of 0.05 V, where the chemical potentials of both electrodes are shifted by Vb/2 and -Vb/2, respectively. Figure 4b shows that the currents linearly increase for the P-SC case, whereas they increase more slowly for the AP-SC case with current decreasing from 0.10 to 0.15 V. The average MR value over the whole range is obtained to be 114%. Finally, we studied the changes in transmission function with respect to the length of the pure graphene region. Here, the device has a single Ni layer in electrode parts. We investigated it for the P-SC case with the length of 0.85, 1.70, 2.55, and 3.40 nm. The location and the size of the ZTG are almost unchanged through the whole length scale, as shown in Figure 5. The magnitude of transmission values slightly decreases as the length increases from 0.85 to 1.70 nm, whereas it changes by only a small amount as the length increases from 2.55 to 3.40 nm. This suggests that the device would maintain characteristics for a spin valve up to the experimentally feasible length scale. One may concern that the current theoretical scheme describes electron transport only in the coherent tunneling regime and that it should be limitedly applied to long length scales like a few nanometers. We stress, however, that the above discussions regarding band structures and transport channels, which explain spin-dependent characteristics of our device, are not lengthdependent as well. Thus, spin-dependent transport properties of our device are expected to be robust under the change of the length. ) )

an energy state of the left electrode for a specific spin is coupled to the central graphene region, there is a corresponding state at the right electrode for the same spin. Hence, the transmission function for each spin reflects electronic structure of electrodes for the corresponding spin. Figure 3 is a confirmation of this reasoning. On the other hand, for the AP-SC case, the electronic structure of the right electrode is reversed in terms of spin from that of the left. The majority-spin electronic structure of the left corresponds to the minority-spin electronic structure of the right. Therefore, it looks as if an electron from the left electrode goes to the opposite spin channel at the right. Consequently, the energy range for the current flow in the AP-SC case is the intersection of those for majority and minority spin channels in the P-SC case, and the transmission function for a majority spin is similar to that for a minority spin. Therefore, the ZTG regions for both spin channels of the P-SC case should be summed to give the ZTG regions for each spin channel of the AP-SC case.

ARTICLE

Figure 4. Magnetoresistance of the Ni|Gr Gr Gr|Ni device having one layer of Ni in the electrode parts. (a) Transmission functions for both parallel and antiparallel spin configurations. Dotted, dashed, and solid lines indicate the transmissions for majority spin, minority spin, and sum of both spins, respectively. (b) Current versus voltage curves for the parallel (P-SC) and antiparallel (AP-SC) cases. 6022

dx.doi.org/10.1021/jp111504q |J. Phys. Chem. C 2011, 115, 6019–6023

The Journal of Physical Chemistry C

) )

Figure 5. Transmission function with respect to the length of the pure graphene region for the Ni|Gr Gr Gr|Ni device having a single layer of Ni in the electrode part, each electrode having parallel spin configuration.

a possibility that substrates play a decisive role in spintronic applications.

’ AUTHOR INFORMATION Corresponding Author

*Tel.: þ82-54-279-2110. Fax: þ82-54-279-8137. E-mail: kim@ postech.ac.kr. Author Contributions †

These authors contributed equally to this work.

Present Addresses ‡

Corporate R&D LG Chem. Ltd. Research Park, Daejeon 305380, Korea

’ ACKNOWLEDGMENT This work was supported by the NRF (National Honor Scientist Program 2010-0020414, WCU: R32-2008=000-10180-0) and KISTI (KCS-2008-K08-0002). Y.C. is grateful for a TJ Park Doctoral Fellowship. ’ REFERENCES (1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Science 2004, 306, 666. (2) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Nature 2005, 438, 197. (3) Zhang, Y.; Tan, Y.-W.; Stormer, H. L.; Kim, P. Nature 2005, 438, 201. (4) Hill, E. W.; Geim, A. K.; Novoselov, K.; Schedin, F.; Blake, P. IEEE Trans. Magn. 2006, 42, 2694. (5) Son, Y.-W.; Cohen, M. L.; Louie, S. G. Nature 2006, 444, 347. (6) Kim, W. Y.; Kim, K. S. Nat. Nanotechnol. 2008, 3, 408. (7) Geim, A. K.; Novoselov, K. S. Nat. Mater. 2007, 6, 183. (8) Kim, W. Y.; Choi, Y. C.; Min, S. K.; Cho, Y.; Kim, K. S. Chem. Soc. Rev. 2009, 38, 2319. (9) Munoz-Rojas, F.; Fernandez-Rossier, J.; Palacios, J. J. Phys. Rev. Lett. 2009, 102, 136810. (10) Di Ventra, M.; Pantelides, S. T.; Lang, N. D. Phys. Rev. Lett. 2000, 84, 979. € (11) Han, M. Y.; Ozyilmaz, B.; Zhang, Y.; Kim, P. Phys. Rev. Lett. 2007, 98, 206805.

ARTICLE

(12) Zhang, Y.; Small, J. P.; Pontius, W. V.; Kim, P. Appl. Phys. Lett. 2005, 86, 073104. (13) Tombros, N.; Jozsa, C.; Popincius, M.; Jonkman, H. T.; van Wees, B. J. Nature 2007, 448, 571. (14) Bae, S.; Kim, H.; Lee, Y.; Xu, X.; Park, J.-S.; Zheng, Y.; Balakrishnan, J.; Lei, T.; Kim, H. R.; Song, Y. I.; Kim, Y.-J.; Kim, K. S.; € Ozyilmaz, B.; Ahn, J.-H.; Hong, B. H.; Iijima, S. Nat. Nanotechnol. 2010, 5, 574. (15) Myung, S.; Park, J.; Lee, H.; Kim, K. S.; Hong, S. Adv. Mater. 2010, 22, 2045. (16) Chandra, V.; Park, J.; Chun, Y.; Lee, J. W.; Hwang, I.-C.; Kim, K. S. ACS Nano 2010, 4, 3979. (17) Yu, Y.-J.; Zhao, Y.; Ryu, S.; Brus, L. E.; Kim, K. S.; Kim, P. Nano Lett. 2009, 9, 3430. (18) Lakshmi, S.; Roche, S.; Cuniberti, G. Phys. Rev. B 2009, 80, 193404. (19) Avouris, P.; Chen, Z.; Perebeinos, V. Nat. Nanotechnol. 2007, 2, 605. (20) Zhou, S. Y.; Gweon, G. H.; Fedorov, A. V.; First, P. N.; De Heer, W. A.; Lee, D. H.; Guinea, F.; Neto, A. H. C.; Lanzara, A. Nat. Mater. 2007, 6, 770. (21) Varchon, F.; Feng, R.; Hass, J.; Li, X.; Nguyen, B. N.; Naud, C.; Mallet, P.; Veuillen, J.-Y.; Berger, C.; Conrad, E. H.; Magaud, L. Phys. Rev. Lett. 2007, 99, 126805. (22) Schedin, F.; Geim, A. K.; Morozov, S. V.; Hill, E. W.; Blake, P.; Katsnelson, M. I.; Novoselov, K. S. Nat. Mater. 2007, 6, 652. (23) Lu, Y. H.; Chen, W.; Feng, Y. P. J. Phys. Chem. B 2009, 113, 2. (24) Hueso, L. E.; Pruneda, J. M.; Ferrari, V.; Burnell, G.; ValdesHerrera, J. P.; Simons, B. D.; Littlewood, P. B.; Artacho, E.; Fert, A.; Mathur, N. D. Nature 2007, 445, 410. (25) Cho, Y.; Kim, W. Y.; Kim, K. S. J. Phys. Chem. A 2009, 113, 4100. (26) Bertoni, G.; Calmels, L.; Altibelli, A.; Serin, V. Phys. Rev. B 2005, 71, 075402. (27) 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. Nature 2009, 457, 706. (28) Shikin, A. M.; Farías, D.; Adamchuk, V. K.; Rieder, K.-H. Surf. Sci. 1999, 424, 155. (29) Karpan, V. M.; Giovannetti, G.; Khomyakov, P. A.; Talanana, M.; Starikov, A. A.; Zwierzycki, M.; van den Brink, J.; Brocks, G.; Kelly, P. J. Phys. Rev. Lett. 2007, 99, 176602. (30) Karpan, V. M.; Khomyakov, P. A.; Starikov, A. A.; Giovannetti, G.; Zwierzycki, M.; Talanana, M.; Brocks, G.; van den Brink, J.; Kelly, P. J. Phys. Rev. B 2008, 78, 195419. (31) Kim, W. Y.; Kim, K. S. J. Comput. Chem. 2008, 29, 1073. (32) Kim, W. Y.; Choi, Y. C.; Kim, K. S. J. Mater. Chem. 2008, 18, 4510. (33) Kim, W. Y.; Kim, K. S. Acc. Chem. Res. 2010, 43, 111. (34) Soler, J. M.; Artacho, E.; Gale, J. D.; García, A.; Junquera, J.; Ordejon, P.; Sanchez-Portal, D. J. Phys.: Condens. Matter 2002, 14, 2745. (35) Ibach, H.; L€uth, H. Solid-State Physics, 2nd ed.; Springer-Verlag: Berlin, 1995.

6023

dx.doi.org/10.1021/jp111504q |J. Phys. Chem. C 2011, 115, 6019–6023