Electrically Tunable In-Plane Anisotropic Magnetoresistance in

Letter pubs.acs.org/NanoLett

Electrically Tunable In-Plane Anisotropic Magnetoresistance in Topological Insulator BiSbTeSe2 Nanodevices Azat Sulaev,†,⬡ Minggang Zeng,‡,⬡ Shun-Qing Shen,§ Soon Khuen Cho,† Wei Guang Zhu,∥ Yuan Ping Feng,‡ Sergey V. Eremeev,¶,# Yoshiyuki Kawazoe,∇,○ Lei Shen,*,▲ and Lan Wang*,†,⊥ †

School of Physical and Mathematical Sciences, Division of Physics and Applied Physics, Nanyang Technological University, Singapore 637371 ‡ Department of Physics, National University of Singapore, Singapore 117542 § Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, People’s Republic of China ∥ School of Electronics and Electrical Engineering, Nanyang Technological University, Singapore 639789 ⊥ Physics, School of Applied Sciences, RMIT University, Melbourne, Victoria 3000, Australia ¶ Institute of Strength Physics and Materials Science, 634021 Tomsk, Russia # Tomsk State University, 634050 Tomsk, Russia ∇ New Industry Creation Hatchery Center, Tohoku University, Sendai 980-8579, Japan ○ Institute of Thermophysics, Siberian Branch of Russian Academy of Sciences, Novosibirsk 630090, Russia ▲ Engineering Science Programme, National University of Singapore, Singapore 117579 S Supporting Information *

ABSTRACT: We report tunable in-plane anisotropic magnetoresistance (AMR) in nanodevices based on topological insulator BiSbTeSe2 (BSTS) nanoflakes by electric gating. The AMR can be changed continuously from negative to positive when the Fermi level is manipulated to cross the Dirac point by an applied gate electric field. We also discuss effects of the gate electric field, current density, and magnetic field on the in-plane AMR with a simple physical model, which is based on the in-plane magnetic field induced shift of the spin-momentum locked topological two surface states that are coupled through side surfaces and bulk weak antilocalization (WAL). The large, tunable and bipolar inplane AMR in BSTS devices provides the possibility of fabricating more sensitive logic and magnetic random access memory AMR devices. KEYWORDS: topological insulator, in-plane magnetic field, gate electric field, anisotropic magnetoresistance, ab initio calculations

T

AMR of TI has never been reported. Recently, (Bi1−xSbx)2(Te1−ySey)3 has been confirmed to be a TI system with large bulk resistivity for certain x and y values.34,36,37,56 In recent works, surface dominated transport and significant ambipolar behavior have been realized in devices based on Bi1.5Sb0.5Te1.8Se1.2 nanoflakes, Sb-doped Bi2Se3 nanoplates,57 and BiSbTeSe 2 with the simplest stoichiometric ratio (1:1:1:2),58 which is simply abbreviated as BSTS in this paper, which provides an opportunity for further study on electron and spin transport in TIs under an applied gate voltage. Here, we report tunable in-plane AMR in nonmagnetic devices based on topological insulating BiSbTeSe2 nanoflakes. We demonstrate, for the first time, continuous tuning of the in-

opological insulator (TI), including 3D, 2D, and 1D structures,1−6 is a novel state of quantum matter characterized by the Z2 invariant. TIs are composed of fully filled insulating bulk states and metallic topological surface states (TSS).7−9 The spin and momentum of the Dirac electrons in TSS satisfy a helical lock-in relation, which has been confirmed experimentally by angle-resolved photoemission spectroscopy (ARPES).10−16 To date, extensive transport measurements on TI have been performed,17−39 including the in-plane magnetoresistance in Bi2Se3 and (BiSb)2Se3 thin films35,39 and the anisotropic magnetoresistance (AMR) effect in TI/ferromagnet heterostructure,38 in which the resistivity of materials depends on the relative orientation of the current density J ⃗ and applied magnetic field.40−49 Several theoretical predictions have also been made about the effect of in-plane magnetic field and electric field on topological surface states.50−52 However, due to large bulk conductance contribution in prototype three-dimensional (3D) TIs, such as Bi2Se3 and Bi2Te3, electric gate tuned in-plane © XXXX American Chemical Society

Received: December 24, 2014 Revised: February 2, 2015

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Figure 1. (a, b) Image of BSTS devices and a schematic diagram of the AMR measurement setup. The direction of the in-plane magnetic field is perpendicular (parallel) to the current direction at θ = 0° and 180° (90° and 270°). (c, d) Gate voltage dependence of the ambipolar effect (the purple circles) and AMR amplitude under the magnetic field of 1 and 9 T respectively (T = 2 K). (e) In-plane AMR of device 1 under 1 T magnetic field at 2 K with Vg = +50 V, +30 V, 0 V, −10 V, −30 V, and −50 V, respectively. (f) In-plane AMR of device 1 under 9 T magnetic field at 2 K with Vg = +50 V, +30 V, 0 V, −10 V, −30 V, and −50 V, respectively.

plane AMR, from positive to negative, by an electric gate voltage. Furthermore, the in-plane AMR value of BSTS devices can reach 9%, which is larger than that of transition FM metals, such as Fe, Ni, and Co. The AMR amplitude can be controlled by applied magnetic field and is robust against the variation in current density. To understand the mechanism behind the inplane AMR in BSTS devices, we carry out first-principles calculations and propose a simple physical model, based on the spin-momentum locked two topological surface states and the shift in their Fermi surfaces induced by in-plane magnetic fields. The large, tunable, and bipolar in-plane AMR in BSTS devices provides the possibility of fabricating more sensitive AMR logic and MRAM device using topological insulators. Figure 1a and 1b show the image of BSTS devices and a schematic experimental setup, where θ is the angle between the magnetic field and the direction perpendicular to the current. As shown in the purple curves in Figure 1c and 1d, and Supporting Information (Figure S1), the typical Dirac-type ambipolar current−voltage curve indicates gate-tunable charge transports contributed by topological surface states. Moreover, a pronounced gate-tuned in-plane AMR effect is observed. The

results of the in-plane AMR measurements at 1 and 9 T under various gate voltage are shown in Figures 1e and 1f, respectively. The AMR amplitudes are calculated using AMR amplitude =

ρmax − ρmin ρmin

(4)

where ρmax and ρmin are the maximum and minimum values of the resistivity, respectively. The AMR exhibits an oscillatory behavior with a period of 180°. Furthermore, the AMR at 9 T field evolves gradually from positive (ρ∥ < ρ⊥) to negative (ρ∥ > ρ⊥) when Vg varies from +50 V to −50 V, which has never been reported in any systems prior to our work. As shown in Figure 1f, at Vg = +50 V, a positive AMR is observed, whereas a negative AMR is observed at Vg = −50 V. The in-plane AMR peaks shift gradually when Vg is varied from +50 V to −50 V. Besides, the maximum in AMR amplitude occurs near the charge neutrality point at Vg = +10 V. Although BSTS is a nonferromagnetic material, its AMR amplitude can reach 9%, which is larger than that in transition metals with strong ferromagnetism, such as Fe, Ni, and so forth. Furthermore, we B

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Figure 2. (a) In-plane AMR of device 1 under 1 T magnetic field and Vg = +10 V at 2 K with different current densities. (b) Variation of AMR amplitude with increasing current density at 2 K for three different measurement conditions, (1) B = 1 T and Vg = +10 V, (2) B = 1 T and Vg = −50 V, and (3) B = 9 T and Vg = −50 V.

Figure 3. (a) and (b) In-plane AMR of device 1 at 2 K under various magnetic fields with Vg = +10 V and −50 V, respectively. (c), (d), and (e) Magnetic field dependence of AMR amplitude at 2 K with Vg = +10 V, −50 V, and +25 V, respectively.

find the in-plane AMR in BSTS devices is very robust against the variation in current density. Figure 2a shows that the shape and value of the AMR at Vg = 10 V and B = 1 T are almost unchanged when the current density varies from 25 nA to 500 nA. Under other conditions, the AMR shows the same trend and the calculated AMR amplitude in Figure 2b remains almost constant against the current density with fixed applied magnetic field and gate voltage. In addition, we investigate the magnetic field dependences of the in-plane AMR. The sign of AMR in Figure 3a (Vg = +10 V) and Figure 3b (Vg = −50 V) does not change with increasing magnetic field. The ρ⊥ is always larger than ρ∥ at Vg = +10 V, whereas ρ⊥ remains smaller than ρ∥ at Vg = −50

V. Figures 3c−e show that the amplitude of AMR increases with magnetic field; and a saturated AMR amplitude is found with Vg = +25 V (Figure 3e). The large bulk resistivity and the proximity of the charge neutrality point to 0 V in Figure 1b and c indicate that the Fermi level of our devices lies in vicinity to the Dirac point and the transport carriers come from topological surface states. Moreover, the largest AMR value can be obtained near the charge neutrality point; and the AMR decreases when the gate voltage shifts the Fermi level close to the bulk band. Besides, the AMR effect decreases in aged BSTS devices with degraded surface states; and the AMR effect is not found in our samples without TSS (Device 3 in Supporting Information). All these C

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Figure 4. (a) Schematic of coupling of two surface states in a 3D topological insulator (see detailed in Supporting Information Figure S6). (b) Inplane magnetic field induced Dirac cone shift of the top and bottom topological surface states. (c) and (d) Schematic diagram of the Fermi circle shift and its generated net spin polarization. (e) Relationship between the value of the net spin polarization and the magnitude of magnetic field.

by the spin polarization rotating with applied magnetic field, which generates scattering probability dependent on the angle between the current and applied magnetic field. This explains the observed in-plane AMR with a period of 180° in our experiment (Figures 1−3). This simple model can also explain the evolution of the inplane AMR with gate-voltage, current densities, and magnitude of magnetic field shown in Figures 1−3. Figure 5 shows the

results suggest that the in-plane AMR should originate from the topological surface state. Our first-principles calculations (see details in Supporting Information) on the band structure of BSTS prove the existence of topological surface states and the 0.21 eV bulk band gap, which is in agreement with the experimental results59 and similar to the calculated band structure of the Bi2Se3 slab.60 Furthermore, the spin texture of topological surface states in BSTS slab is also calculated for the next evaluation of the relative shift of the Fermi contours of the top and bottom surface states caused by the in-plane magnetic field. Notice that under a bias voltage (for example the x direction in Figure 4a), the Dirac electrons in the top and bottom surfaces can couple either through side surfaces as shown in Figure 4a or through the bulk state in the weak antilocalization (WAL) effect (see Supporting Information Figure S6), which occurs over a length scale far greater than the critical thickness (6QLs or 6 nm) of direct coupling.24,26,28,61−69 Oh’s group reported the robustness of the WAL effect even in 3,600 QLs (∼3,600 nm) in TI of Bi2Se3.61 If an in-plane magnetic field is applied on the surface of the TI, for example, B = By ŷ, a relative momentum shift, px = q, between the top and bottom surface states occurs as shown in Figure 4b, where q = eBydx̂. Such an opposite in-plane momentum shift is similar to a Rashba splitting with the Rashba coefficient of q/2.70,71 The Fermi momentum is defined as pF = (EF/v), where EF is the Fermi level and v is the velocity. The momentum shift of two TSS induced by the in-plane magnetic field can generate net spin polarization (Snet). Figure 4c and d show that the orientation of the net spin polarization is parallel (or antiparallel) to the applied magnetic field and hence rotates with the magnetic field relative to the current in our experiment. Moreover, the NET spin polarization is proportional to the magnetic field as shown in Figure 4e. We can estimate the net spin polarization based on our first-principles calculations of in-plane spin polarization, Sxy (⟨Sxy(k⇀)⟩/ℏ) = 0.3, of the two topological surface states at E = EF + 50 meV (see Supporting Information Figure S5), and equations q = eBydx̂, pF = (EF/v). If we take the realistic value v = 5 × 105 m/ s, EF = 50 meV, l′=100 nm, the estimated net polarization is 0.04 and 0.36 under the magnetic field of 1T and 9T, respectively, for BSTS, which indicates the net polarization is in proportion to the external in-plane magnetic field. The theory of McGuire and Potter suggests that in-plane AMR is induced

Figure 5. Schematic diagram of the top and bottom topological surface states with an in-plane magnetic field under different gate voltages. (a) The Fermi level is higher the Dirac point. The carriers are n-type Dirac electrons; (b) the Fermi level is lower than the Dirac point. The carriers are p-type Dirac holes. It shows that the same direction of applied magnetic field can generate different direction of net spin polarization because of the different helical spin characters of Dirac electrons and holes.

schematic diagram of two topological surface states under different gate voltages. The chemical potential of the two Dirac cones is shifted by the gate voltage.26 Because of the opposite spin helicities of Dirac electrons and holes in the topological surface states, the net spin, Snet, reverses its orientation when the bias direction is changed (lower panel of Figure 5a and b). According to the theory of McGuire and Potter50 and experiments on a tunable highly spin polarized system,58,59 the sign of the in-plane AMR is determined by the sign of the spin polarization. The opposite net spin polarization of Dirac carriers (electrons and holes) is the reason for the opposite sign of AMR in the experiment under +50 V and −50 V gate voltages (Figure 1e and f). Because the net spin polarization is D

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(10) King, P. D. C.; Hatch, R. C.; Bianchi, M.; Ovsyannikov, R.; Lupulescu, C.; Landolt, G.; Slomski, B.; Dil, J. H.; Guan, D.; Mi, J. L.; Rienks, E. D. L.; Fink, J.; Lindblad, A.; Svensson, S.; Bao, S.; Balakrishnan, G.; Iversen, B. B.; Osterwalder, J.; Eberhardt, W.; Baumberger, F.; Hofmann, P. Phys. Rev. Lett. 2011, 107, 096802− 096805. (11) Chen, L.; Analytis, J. G.; Chu, J. H.; Liu, Z. K.; Mo, S. K.; Qi, X. L.; Zhang, H. J.; Lu, D. H.; Dai, X.; Fang, Z.; Zhang, S. C.; Fisher, I. R.; Hussain, Z.; Shen, Z. X. Science 2009, 325, 178−181. (12) Hsieh, D.; Xia, Y.; Wray, L.; Qian, D.; Pal, A.; Dil, J. H.; Osterwalder, J.; Meier, F.; Bihlmayer, G.; Kane, C. L.; Hor, Y. S.; Cava, R. J.; Hasan, M. Z. Science 2009, 323, 919−922. (13) Hirahara, T.; Sakamoto, Y.; Takeichi, Y.; Miyazaki, H.; Kimura, S. I.; Matsuda, I.; Kakizaki, A.; Hasegawa, S. Phys. Rev. B 2010, 82, 155309−6. (14) Jozwiak, C.; Chen, Y. L.; Fedorov, A. V.; Analytis, J. G.; Rotundu, C. R.; Schmid, A. K.; Denlinger, J. D.; Chuang, Y. D.; Lee, D. H.; Fisher, I. R.; Birgeneau, R. J.; Shen, Z. X.; Hussain, Z.; Lanzara, A. Phys. Rev. B 2011, 84, 165113−9. (15) Miyamoto, K.; Kimura, A.; Okuda, T.; Miyahara, H.; Kuroda, K.; Namatame, H.; Taniguchi, M.; Eremeev, S. V.; Menshchikova, T. V.; Chulkov, E. V.; Kokh, K. A.; Tereshchenko, O. E. Phys. Rev. Lett. 2012, 109, 166802−5. (16) Souma, S.; Kosaka, K.; Sato, T.; Komatsu, M.; Takayama, A.; Takahashi, T.; Kriener, M.; Segawa, K.; Ando, Y. Phys. Rev. Lett. 2011, 106, 216803−4. (17) Analytis, J. G.; Chu, J. H.; Chen, Y.; Corredor, F.; McDonald, R. D.; Shen, Z. X.; Fisher, I. R. Phys.Rev. B 2010, 81, 205407−5. (18) Yuan, H.; Liu, H.; Shimotani, H.; Guo, H.; Chen, M.; Xue, Q.; Iwasa, Y. Nano Lett. 2011, 11, 2601−2605. (19) Checkelsky, J. G.; Hor, Y. S.; Cava, R. J.; Ong, N. P. Phys. Rev. Lett. 2011, 106, 196801−4. (20) Hor, Y. S.; Richardella, A.; Roushan, P.; Xia, Y.; Checkelsky, J. G.; Yazdani, A.; Hasan, M. Z.; Ong, N. P.; Cava, R. J. Phys. Rev. B 2009, 79, 195208−5. (21) Qu, D. X.; Hor, Y. S.; Xiong, J.; Cava, R. J.; Ong, N. P. Science 2010, 329, 821−821. (22) Kim, D.; Cho, S.; Butch, N. P.; Syers, P.; Kirshenbaum, K.; Adam, S.; Paglione, J.; Fuhrer, M. S. Nat. Phys. 2012, 8, 459−463. (23) Butch, N. P.; Kirshenbaum, K.; Syers, P.; Sushkov, A. B.; Jenkins, G. S.; Drew, H. D.; Paglione, J. Phys. Rev. B 2010, 81, 241301−4. (24) Cha, J. J.; Claassen, M.; Kong, D.; Hong, S. S.; Koski, K. J.; Qi, X. L.; Cui, Yi. Nano Lett. 2012, 12, 4355−4359. (25) Peng, H.; Lai, K.; Kong, D.; Meister, S.; Chen, Y.; Qi, X.-L.; Zhang, S.-C.; Shen, Z.-X.; Cui, Y. Nat. Mater. 2010, 9, 225−229. (26) Chen, J.; Qin, H. J.; Yang, F.; Liu, J.; Guan, T.; Qu, F. M.; Zhang, G. H.; Shi, J. R.; Xie, X. C.; Yang, C. L.; Wu, K. H.; Li, Y. Q.; Lu, L. Phys. Rev. Lett. 2010, 105, 176602−4. (27) Kim, Y. S.; Brahlek, M.; Bansal, N.; Edrey, E.; Kapilevich, G. A.; Iida, K.; Tanimura, M.; Horibe, Y.; Cheong, S. W.; Oh, S. Phys. Rev. B 2011, 84, 073109−5. (28) Liu, M.; Zhang, J.; Chang, C. Z.; Zhang, Z.; Feng, X.; Li, K.; He, K.; Wang, L. L.; Chen, X.; Dai, X.; Fang, Z.; Xue, Q. K.; Ma, X.; Wang, Y. Phys. Rev. Lett. 2012, 108, 036805−5. (29) Cao, H. L.; Tian, J. F.; Miokowsky, I.; Shen, T.; Hu, J. N.; Qiao, S.; Chen, Y. P. Phys. Rev. Lett. 2012, 108, 216803−5. (30) He, H. T.; Wang, G.; Zhang, T.; Sou, I. K.; Wong, G. K. L.; Wang, J. N.; Lu, H. Z.; Shen, S. Q.; Zhang, F. C. Phys. Rev. Lett. 2011, 106, 166805−4. (31) Matsuo, S.; Koyama, T.; Shimamura, K.; Arakawa, T.; Nishihara, Y.; Chiba, D.; Kobayashi, K.; Ono, T.; Chang, C. Z.; He, K.; Ma, X. C.; Xue, Q. K. Phys. Rev. B 2012, 85, 075440−6. (32) Barreto, L.; Kuhnemund, L.; Edler, F.; Tegenkamp, C.; Mi, J. L.; Bremholm, M.; Iversen, B. B.; Frydendahl, C.; Bianchi, M.; Hofmann, P. Nano Lett. 2014, 14, 3755−3760. (33) Tang, J. S.; Chang, L. T.; Kou, X. F.; Murata, K.; Choi, E. S.; Lang, M. R.; Fang, Y. B.; Jiang, Y.; Montazeri, M.; Jiang, W. J.; Wang, Y.; He, L.; Wang, K. L. Nano Lett. 2014, 14, 5423−5429.

irrelevant to the current density, the variation in current density does not change the shape and value of the AMR. Moreover, the magnitude of magnetic field only determines the value of net spin, and thus the amplitude of the AMR increases with the magnetic field, whereas the sign of AMR does not change. In conclusion, we have observed a large and electrically tunable in-plane AMR effect in devices of nonmagnetic TI BSTS nanoflakes. For the first time, a large in-plane AMR, which can be tuned from negative to positive by electric gate voltage, is realized. The effects of gate electric field, current density and magnetic field on the in-plane AMR are explained by a physical model and first-principles calculations. Our results indicate BSTS as a promising topological material for fabricating in-plane AMR based logic and magnetic random access memory devices.

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ASSOCIATED CONTENT

* Supporting Information S

Device fabrication and magnetotransport measurement, aging effect, and contrast experiment for devices with and without TSS, the temperature dependence of the in-plane AMR, computational method, atomic structure of BSTS, and bandstructure/spin-texture of BSTS. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (theory). *E-mail: [email protected] (experiment). Author Contributions ⬡

These authors contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Ministry of Education of Singapore (Grant No. MOE2010-T2-2-059), the Research Grant Council of Hong Kong under Grant No. HKU705110P, and the National Science Foundation of China, Grant No. 61376127. The calculation part of this work was carried out by using the CCMS SR16000 Supercomputer System at Institute for Materials Research, Tohoku University, Japan. One of the authors (Y. K.) is thankful to the Russian Megagrant Project No. 14.B25.31.0030 “New energy technologies and energy carriers” for supporting the present research.

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REFERENCES

(1) Steinberg, H.; Gardner, D. R.; Lee, Y. S.; Jarillo-Herrero, P. Nano Lett. 2010, 10, 5032−5036. (2) Lu, Y.; Xu, W.; Zeng, M.; Yao, G.; Shen, L.; Yang, M.; Luo, Z.; Pan, F.; Wu, K.; Das, T.; He, P.; Jiang, J.; Martin, J.; Feng, Y. P.; Lin, H.; Wang, X.-S. Nano Lett. 2015, 15, 80−87. (3) Wang, Z. F.; Su, N. H.; Liu, F. Nano Lett. 2013, 13, 2842−2845. (4) Hong, S. S.; Zhang, Y.; Cha, J. J.; Qi, X.-L.; Cui, Y. Nano Lett. 2014, 14, 2815−2821. (5) Kong, D. S.; Randel, J. C.; Peng, H. L.; Cha, J. J.; Meister, S.; Lai, K. J.; Chen, Y. L.; Shen, Z. X.; Manoharan, H. C.; Cui, Y. Nano Lett. 2010, 10, 329−333. (6) Safdar, M.; Wang, Q. S.; Mirza, M.; Wang, Z. X.; Xu, K.; He, J. Nano Lett. 2013, 13, 5344−5349. (7) Moore, J. E. Nature 2010, 464, 194−198. (8) Qi, X. L.; Zhang, S. C. Phys. Today 2010, 63, 33−38. (9) Hasan, M. Z.; Kane, C. L. Rev. Mod. Phys. 2010, 82, 3045−3067. E

DOI: 10.1021/nl504956s Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters (34) Ren, Z.; Taskin, A. A.; Sasaki, S.; Segawa, K.; Ando, Y. Phys. Rev. B 2010, 82, 241306−4. (35) Lin, C. J.; He, X. Y.; Liao, J.; Wang, X. X.; Sacksteder, V.; Yang, W. M.; Guan, T.; Zhang, Q. M.; Gu, L.; Zhang, G. Y.; Zeng, C. G.; Dai, X.; Wu, K. H.; Li, Y. Q. Phys. Rev. B 2013, 88, 041307−6. (36) Taskin, A. A.; Ren, Z.; Sasaki, S.; Segawa, K.; Ando, Y. Phys. Rev. Lett. 2011, 107, 016801−4. (37) Hong, S. S.; Chua, J. J.; Kong, D. S.; Cui, Y. Nat. Commun. 2012, 3, 757−762. (38) Xia, B.; Ren, P.; Sulaev, A.; Li, Z. P.; Liu, P.; Dong, Z. L.; Wang, L. AIP Adv. 2012, 2, 042171−11. (39) Wang, J.; Li, H. D.; Chang, C. Z.; He, K.; Lee, J. S.; Lu, H. Z.; Sun, Y.; Ma, X. C.; Samarth, N.; Shen, S. Q.; Xue, Q. K.; Xie, M. H.; Chan, M. H. W. Nano Res. 2012, 5, 739−746. (40) McGuire, T. R.; Potter, R. I. IEEE Trans. Magn. 1975, 11, 1018−1038. (41) Thompson, D. A.; Romankiw, L. T.; Mayadas, A. F. IEEE Trans. Magn. 1975, 11, 1039−1050. (42) Li, G. H.; Yang, T.; Hu, Q.; Jiang, H. G.; Lai, W. Y. Phys. Rev. B 2002, 65, 134421−5. (43) Chiba, D.; Sawicki, M.; Nishitani, Y.; Nakatani, Y.; Matsukura, F.; Ohno, H. Nature 2008, 455, 515−518. (44) Tang, H. X.; Kawakami, K. K.; Awschalon, D. D.; Roukes, M. L. Phys. Rev. Lett. 2003, 90, 107201−4. (45) Bason, Y.; Klein, L.; Yau, J. B.; Hong, X.; Ahn, C. H. Appl. Phys. Lett. 2004, 84, 2593−2595. (46) Goennenwen, S. T. B.; Keizer, R. S.; Schnik, S. W.; Van Dijk, I.; Klapwijk, T. M.; Miao, G. X.; Xiao, G.; Gupta, A. Appl. Phys. Lett. 2007, 90, 142509−142511. (47) Bason, Y.; Klein, L.; Yau, J. B.; Hong, X.; Hoffman, J.; Ann, C. H. J. Appl. Phys. 2006, 99, 08R701−08R701−3. (48) Wang, L.; Umemoto, K.; Wentzcovitch, R. M.; Chen, T. Y.; Chien, C. L.; Checkelsky, J. G.; Eckert, J. C.; Dahlberg, E. D.; Leighton, C. Phys. Rev. Lett. 2005, 94, 056602−4. (49) Wang, L.; Chen, T. Y.; Chien, C. L.; Checkelsky, J. G.; Eckert, J. C.; Dahlberg, E. D.; Umemoto, K.; Wentzcovitch, R. M.; Leighton, C. Phys. Rev. B 2006, 73, 144402−4. (50) Zhang, W.; Yu, R.; Zhang, H. J.; Dai, X.; Fang, Z. New J. Phys. 2010, 12, 065013−14. (51) Zyuzin, A. A.; Hook, M. D.; Burkov, A. A. Phys. Rev. B 2011, 83, 245428−4. (52) Yazyev, O. V.; Moore, J. E.; Louie, S. G. Phys. Rev. Lett. 2001, 105, 266806−4. (53) Yazyev, O. V.; Kioupakis, E.; Moore, J. E.; Louie, S. G. Phys. Rev. B 2012, 85, 161101−4. (54) Gargiulo, F.; Yazyev, O. V. Nano Lett. 2014, 14, 250−254. (55) Kong, D. S.; Dang, W. H.; Cha, J. J.; Li, H.; Meister, S.; Peng, H. L.; Liu, Z. F.; Cui, Y. Nano Lett. 2010, 10, 2245−2250. (56) Arakane, T.; Sato, T.; Souma, S.; Kosaka, K.; Nakayama, K.; Komatsu, M.; Takahashi, T.; Ren, Z.; Segawa, K.; Ando, Y. Nat. Commun. 2012, 3, 636. (57) Kong, D. S.; Koski, K. J.; Cha, J. J.; Hong, S. S.; Cui, Y. Nano Lett. 2013, 13, 632−636. (58) Xia, B.; Ren, P.; Sulaev, A.; Liu, P.; Shen, S. Q.; Wang, L. Phys. Rev. B 2013, 87, 085442−8. (59) Xu, Y.; Miotkowski, I.; Liu, C.; Tian, J.; Nam, H.; Alidoust, N.; Hu, J.; Shih, C.-K.; Hasan, M. Z.; Chen, Y. P. Nat. Phys. 2014, 10, 956−963. (60) Shen, L.; Zeng, M. G.; Lu, Y. H.; Yang, M.; Feng, Y. P. Phys. Rev. Lett. 2013, 111, 236803−5. (61) Kim, Y. S.; Brahlek, M.; Bansal, N.; Edrey, E.; Kapilevich, G. A.; Iida, K.; Tanimura, M.; Horibe, Y.; Cheong, S.-W.; Oh, S. Phys. Rev. B 2011, 84, 073109−5. (62) Brahlek, M.; Koirala, N.; Salehi, M.; Bansal, N.; Oh, S. Phys. Rev. Lett. 2014, 113, 026801−5. (63) Bansal, N.; Kim, Y. S.; Brahlek, M.; Edrey, E.; Oh, S. Phys. Rev. Lett. 2012, 109, 116804−5. (64) Lu, H.-Z.; Shi, J.; Shen, S.-Q. Phys. Rev. Lett. 2011, 107, 076801−5.

(65) Liu, M.; Chang, C.-Z.; Zhang, Z.; Zhang, Y.; Ruan, W.; He, K.; Wang, L.; Cheng, X.; Jia, J.-F.; Zhang, S.-C.; Xue, Q.-K.; Ma, X.; Wang, Y. Phys. Rev. B 2011, 83, 165440−6. (66) Cha, J. J.; Kong, D.; Hong, S.-S.; Analytis, J. G.; Lai, K.; Cui, Y. Nano Lett. 2012, 12, 1107−1111. (67) Lee, J.; Park, J.; Lee, J.-H.; Kim, J. S.; Lee, H.-J. Phys. Rev. B 2012, 86, 245321−10. (68) Taskin, A. A.; Sasaki, S.; Segawa, K.; Ando, Y. Phys. Rev. Lett. 2012, 109, 066803−5. (69) Steinberg, H.; Laloe, J.-B.; Fatemi, V.; Moodera, J. S.; JarilloHerrero, P. Phys. Rev. B 2011, 84, 233101−4. (70) Pershoguba, S. S.; Yakovenko, V. M. Phys. Rev. B 2012, 86, 165404−5. (71) Henk, J.; Flieger, M.; Maznichenko, I. V.; Mertig, I.; Ernst, A.; Eremeev, S. V.; Chulkov, E. V. Phys. Rev. Lett. 2012, 109, 076801−5.

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DOI: 10.1021/nl504956s Nano Lett. XXXX, XXX, XXX−XXX