NiO Core–Shell

Oct 10, 2011 - The memory RS is triggered by a high ICC, while the threshold RS appears by .... Resistive random access memory (RRAM) technology: From...
2 downloads 5 Views 5MB Size
Download PDF
LETTER pubs.acs.org/NanoLett

Memory and Threshold Resistance Switching in Ni/NiO Core Shell Nanowires Li He,† Zhi-Min Liao,*,† Han-Chun Wu,*,‡ Xiao-Xue Tian,§ Dong-Sheng Xu,§ Graham L. W. Cross,‡ Georg S. Duesberg,|| I. V. Shvets,‡ and Da-Peng Yu*,† †

State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871, People’s Republic of China CRANN and School of Physics, Trinity College Dublin, Dublin 2, Ireland § Institute of Physical Chemistry, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Peking University, Beijing 100871, People’s Republic of China CRANN and School of Chemistry, Trinity College Dublin, Dublin 2, Ireland

)

‡

bS Supporting Information ABSTRACT: We report on the first controlled alternation between memory and threshold resistance switching (RS) in single Ni/NiO core shell nanowires by setting the compliance current (ICC) at room temperature. The memory RS is triggered by a high ICC, while the threshold RS appears by setting a low ICC, and the Reset process is achieved without setting a ICC. In combination with first-principles calculations, the physical mechanisms for the memory and threshold RS are fully discussed and attributed to the formation of an oxygen vacancy (Vo) chain conductive filament and the electrical field induced breakdown without forming a conductive filament, respectively. Migration of oxygen vacancies can be activated by appropriate Joule heating, and it is energetically favorable to form conductive chains rather than random distributions due to the Vo Vo interaction, which results in the nonvolatile switching from the off- to the on-state. For the Reset process, large Joule heating reorders the oxygen vacancies by breaking the Vo Vo interactions and thus rupturing the conductive filaments, which are responsible for the switching from on- to off-states. This deeper understanding of the driving mechanisms responsible for the threshold and memory RS provides guidelines for the scaling, reliability, and reproducibility of NiO-based nonvolatile memory devices. KEYWORDS: NiO, resistance switching, memory, nanowire, memristors, conductive filament

T

he resistance switching (RS) phenomenon, in which the resistance can be reversibly switched by an external electrical field, has recently received a great deal of attention. Due to the structural simplicity and high switching speed (∼tens of nanoseconds), resistance random access memory (ReRAM) devices have been considered as potential candidates for nonvolatile memory. The RS phenomenon has been observed in many systems, including binary oxides,1 3 silicon,4 sulfides,5,6 perovskite oxides,7 9 and organic materials.10,11 Among them, transition metal oxides, especially NiO, have been extensively investigated for RS devices.12 There are two types of RS effects: memory RS8,13,14 and threshold RS.1,15 In memory RS, both the high resistance state (HRS) and low resistance state (LRS) are stable at zero voltage, which can be used in a nonvolatile memory device. However, in threshold RS, only the HRS is stable at zero bias which hinders its application in nonvolatile memory. Therefore, it is important to know exactly the conditions for occurrence of memory and threshold RS based on a thorough understanding of the underlying mechanisms. Although various models have been proposed to elucidate the RS mechanisms including an r 2011 American Chemical Society

electrical field induced metal insulator transition,16 a dynamic percolation model,17 and the migration of oxygen vacancies (Vo),18 it is still unclear how to clearly distinguish the mechanisms between memory and threshold RS. As a direct consequence, there are many experimental findings that cannot be well understood and leave behind a great deal of confusion and many controversies in this rapidly expanding field. For example, the compliance current (ICC) affects the polarity of the RS19 and the size of the filaments,20 while the thickness of the electrodes21 and environment temperature17 can also affect the type of RS. Therefore, finding an efficient and effective method to control the type of RS and understanding the corresponding mechanisms is highly desirable. NiO Ni nanojunctions provide an ideal approach to reveal the switching mechanisms, minimize the size of devices, and develop applications. Although the resistance switching behavior Received: June 15, 2011 Revised: September 26, 2011 Published: October 10, 2011 4601

dx.doi.org/10.1021/nl202017k | Nano Lett. 2011, 11, 4601–4606

Nano Letters of NiO Ni nanojunction arrays in an anodic aluminum oxide (AAO) template has been studied using a gold paint layer as the top electrode, the sample contains ∼106 nanowires and so its size is not really of the nanoscale.22 It has been demonstrated that the collective NiO Ni nanojunction arrays can serve as a switching cell,22 whereas it is highly important to know if a single NiO Ni nanowire can act as a switching element or not. For certain applications, the NiO Ni nanowires should be released from the AAO template to construct integrated devices using the nanowires as building blocks. For fundamental research, the data from collective measurements are the average over a large amount of nanowires, while the study of the resistance switching of a single NiO Ni nanowire can be conducted under a more controllable way and is helpful to reveal the formation and rupture of the conductive filaments. The above reasons motivated us to study the electrical switching of a single Ni NiO core shell nanowire rather than the assembled nanowires in an AAO template. In this paper, we report on the first controllable and reproducible alternation between threshold RS and memory RS in a single Ni/NiO core shell nanowire at room temperature. In combination with first-principles calculations, we show that the threshold RS is purely due to an electric field effect without forming a conductive filament, while the memory RS and RESET processes (i.e., switching from ON to OFF states) are related to the formation and rupture of oxygen vacancy chain conductive filaments which are due to the presence of the Vo Vo interaction and the breakdown in the Vo Vo interaction by Joule heating. Ni/NiO core shell nanowires were prepared by electrodepositing Ni in the pores of AAO templates and then oxidizing them in air. Ni nanowires were electrodeposited at a constant voltage of 1 V for 10 h at room temperature in an electrolyte of 0.1 mol/L NiCl and 0.5 mol/L H3BO3. Next, the AAO membrane was dissolved in a 1 mol/L NaOH solution for 1 h at room temperature, and the nanowires were then washed with doubledistilled water to get a clean Ni nanowire solution. The device fabrication process is illustrated in Figure 1a. First, as-synthesized fresh Ni nanowires were dispersed onto a Si substrate covered with an 800 nm SiO2 layer. Then three Au electrodes, denoted as 1, 3, and 4, were immediately fabricated on the Ni nanowire via standard processes including e-beam lithography, metal deposition, and lift-off. The Ni nanowire devices were then naturally oxidized in air for 3 days to form the Ni/NiO core shell structures due to the self-limiting oxidation process with the exception of the Ni nanowire surface regions covered by Au electrodes. Finally, an Au electrode, as is marked with the numeral 2, was fabricated on top of NiO layer, as shown in Figure 1b by the scanning electron microscopy (SEM) image of a typical device. To verify the formation of the NiO layer, we performed transmission electron microscopy (TEM) characterization of the Ni (core)/NiO (shell) nanowires synthesized through oxidation of Ni nanowires using a similar method (see Figure 1c). The nanowire has an average diameter of ∼75 nm and an amorphous NiO layer with a thickness of ∼4.5 nm. Figure 1d is a highresolution TEM image of part of the nanowire, which shows the crystalline Ni and amorphous NiO structures. The lattice fringes with an interplanar spacing of 0.204 nm correspond to Ni(111) planes. Energy-dispersive X-ray spectrum (EDS) (See Figure S1 in the Supporting Information) analysis of the amorphous NiO shows that the atomic ratio between Ni and O is about 1:0.87, indicating the presence of the oxygen vacancies in the NiO shell.

LETTER

Figure 1. (a) Sketch of the device fabrication. First, three Au electrodes were fabricated in contact with a single Ni nanowire. The surface layer of the Ni nanowire was then oxidized to form NiO except for the regions covered by the Au electrodes. After that, another Au electrode (marked with the number 2) was fabricated to form contact directly with the NiO. The dotted line indicates the current path for the memory device. (b) SEM image of a typical fabricated device. Electrodes 1, 3, and 4 are in direct contact with the Ni core. Electrode 2 is in direct contact with the NiO shell layer. (c) TEM image of an individual Ni/NiO nanowire. (d) HRTEM image shows the crystalline Ni(111) planes and the amorphous NiO.

The resistive switching characteristics were measured using a Keithley 4200 semiconductor characterization system at room temperature. To verify the reliability of the device, we measured the respective resistances of the nanowire segments (Figure 1b) between electrodes 1 and 3, 1 and 4, and 2 and 3, and the corresponding current voltage (I V) curves are shown in Figure 2a. The resistances between electrodes 1 and 3, and 1 and 4 are 580 and 940 Ω, respectively, which are consistent with the fact that electrodes 1, 3, and 4 are in direct contact with Ni nanowire and low resistances are expected. The resistance between electrodes 2 and 3 is much greater, 4.5  105 Ω, as they are separated by a layer of NiO. Such high resistance also indicates a closed layer of NiO is formed following the oxidization process. The current path through the NiO layer is indicated by the dotted line in Figure 1a. Figure 2b shows the I V curves of the NiO/Ni core shell nanowire measured using electrodes 2 and 3. The changes in resistance of the device under different electric fields result from changes in resistance of the NiO layer. At ∼1 V, the device changed from a HRS to a LRS, which is called the SET process. Control of the type of RS by means of compliance current was clearly demonstrated. The threshold RS is triggered by setting ICC = 10 5 A (corresponding to current density ∼6.7  10 5 A/μm2, and deposited charges ∼1.5  10 2 C μm 3 s 1), as shown by the red curve in Figure 2b. The memory RS is initiated by setting ICC = 10 4 A (∼6.7  10 4 A/μm2 in current density and ∼0.15 C μm 3 s 1 in deposited charge), as shown by the black curve in Figure 2b. In memory RS, without setting the ICC, the device can be reset to HRS again (the blue curve in Figure 2b). 4602

dx.doi.org/10.1021/nl202017k |Nano Lett. 2011, 11, 4601–4606

Nano Letters

Figure 2. (a) The I V curves were measured between electrodes 1 and 3, 1 and 4, and 2 and 3 at room temperature. (b) The I V curves show the resistance switching behaviors of the Ni/NiO core shell nanowire. The threshold RS, memory RS, and the RESET processes were achieved by setting different compliance currents. (c) The on and off resistances for a device for the first 25 cycles. (d) Retention performance of the memory device. (e, f) The cumulative distribution of the SET voltage and RESET voltage varying with (e) number of cycles and (f) different devices.

To demonstrate further the reproducibility of the switching phenomena, devices were set and reset by sweeping the voltage through multiple consecutive cycles. The Ron and Roff for the first 25 cycles for a typical device are shown in Figure 2c, where Ron and Roff correspond to the resistance of the ON state after SET process of memory RS and the resistance of the OFF state after RESET process, respectively. Therefore, the switching behaviors of the device are reproducible. We also found that the devices usually have a sudden failure after tens of continuous switching cycles through sweeping voltage, as shown in Figure S2. The degradation of the device was attributed to the high current density in the Reset process which breaks down the Ni nanowire, as shown by the SEM images in Figure S3 (Supporting Information). Figure 2d shows the retention performance of the memory cell at room temperature. A retention time of 40 days has been demonstrated for both the ON and OFF states and the information stored in this device is likely to persist for an even longer time as judged from the present trend of the data. Panels e and f of Figure 2 show the cumulative distribution of the conductive filament formation voltage (SET voltage) and the filament rupture voltage (RESET voltage) for a device undergoing about 25 consecutive cycles and for about 41 devices, respectively. It is found that the SET and RESET voltages range from ∼0.5 to 3.5 V, and the SET voltage is generally larger than the RESET voltage. The experimental results indicate that the

LETTER

switching performances are reproducible from cycle to cycle and from device to device. To reveal the mechanisms responsible for the two types of RS effects and the RESET process, we first investigate the effect of oxygen vacancies on the electronic structure of their nearestneighbor (NN) Ni atoms. Figure 3 shows the partial density of states (PDOS) of Ni atoms with a variety of first NN oxygen vacancy combinations. In our calculations, a supercell of Ni64O64 (4  4  4) was used. The electronic structures were calculated using the Vienna ab initio simulation package.23,24 We employed the projected augmented plane wave method and valence configurations of 3d84s2 for Ni and 2s22p4 for O were used.25 The socalled local density approximation (LDA) with on-site Coulomb interaction (U) has been used to calculate the electronic structure.26 For the LDA+U simulations in this study, we use U = 6.3 eV and the Hund’s rule exchange parameter J = 1 eV.18 The lattice constant is set to be 4.19 Å and a Monkhorst Pack 2  2  2 k-point grid was applied to sample the Brillouin zone. Figure 3b shows the PDOS of Ni atoms for an ideal NiO. The energy gap is found to be 3.2 eV, and the total antiferromagnetic spin moment is 1.7 μB (Figure 3b). Both values are in good agreement with the experimental and theoretical reports.18 By removal of a single first NN oxygen atom from a Ni atom (marked green in Figure 3a), an impurity level appears between the valence band and the conduction band with an energy gap of 0.8 eV (Figure 3c). It is clear that the oxygen vacancy breaks the symmetry and causes splitting of the Ni eg state. It also modifies the charge-transfer between the Ni and O atoms, which results in a redistribution of the charge density. As shown in panels c f of Figure 3, removing additional first NN oxygen atoms further decreases the energy gap between the valence band and the impurity level. When four first NN oxygen atoms are removed (Figure 3f), no energy gap between the valence band and the impurities level is observed. Therefore, when two first NN oxygen vacancy chains are established, a conductive filament will be formed and the system will be in “ON” state. We also show in panels c f of Figure 3 using dashed lines the PDOS of the Ni atom marked in yellow in Figure 3a which is located away from the green Ni atom. One can see that the Ni atom marked in yellow retains the bulk properties, which suggests that the effect of oxygen vacancies is localized and limited to their first NN and the DOS of Ni atoms more distant from the oxygen vacancy sites will not be affected. Therefore, oxygen vacancies surrounding the Ni atoms close the gap in the Ni 3d band and thus the conductive path is localized to the Ni atom chain (the same meaning as oxygen vacancy chain). The current in such devices should be confined to the narrow path of the oxygen vacancy chain, which is consistent with the direct TEM observation of the “Ni” nanofilament.27 There are other oxide resistance-change systems utilizing oxygen vacancies to form or disperse conductive channels. Janousch et al. reported resistance switching in Cr-doped SrTiO3 where Cr serves as a seed for the oxygen vacancies.28 Yang et al. reported electrical switching in nanoscale TiO2 junction devices, where the drift of positively charged oxygen vacancies under an electric field leads to a spatially heterogeneous Vo distribution and variation of the system resistance.29 In our systems, as the NiO layer was formed by natural oxidation of the Ni nanowire surface, the oxidation was in Ni-rich conditions and large numbers of oxygen vacancies are expected to exist in the NiO layer. Since an ordered configuration of oxygen vacancies corresponds to a LRS and a disordered configuration results in a HRS, 4603

dx.doi.org/10.1021/nl202017k |Nano Lett. 2011, 11, 4601–4606

Nano Letters

LETTER

Figure 3. (a) Atomic structure of Ni64O64. (b f) Partial density of states (solid lines) of Ni atom (marked as green in panel a) with 0, 1, 2, 3, and 4 nearest-neighbor oxygen vacancies, respectively. For comparison, dashed lines represent the partial density of states of the Ni atom marked in yellow in panel a. Insets are the calculated electronic charge density distributions of Ni atoms in real space for spin up (orange) and spin down (blue) states. The isosurface is set to be 0.001 Bohr radius.

Figure 4. (a c) Schematic diagrams of the three modeled configurations each comprising of four oxygen vacancies (blue open circles). (d) Schematics and calculated migration energy of an oxygen atom (blue filled circle) migrates to first nearest-neighbor oxygen vacancy site to rupture the oxygen vacancy chain (black arrow), and to form the oxygen vacancy chain (red arrow).The direction of arrows indicates the migration direction (from initial state to final state).

we now compare energy stability of the system with three different oxygen vacancies configurations, i.e., the four oxygen vacancies are in a disordered configuration (Figure 4a), part of the oxygen vacancies are in a chain (Figure 4b), and four oxygen vacancies forms a chain along the Æ110æ direction (Figure 4c). The total energy for those three oxygen vacancies configurations are 622.81 eV (a), 623.02 eV (b), and 623.15 eV (c),

respectively. It is clear that the system with ordered oxygen vacancy configuration has the lowest energy due to Vo Vo interactions. A similar effect has also been observed in SrTiO330 and BaTiO3 systems.31 Although the ordered oxygen vacancy configuration is more energetically favorable, the oxygen vacancies cannot spontaneously transform from a disordered to an ordered configuration 4604

dx.doi.org/10.1021/nl202017k |Nano Lett. 2011, 11, 4601–4606

Nano Letters due to the existence of energy barriers for migration of oxygen vacancies. We now discuss how the chains of oxygen vacancies and thus conductive filaments are formed by considering the oxygen vacancy migration. On the basis of the nudged elastic band (NEB) method,32 we simulated two situations: an oxygen atom (blue ball in Figure 4d) migrates to rupture or form the oxygen vacancy chain. In our NEB calculations, eight images between the initial and final states were used to simulate the migration process and the migration path was set along the Æ110æ direction, which is consistent with the direction of the chain of oxygen vacancies. A spring interaction between adjacent images is added to ensure continuity of the path, and all atoms were allowed to relax. Figure 4d shows schematics and the calculated migration energy of an oxygen atom (blue filled circle) as it migrates to its first NN oxygen vacancy site to rupture the oxygen vacancy chain (black arrow, migrate from left to right state) or to form the oxygen vacancy chain (red arrow, migrate from right to left state). ER and EC in Figure 4d correspond to migration energy barriers to rupture the oxygen vacancy chain and to form an oxygen vacancy cluster, respectively. One can clearly see from Figure 4d that, Vo Vo interactions (EVo Vo) decrease EC while increasing ER, thus resulting in an asymmetric migration process. ER > EC means oxygen vacancies tend to cluster. One can also see from Figure 4d that in order to break Vo Vo interactions, an energy barrier of ER has to be overcome. It is clear that there are three possible migration situations. First, electric field and thermal energy are insufficient to migrate the oxygen vacancy, no migration will be allowed. Second, electric field and Joule heating are high enough to drive the oxygen vacancy to form an oxygen vacancy chain but not high enough to rupture the oxygen vacancy chain, and an oxygen vacancies conductive filament will be formed. Third, Joule heating and electric field are able to force the oxygen atom to migrate to an oxygen vacancy chain and thus can rupture the oxygen vacancy chain. In our amorphous NiO sample, the migration energy can be much smaller than the calculated value ∼3.5 V due to high oxygen vacancy concentrations and also due to the migration of the oxygen interstitial. It was shown recently that for an amorphous system, like SiO2 with an increased oxygen concentration, the migration energy of an oxygen atom can be decreased significantly from 3.5 to 1 eV33 and the oxygen atoms in the interstitial sites state may also have a much lower migration energy.34 On the basis of the theoretical calculations, we proposed a general model to explain our experimental results. Setting the compliance current to a relatively low value, the threshold RS is mainly due to an electric-field-driven transition16,35 and no conductive filament is formed during the cycle. First, if the conductive filament is formed, it can survive at a much higher compliance current (memory RS), and so withdrawing the applied electric field cannot change the system from LRS to HRS. Second, the observed threshold electric field (106 V/cm) is comparable to the critical field of Zener breakdown.16 As no conductive filament is formed, the applied electric field is not high enough to migrate the oxygen vacancy. In the presence of an electric field E, the migration energies for both cases will be decreased by 2λeE (Figure 5b), where λ is the jump length of oxygen anions. For NiO, both our experimental results and published data1,17 show that the typical electric field is around 1 V/5 nm and λ is set to be 3 Å (the distance between the two first NN oxygen atoms). Therefore, the migration energy for our device is larger than 0.12 eV. The observed small loop (red curve in Figure 2b) is due to the negative temperature coefficient of the Zener effect; that is,

LETTER

Figure 5. (a, b) Schematics of the electric field effect on the activation energy.

the breakdown voltage decreases with increasing temperature. Because of the heating accumulation induced by the current, the local temperature of the nanowire for backward sweeping voltage is higher than that for the forward sweeping voltage. This is also responsible for the fact that the breakdown voltage in the backward sweeping process is smaller than that in the forward sweeping process (red curve in Figure 2b). By setting the compliance current to an appropriate value which corresponds to the Joule heating plus an electric field is sufficient to drive the oxygen vacancies migration to join in the Vo cluster but not enough to depart from the Vo cluster, a conductive oxygen vacancy filament will be formed. The system will then change from HRS to LRS. Withdrawing the applied electric field cannot change the system from LRS to HRS which corresponds to the memory RS (the black curve in Figure 2b). As the voltage for the RESET process is even less than that for the SET process, the electric field is not the dominant factor. Thus, the RESET in our devices is primarily due to large Joule heating as no compliance current is set. Therefore, in the presence of an extremely high current density (without setting the ICC), which leads to a very high local temperature (thermal energy), both kinds of oxygen vacancy hopping can occur. The Vo Vo interactions will be overcome, which results in the rupture of the Vo chain. As long as the conductive filament is destroyed, the current will reduce dramatically and the system is frozen to a state with disordered Vo configuration. As a result, the resistance of the system changes from LRS to HRS, which corresponds to the RESET process (the blue curve in Figure 2b). In conclusion, the controllable and reproducible alternation between memory and threshold RS was demonstrated for the first time in a single Ni/NiO core shell nanowire. The underlying mechanisms of electric field induced threshold RS and Joule heating plus electric field induced conductive filament formation during memory RS are described and well understood. Our findings may provide guidelines for the scaling, reliability, and reproducibility of NiO-based nonvolatile memory devices.

’ ASSOCIATED CONTENT

bS

Supporting Information. EDS spectrum of the NiO layer, I V curves, and SEM images show the degradation of the RS devices. This material is available free of charge via the Internet at http://pubs.acs.org.

4605

dx.doi.org/10.1021/nl202017k |Nano Lett. 2011, 11, 4601–4606

Nano Letters

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (Z.M.L.), [email protected] (H.C.W.), and [email protected] (D.P.Y.).

’ ACKNOWLEDGMENT This work was supported by NSFC (No. 10804002), MOST (Nos. 2007CB936202, 2009CB623703), the Sino-Swiss Science and Technology Cooperation Program (2010DFA01810), and the Science Foundation of Ireland (SFI Nos. 06/IN.1/I91 and 008/IN.1/I1932). This work made use of computing facilities at the Trinity Centre for High Performance Computing, supported by SFI. ’ REFERENCES (1) Seo, S.; Lee, M. J.; Seo, D. H.; Jeoung, E. J.; Suh, D. S.; Joung, Y. S.; Yoo, I. K.; Hwang, I. R.; Kim, S. H.; Byun, I. S.; Kim, J. S.; Choi, J. S.; Park, B. H. Appl. Phys. Lett. 2004, 85, 5655–5657. (2) Shima, H.; Takano, F.; Muramatsu, H.; Akinaga, H.; Tamai, Y.; Inoue, I. H.; Takagi, H. Appl. Phys. Lett. 2008, 93, 113504. (3) Lee, S.; Fursina, A.; Mayo, J. T.; Yavuz, C. T.; Colvin, V. L.; Sofin, R. G. S.; Shvets, I. V.; Natelson, D. Nat. Mater. 2008, 7, 130–133. (4) (a) Jo, S. H.; Kim, K.-H.; Lu, W. Nano Lett. 2009, 9, 870–874. (b) Dong, Y.; Yu, G.; McAlpine, M.; Lu, W.; Lieber, C. M. Nano Lett. 2008, 8, 386–391. (5) Liao, Z. M.; Hou, C.; Zhao, Q.; Wang, D. S.; Li, Y. D.; Yu, D. P. Small 2009, 5, 2377–2381. (6) Waser, R.; Aono, M. Nat. Mater. 2007, 6, 833–840. (7) Nian, Y. B.; Strozier, J.; Wu, N. J.; Chen, X.; Ignatiev, A. Phys. Rev. Lett. 2007, 98, 146403. (8) Rozenberg, M. J.; Inoue, I. H.; Sanchez, M. J. Phys. Rev. Lett. 2004, 92, 178302. (9) Fors, R.; Khartsev, S. I.; Grishin, A. M. Phys. Rev. B 2005, 71, 045305. (10) Liu, Z. M.; Yasseri, A. A.; Lindsey, J. S.; Bocian, D. F. Science 2003, 302, 1543–1545. (11) Henisch, H. K.; Smith, W. R. Appl. Phys. Lett. 1974, 24, 589–591. (12) Sawa, A. Mater. Today 2008, 11, 28–36. (13) Sanchez, M. J.; Rozenberg, M. J.; Inoue, I. H. Appl. Phys. Lett. 2007, 91, 252101. (14) Jung, K.; Seo, H.; Kim, Y.; Im, H.; Hong, J.; Park, J. W.; Lee, J. K. Appl. Phys. Lett. 2007, 90, 052104. (15) Chae, S. C.; Lee, J. S.; Kim, S.; Lee, S. B.; Chang, S. H.; Liu, C.; Kahng, B.; Shin, H.; Kim, D. W.; Jung, C. U.; Seo, S.; Lee, M. J.; Noh, T. W. Adv. Mater. 2008, 20, 1154–1159. (16) Sugimoto, N.; Onoda, S.; Nagaosa, N. Phys. Rev. B 2008, 78, 155104. (17) Chang, S. H.; Lee, J. S.; Chae, S. C.; Lee, S. B.; Liu, C.; Kahng, B.; Kim, D. W.; Noh, T. W. Phys. Rev. Lett. 2009, 102, 026801. (18) Lee, H. D.; Magyari-Kope, B.; Nishi, Y. Phys. Rev. B 2010, 81, 193202. (19) Jeong, D. S.; Schroeder, H.; Waser, R. Electrochem. Solid-State Lett. 2007, 10, G51–G53. (20) Chae, S. C.; Lee, J. S.; Choi, W. S.; Lee, S. B.; Chang, S. H.; Shin, H.; Kahng, B.; Noh, T. W. Appl. Phys. Lett. 2009, 95, 093508. (21) Chang, S. H.; Chae, S. C.; Lee, S. B.; Liu, C.; Noh, T. W.; Lee, J. S.; Kahng, B.; Jang, J. H.; Kim, M. Y.; Kim, D. W.; Jung, C. U. Appl. Phys. Lett. 2008, 92, 183507. (22) Sun, J. L.; Zhao, X. C.; Zhu, J. L. Nanotechnology 2009, 20, 455203. (23) Kresse, G.; Hafner, J. Phys. Rev. B 1993, 47, 558–561. (24) Kresse, G.; Furthmuller, J. Comput. Mater. Sci. 1996, 6, 15–50. (25) Payne, M. C.; Teter, M. P.; Allan, D. C.; Arias, T. A.; Joannopoulos, J. D. Rev. Mod. Phys. 1992, 64, 1045–1097.

LETTER

(26) Bengone, O.; Alouani, M.; Bl€ochl, P.; Hugel, J. Phys. Rev. B 2000, 62, 16392–16401. (27) Lee, M. J.; Han, S.; Jeon, S. H.; Park, B. H.; Kang, B. S.; Ahn, S. E.; Kim, K. H.; Lee, C. B.; Kim, C. J.; Yoo, I. K.; Seo, D. H.; Li, X. S.; Park, J. B.; Lee, J. H.; Park, Y. Nano Lett. 2009, 9, 1476–1481. (28) Janousch, M.; Meijer, G. I.; Staub, U.; Delley, B.; Karg, S. F.; Andreasson, B. P. Adv. Mater. 2007, 19, 2232–2235. (29) Yang, J. J.; Pickett, M. D.; Li, X. M.; Ohlberg, D. A. A.; Stewart, D. R.; Williams, R. S. Nat. Nanotechnol. 2008, 3, 429–433. (30) Muller, D. A.; Nakagawa, N.; Ohtomo, A.; Grazul, J. L.; Hwang, H. Y. Nature 2004, 430, 657–661. (31) Woodward, D. I.; Reaney, I. M.; Yang, G. Y.; Dickey, E. C.; Randall, C. A. Appl. Phys. Lett. 2004, 84, 4650–4652. (32) Henkelman, G.; Jonsson, H. J. Chem. Phys. 2000, 113, 9978. (33) Orlandini, S.; Meloni, S.; Ippolito, M.; Colombo, L. Phys. Rev. B 2010, 81, 014203. (34) Mulroue, J.; Duffy, D. M. Proc. R. Soc. London, Ser. A 2011, 467, 2131. (35) Bonilla, L. L.; Malomed, B. A. Phys. Rev. B 1991, 43, 11539– 11541.

4606

dx.doi.org/10.1021/nl202017k |Nano Lett. 2011, 11, 4601–4606