Bilinear magnetoelectric resistance as a probe of three-dimensional spin texture in topological surface states

Abstract

Surface states of three-dimensional topological insulators exhibit the phenomenon of spin–momentum locking, whereby the orientation of an electron spin is determined by its momentum. Probing the spin texture of these states is of critical importance for the realization of topological insulator devices, but the main technique currently available is spin- and angle-resolved photoemission spectroscopy. Here we reveal a close link between the spin texture and a new kind of magnetoresistance, which depends on the relative orientation of the current with respect to the magnetic field as well as the crystallographic axes, and scales linearly with both the applied electric and magnetic fields. This bilinear magnetoelectric resistance can be used to map the spin texture of topological surface states by simple transport measurements. For a prototypical Bi2Se3 single layer, we can map both the in-plane and out-of-plane components of the spin texture (the latter arising from hexagonal warping). Theoretical calculations suggest that the bilinear magnetoelectric resistance originates from conversion of a non-equilibrium spin current into a charge current under application of the external magnetic field.

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Fig. 1: Schematic of the spin texture of surface states of a 3D TI with hexagonal warping and conversion of spin current to charge current by applying an external magnetic field.
Fig. 2: First (R ω ) and second (R2ω) harmonic magnetoresistances in three different geometries.
Fig. 3: Detection of hexagonally warped helical spin texture of TSS.
Fig. 4: Comparison of field and spin canting angles.
Fig. 5: Current and magnetic field dependence of R2ω.

References

  1. 1.

    Fu, L., Kane, C. L. & Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007).

    ADS  Article  Google Scholar 

  2. 2.

    Hasan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

    ADS  Article  Google Scholar 

  3. 3.

    Qi, X.-L. & Zhang, S.-C. The quantum spin Hall effect and topological insulators. Phys. Today 63, 33–38 (2010).

    Article  Google Scholar 

  4. 4.

    Yazyev, O. V., Moore, J. E. & Louie, S. G. Spin polarization and transport of surface states in the topological insulators Bi2Se3 and Bi2Te3 from first principles. Phys. Rev. Lett. 105, 266806 (2010).

    ADS  Article  Google Scholar 

  5. 5.

    Garate, I. & Franz, M. Inverse spin-galvanic effect in the interface between a topological insulator and a ferromagnet. Phys. Rev. Lett. 104, 146802 (2010).

    ADS  Article  Google Scholar 

  6. 6.

    Pesin, D. & MacDonald, A. H. Spintronics and pseudospintronics in graphene and topological insulators. Nat. Mater. 11, 409–416 (2012).

    ADS  Article  Google Scholar 

  7. 7.

    Hsieh, D. et al. A tunable topological insulator in the spin helical Dirac transport regime. Nature 460, 1101–1105 (2009).

    ADS  Article  Google Scholar 

  8. 8.

    Hsieh, D. et al. Observation of unconventional quantum spin textures in topological insulators. Science 323, 919–922 (2009).

    ADS  Article  Google Scholar 

  9. 9.

    Nishide, A. et al. Direct mapping of the spin-filtered surface bands of a three-dimensional quantum spin Hall insulator. Phys. Rev. B 81, 041309 (2010).

    ADS  Article  Google Scholar 

  10. 10.

    Fu, L. Hexagonal warping effects in the surface states of the topological insulator Bi2Te3. Phys. Rev. Lett. 103, 266801 (2009).

    ADS  Article  Google Scholar 

  11. 11.

    Kuroda, K. et al. Hexagonally deformed fermi surface of the 3D topological insulator Bi2Se3. Phys. Rev. Lett. 105, 076802 (2010).

    ADS  Article  Google Scholar 

  12. 12.

    Alpichshev, Z. et al. STM imaging of electronic waves on the surface of Bi2Te3: topologically protected surface states and hexagonal warping effects. Phys. Rev. Lett. 104, 016401 (2010).

    ADS  Article  Google Scholar 

  13. 13.

    Wang, Y. H. et al. Observation of a warped helical spin texture in Bi2Se3 from circular dichroism angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 107, 207602 (2011).

    ADS  Article  Google Scholar 

  14. 14.

    Souma, S. et al. Direct measurement of the out-of-plane spin texture in the Dirac-cone surface state of a topological insulator. Phys. Rev. Lett. 106, 216803 (2011).

    ADS  Article  Google Scholar 

  15. 15.

    Xu, S.-Y. et al. Realization of an isolated Dirac node and strongly modulated spin texture in the topological insulator Bi2Te3. Preprint at https://arxiv.org/abs/1101.3985 (2011).

  16. 16.

    Nomura, M. et al. Relationship between Fermi surface warping and out-of-plane spin polarization in topological insulators: a view from spin- and angle-resolved photoemission. Phys. Rev. B 89, 045134 (2014).

    ADS  Article  Google Scholar 

  17. 17.

    McIver, J. W., Hsieh, D., Steinberg, H., Jarillo-Herrero, P. & Gedik, N. Control over topological insulator photocurrents with light polarization. Nat. Nanotech. 7, 96–100 (2012).

    ADS  Article  Google Scholar 

  18. 18.

    Besbas, J. et al. Helicity-dependent photovoltaic effect in Bi2Se3 under normal incident light. Adv. Opt. Mater. 4, 1642–1650 (2016).

    Article  Google Scholar 

  19. 19.

    Li, C. H. et al. Electrical detection of charge-current-induced spin polarization due to spin–momentum locking in Bi2Se3. Nat. Nanotech. 9, 218–224 (2014).

    ADS  Article  Google Scholar 

  20. 20.

    Ando, Y. et al. Electrical detection of the spin polarization due to charge flow in the surface state of the topological insulator Bi1.5Sb0.5Te1.7Se1.3. Nano Lett. 14, 6226–6230 (2014).

    ADS  Article  Google Scholar 

  21. 21.

    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).

    ADS  Article  Google Scholar 

  22. 22.

    Tian, J., Miotkowski, I., Hong, S. & Chen, Y. P. Electrical injection and detection of spin-polarized currents in topological insulator Bi2Te2Se. Sci. Rep. 5, 14293 (2015).

    ADS  Article  Google Scholar 

  23. 23.

    Dankert, A., Geurs, J., Kamalakar, M. V., Charpentier, S. & Dash, S. P. Room temperature electrical detection of spin polarized currents in topological insulators. Nano Lett. 15, 7976–7981 (2015).

    ADS  Article  Google Scholar 

  24. 24.

    Chen, J. et al. Gate-voltage control of chemical potential and weak antilocalization in Bi2Se3. Phys. Rev. Lett. 105, 176602 (2010).

    ADS  Article  Google Scholar 

  25. 25.

    Steinberg, H., Laloë, J. B., Fatemi, V., Moodera, J. S. & Jarillo-Herrero, P. Electrically tunable surface-to-bulk coherent coupling in topological insulator thin films. Phys. Rev. B 84, 233101 (2011).

    ADS  Article  Google Scholar 

  26. 26.

    Banerjee, K. et al. Defect-induced negative magnetoresistance and surface state robustness in the topological insulator BiSbTeSe2. Phys. Rev. B 90, 235427 (2014).

    ADS  Article  Google Scholar 

  27. 27.

    Tang, H., Liang, D., Qiu, R. L. J. & Gao, X. P. A. Two-dimensional transport-induced linear magneto-resistance in topological insulator Bi2Se3 nanoribbons. ACS Nano 5, 7510–7516 (2011).

    Article  Google Scholar 

  28. 28.

    Wang, X., Du, Y., Dou, S. & Zhang, C. Room temperature giant and linear magnetoresistance in topological insulator Bi2Te3 nanosheets. Phys. Rev. Lett. 108, 266806 (2012).

    ADS  Article  Google Scholar 

  29. 29.

    He, H. et al. High-field linear magneto-resistance in topological insulator Bi2Se3 thin films. Appl. Phys. Lett. 100, 032105 (2012).

    ADS  Article  Google Scholar 

  30. 30.

    Wang, J. et al. Anomalous anisotropic magnetoresistance in topological insulator films. Nano Res. 5, 739–746 (2012).

    ADS  Article  Google Scholar 

  31. 31.

    Sulaev, A. et al. Electrically tunable in-plane anisotropic magnetoresistance in topological insulator BiSbTeSe2 nanodevices. Nano Lett. 15, 2061–2066 (2015).

    ADS  Article  Google Scholar 

  32. 32.

    Yasuda, K. et al. Large unidirectional magnetoresistance in a magnetic topological insulator. Phys. Rev. Lett. 117, 127202 (2016).

    ADS  Article  Google Scholar 

  33. 33.

    Avci, C. O. et al. Unidirectional spin Hall magnetoresistance in ferromagnet/normal metal bilayers. Nat. Phys. 11, 570–575 (2015).

    Article  Google Scholar 

  34. 34.

    Olejník, K., Novák, V., Wunderlich, J. & Jungwirth, T. Electrical detection of magnetization reversal without auxiliary magnets. Phys. Rev. B 91, 180402 (2015).

    ADS  Article  Google Scholar 

  35. 35.

    Kim, K. J. et al. Current-induced asymmetric magnetoresistance due to energy transfer via quantum spin-flip process. Preprint at https://arxiv.org/abs/1603.08746 (2016).

  36. 36.

    Zhang, S. S. L. & Vignale, G. Theory of unidirectional spin Hall magnetoresistance in heavy-metal/ferromagnetic-metal bilayers. Phys. Rev. B 94, 140411 (2016).

    ADS  Article  Google Scholar 

  37. 37.

    Zhang, H. et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nat. Phys. 5, 438 (2009).

    Article  Google Scholar 

  38. 38.

    Xia, Y. et al. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nat. Phys. 5, 398–402 (2009).

    Article  Google Scholar 

  39. 39.

    Manchon, A., Koo, H. C., Nitta, J., Frolov, S. M. & Duine, R. A. New perspectives for Rashba spin–orbit coupling. Nat. Mater. 14, 871–882 (2015).

    ADS  Article  Google Scholar 

  40. 40.

    Ideue, T. et al. Bulk rectification effect in a polar semiconductor. Nat. Phys. 13, 578 (2017).

    Article  Google Scholar 

  41. 41.

    Wang, Q. H., Kalantar-Zadeh, K., Kis, A., Coleman, J. N. & Strano, M. S. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat. Nanotech. 7, 699–712 (2012).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

This work was partially supported by A*STAR’s Pharos Programme on Topological Insulators, Ministry of Education–Singapore Academic Research Fund Tier 1 (R-263-000-B47-112). The work by S.S.-L.Z. and G.V. was supported by National Science Foundation (NSF) grant DMR-1406568, and work on the revised manuscript by S.S.-L.Z. at Argonne National Laboratory was supported by Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. S.S.-L.Z. thanks O. Heinonen, A. Hoffmann, G. Bian, A. Fert, X. Jin, D. Loss and S. Zhang for helpful discussions.

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P.H. and H.Y. planned the study. D.Z. and P.H. fabricated devices. P.H. and D.Z. measured transport properties. Y.L., Y.W. and J.Y. helped with characterization. S.S.-L.Z. and G.V. devised the theory. All authors discussed the results. P.H., S.S.-L.Z., D.Z., G.V. and H.Y. wrote the manuscript. H.Y. supervised the project.

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Correspondence to Hyunsoo Yang.

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He, P., Zhang, S.SL., Zhu, D. et al. Bilinear magnetoelectric resistance as a probe of three-dimensional spin texture in topological surface states. Nature Phys 14, 495–499 (2018). https://doi.org/10.1038/s41567-017-0039-y

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