Jonker, B. T.

Li, C. H.

Li, L.

Rajput, S.

van ‘t Erve, O. M. J.

English

The Research Repository @ WVU (West Virginia University)

Faculty Scholarship 2019 Reply to: “On the Understanding of Current-induced Spin Polarization of Three-dimensional Topological Insulators” C. H. Li O. M. J. van ‘t Erve S. Rajput L. Li B. T. Jonker Follow this and additional works at: https://researchrepository.wvu.edu/faculty_publications  Part of the Astrophysics and Astronomy Commons, and the Physics Commons MATTERS ARISINGReply to: “On the understanding of current-inducedspin polarization of three-dimensional topologicalinsulators”C.H. Li1, O.M.J. van ‘t Erve1, S. Rajput2, L. Li3 & B.T. Jonker1REPLYING TO J. Tian et al. Nature Communications https://doi.org/10.1038/s41467-019-09271-1 (2019)Spin potentiometric measurements have been used to elec-trically detect spin polarization arising from spin-momentum locking in topological insulator (TI) surfacestates1–10, albeit with conflicting signs of the measured spinvoltage. A model based upon spin-dependent potentials in the TIchannel4 has often been used to interpret these data. We used thismodel in ref. 9, but have subsequently concluded that it is mis-leading and does not consider the real and morecomplex situation of the actual measurement.This model postulates parallel spin-dependent potentials in theTI channel, and the issue raised by Tian et al.11 is the specificordering of the spin-up and spin-down electrochemical poten-tials4. We had placed the spin-up (majority) electrochemicalpotential level further from zero due to its greater magnitude9,which may be inconsistent with their original model.We subsequently realized that this model neglects critical spin-dependent parameters such as interface and channel resistances,and believe that is too simplistic to accurately account for the realexperimental systems under study. Specifically, the potentialprofiles include vertical drops at the contact interface to the TIchannel, which would indicate a current discontinuity (i.e., aninfinite current), and therefore is fundamentally unphysical. It isthis inadequacy which has resulted in apparent contradictoryresults from different groups. We have developed a more realisticmodel that includes experimental parameters such as interfaceand spin-dependent channel resistances, and find that a crossingof the spin-up and spin-down voltage levels can occur, which canlead to measured spin voltages of either sign12.Any practical system will have contacts for experimentalaccess, and these interfaces are crucial to electrical transport whencurrent is converted from one type of charge/spin carrier toanother. The interface resistances at the current injecting contactsmay be nonlinear and/or comparable to the TI channel, perhapsdue to oxidation or a blanket layer of tunnel barrier material suchas Al2O3 often deposited for capping purposes and/or to simplifyfabrication1,2,4–10. This creates varying interface resistances thatcan fundamentally change the carrier conversion at the interface.Figure 1a shows a typical I-V curve taken between the currentinjecting Au/Al2O3/Bi2Se3 contacts as used in1,9,12, showing anon-negligible and nonlinear interface resistance where a voltagedrop can be supported.Figure 1b shows a schematic resistor circuit model for spin-upand spin-down electrons traveling in two independentchannels12,13. As electrons travel from the right gold electrode tothe left, different resistances are encountered which can be eitherspin independent, e.g., at the left Au/Al2O3/TI interface whereelectrons enter into the Au electrode (Rint,R↑= Rint,R↓); or spin-dependent, e.g., the interface resistance where the electrons enterthe TI channel (depending on the alignment of the electron spinand the states in the TI14 (Rint,R↑ < Rint,R↓). A detailed discussionis presented in12.Given that the overall voltage drop between the Au contactsmust be the same for the spin-up and down channels, and thatthe spin-up channel is lower resistance, more current flowsthrough the spin-up channel, I↑ > I↓. Consequently, at the left TI/Al2O3/Au interface that is spin independent, the voltage drop isgreater for the spin-up channel, as depicted by the steeper slopefor the spin-up (blue) line within the left interface region inFig. 2a, b.Conversely, at the right Au/Al2O3/TI interface that is spin-dependent, two different outcomes are possible depending uponthe relative magnitudes of Rint,R↑ and Rint,R↓: either Vint,R↑ <Vint,R↓ or Vint,R↑ >Vint,R↓. This leads to potential profiles either withthe spin-down level consistently above the spin-up level (Fig. 2a),or a crossing of these levels at some point within the TI channel(Fig. 2b).It is important to recognize that this crossing does not imply achange in sign of the spin polarization in the channel or directionof the charge flow, but will result in a reversal of the measuredspin voltage loop, as discussed below. Here charge carrierhttps://doi.org/10.1038/s41467-019-10396-6 OPEN1Materials Science and Technology Division, Naval Research Laboratory, Washington, DC 20375, USA. 2 Intel Corporation, Hillsboro, OR 97124, USA.3 Department of Physics and Astronomy, West Virginia University, Morgantown, WV 26506, USA. Correspondence and requests for materials should beaddressed to C.H.L. (email: connie.li@nrl.navy.mil)NATURE COMMUNICATIONS |         (2019) 10:2523 | https://doi.org/10.1038/s41467-019-10396-6 | www.nature.com/naturecommunications 11234567890():,;conversion at the Au/TI interfaces creates boundary conditions toensure the spin and current continuity across the interface, justlike carrier conversion at any ferromagnet/nonmagnetinterfaces12,13. This results in the splitting of the spin-up andspin-down levels near the interface in the TI. However, the spincoherence length in the TI surface states is very large and typicallygreater than the TI channel length. Hence the equilibriumconditions that would be expected for an isolated TI are notreached. Thus different voltage profiles and relative energies ofthe spin-up and spin-down levels can be created depending onthe relative magnitudes of the spin-dependent resistances atinterfaces and within the channel. A detailed treatment is pro-vided in ref. 12.Probing these voltage profiles by a ferromagnet/tunnel barriercontact via potentiometric measurement9 yields hysteresis loopsof opposite sign as shown in Fig. 2c, d. The sign in Fig. 2c isconsistent with observations in refs. 4,6,8, and that of Fig. 2dconsistent with refs. 1,8–10.3a b LeftAu electrodeElectron flow Electron flowSpin-upLow R for spin up eRTI,↑Low interface R forspin up e, Rint,↑Spin-downHigh R for spin down eRTI,↓High interface R forspin down e, Rint,↓Spin-upSpin-downRAu,L Rint,L Rint,R RAu,RRTIesTI/Al2O3/AuinterfaceAu/Al2O3/TIinterfaceRightAu electrodeTI channel210Current (mA)–1–2–3–0.6 0.6Interface resistancenot spin-dependentT = 8 K–0.4 0.4–0.2 0.20Voltage (V)Fig. 1 Typical I-V and schematic of model taking into account spin-dependent interface resistances. a Typical I-V curve taken at 8K between currentinjecting Au/Al2O3/Bi2Se3 contacts, showing a nonlinear behavior. b Schematic of a resistor circuit model for spin-up and spin-down electrons traveling intwo independent channels from the right to the left electrode, where each component of the circuit from the contacts to interfaces are modeled as aresistor, specifically, the right Au electrode RAu,R, the right Au/Al2O3/TI interface Rint,R, TI channel resistance RTI, the left TI/Al2O3/Au interface Rint,L, andthe left Au electrode RAu,LVLVRLeft AuelectrodeVLLeft AuelectrodeRight AuelectrodeLeftTI/AI2O3/AuinterfaceLeftTI/AI2O3/AuinterfaceRightAu/AI2O3/TIinterfaceTI channela bc dTI channelV↑V(–M)seseseV(+M)V↓Vint,R↓Vint,R↑Vint,R↑ < Vint,R↓(Rint,R↑ << Rint,R↓ , I↑ ≥ I↓) (Rint,R↑ ≤ Rint,R↓ , I↑ >> I↓)Vint,R↑ > Vint,R↓VRRight AuelectrodeRightAu/AI2O3/TIinterfaceVint,R↓Vint,R↑FM detectorFM detector+M0–M–M +MVBV(+M) = (V↓ – VR)V(–M) = (V↑ – VR)sese0–M +MVBV(+M) = (V↓ – VR)V(–M) = (V↑ – VR)V↑V(–M)V(+M)V↓–M+MFig. 2 Voltage profile and predicted lineshape of measured spin voltages. Voltage profiles for the spin-up (blue) and spin-down (red) electrons for a leftflowing current, for the case (a) Vint,R↑ < Vint,R↓ (due to for example I↑≥ I↓, Rint,R↑ « Rint,R↓), and (b) Vint,R↑ > Vint,R↓ (due to for example I↑ » I↓, Rint,R↑ ≤ Rint,R↓).Predicted lineshape for the spin voltage measured by a ferromagnet/tunnel barrier detector contact for the voltage profiles in (a, b) are shown in (c, d),respectivelyMATTERS ARISING NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-10396-62 NATURE COMMUNICATIONS |         (2019) 10:2523 | https://doi.org/10.1038/s41467-019-10396-6 | www.nature.com/naturecommunicationsAs noted above, the resistances at the left TI/Al2O3/Au andright Au/Al2O3/TI interfaces are not symmetric, and can be non-ohmic and/or rectifying, due to TI surface oxidation or inclusionof a tunnel barrier1,2,4–10. This can lead to a larger splittingbetween the spin-up and spin-down voltage levels at the higherresistance interface (right contact), pushing the crossing towardsthe opposite end of the TI channel (Fig. 2b)12.Regarding the work on current generated spin in InAs11, wenote that different physical quantities were measured: Johnson/Hammar presented their results in voltage (Refs. 9,10. in ref. 11),whereas Park et al. reported resistance (Refs. 11,12. in ref. 11,which cannot be compared for sign. These papers also lackedadequate documentation of current, magnetic field direction, and/or polarities of voltage probes to enable one to establish a signconvention for their reported spin polarization, and used differentquantum well structures. However, they all report a positive valuefor the Rashba spin-orbit coupling coefficient, α, which is morefundamental and directly addresses the spin ordering of thestates. We specifically addressed this in ref. 9.In summary, the original model4 adapted in ref. 9 is too sim-plistic and unphysical, and any discussion of the precise place-ment of the spin potentials is irrelevant to the determination ofthe sign and origin of the measured spin voltage. Our revisedmodel remedies this by taking into account common experi-mental parameters such as spin-dependent channel and interfaceresistances, which can have a critical impact on the resultant spinvoltage measured. Our conclusion9 that the spin signal we mea-sured originates from Bi2Se3 Dirac surface states is sound. It isindependently supported by the different temperature depen-dences observed for Bi2Se3 and InAs, and the self-cancellation ofcontributions from the spin-split 2DEG states which potentiallycoexist on the Bi2Se3 surface15. The opposite sign of the measuredspin voltage we reported for Bi2Se3 relative to the InAs referenceprovides corroborative evidence, but we now realize is insufficienton its own unless the analysis includes the details of our newmodel12. The InAs(001) surface 2DEG provides an excellentreference for the sign of the spin voltage, because no additionalstates are present, the orientation of the effective electric field iswell established (no modulation doping), and ultra-low resistanceohmic contacts can be obtained. Finally, our findings potentiallyreconcile the inconsistencies reported in the literature, andunderscore the importance of recognizing these contributions inthe interpretation of such data.Data availabilityThe data sets generated during and/or analyzed during the current study are availablefrom the corresponding author on reasonable request.Received: 18 July 2018 Accepted: 9 May 2019References1. Li, C. H. et al. Electrical detection of charge-current-induced spin polarizationdue to spin-momentum locking in Bi2Se3. Nat. Nanotech. 9, 218–224 (2014).2. Tang, J. et al. Electrical detection of spin-polarized surface states conduction in(Bi0.53Sb0.47)2Te3 topological insulator. Nano Lett. 14, 5423–5429 (2014).3. Ando, Y. et al. Electrical detection of the spin polarization due to charge flowin the surface state of the topological insulator Bi1.5Sb0.5Te1.7Se1.3. Nano Lett.14, 6226–6230 (2014).4. Tian, J., Miotkowski, I., Hong, S. & Chen, Y. P. Electrical injection anddetection of spin-polarized currents in topological insulator Bi2Te2Se. Sci. Rep.5, 14293 (2015).5. Lee, J. S., Richardella, A., Hickey, D. R., Mkhoyan, K. A. & Samarth, N.Mapping the chemical potential dependence of current-induced spinpolarization in a topological insulator. Phys. Rev. B 92, 155312 (2015).6. Dankert, A., Geurs, J., Kamalakar, M. V. & Dash, S. P. Room temperatureelectrical detection of spin polarized currents in topological insulators. NanoLett. 15, 7976–7981 (2015).7. Li, C. H., van ‘t Erve, O. M. J., Li, Y. Y., Li, L. & Jonker, B. T. Electricaldetection of the helical spin texture in a p-type topological insulator Sb2Te3.Sci. Rep. 6, 29533 (2016).8. Yang, F. et al. Switching of charge-current-induced spin polarization in thetopological insulator BiSbTeSe2. Phys. Rev. B 94, 075304 (2016).9. Li, C. H., van ‘t Erve, O. M. J., Rajput, S., Li, L. & Jonker, B. T. Directcomparison of current-induced spin polarization in topological insulatorBi2Se3 and InAs Rashba states. Nat. Commun. 7, 13518 (2016).10. Li, C. H., van ‘t Erve, O. M. J., Yan, C., Li, L. & Jonker, B. T. Electricaldetection of charge-to spin and spin-to-charge conversion in a topologicalinsulator Bi2Te3 using BN/Al2O3 hybrid tunnel barrier. Sci. Rep. 8, 10265(2018).11. Tian, J. et al. On the understanding of current-induced spin polarization ofthree-dimensional topological insulators. Nat. Commun. 10, 1461 (2019).12. Li, et al. Modeling electrical detection of current generated spin in topologicalinsulator surface states. Sci. Rep. 9, 6906 (2019).13. Fert, A. & Jaffrès, H. Conditions for efficient spin injection from aferromagnetic metal into a semiconductor. Phys. Rev. B 64, 184420(2001).14. Semenov, Y. G., Duan, X., Li, X.-L. & Kim, K. W. Conductance nonreciprocityon the surface of a topological insulator with magnetic electrodes. J. Phys.Chem. Solids https://doi.org/10.1016/j.jpcs.2017.07.020 (2017).15. Hong, S., Diep, V., Datta, S. & Chen, Y. P. Modeling potentiometricmeasurements in topological insulators including parallel channels. Phys. Rev.B. 86, 085131 (2012).AcknowledgementsWe acknowledge support from Naval Research Laboratory (NRL) core programs, andfrom the Department of Energy (DE-SC0017632) at the West Virginia University.Author contributionsC.H.L., O.M.J.E., and B.T.J. conceived the idea. O.M.J.E. and C.H.L. developed the model.S.R. and L.L. grew the TI films and performed surface characterizations. C.H.L. grew theFe/Al2O3 tunnel barrier contacts, carried out device fabrication and transport mea-surements with assistance from O.M.J.E. C.H.L., O.M.J.E., and B.T.J. carried out theanalysis and wrote the paper, with feedback from all coauthors.Additional informationCompeting interests: The authors declare no competing interests.Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/Journal peer review information: Nature Communications thanks the anonymousreviewer(s) for their contribution to the peer review of this work.Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in any medium or format, as long as you giveappropriate credit to the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made. The images or other third partymaterial in this article are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. If material is not included in thearticle’s Creative Commons license and your intended use is not permitted by statutoryregulation or exceeds the permitted use, you will need to obtain permission directly fromthe copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.This is a U.S. government work and not under copyright protection in the U.S.; foreigncopyright protection may apply 2019NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-10396-6 MATTERS ARISINGNATURE COMMUNICATIONS |         (2019) 10:2523 | https://doi.org/10.1038/s41467-019-10396-6 | www.nature.com/naturecommunications 3

Reply to: “On the Understanding of Current-induced Spin Polarization of Three-dimensional Topological Insulators”

https://researchrepository.wvu.edu/cgi/viewcontent.cgi?article=2955&context=faculty_publications

Reply to: “On the Understanding of Current-induced Spin Polarization of Three-dimensional Topological Insulators”

Abstract

Similar works

Full text

Available Versions

The Research Repository @ WVU (West Virginia University)