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Concurrence of quantum anomalous Hall and topological Hall effects in magnetic topological insulator sandwich heterostructures


The quantum anomalous Hall (QAH) effect is a consequence of non-zero Berry curvature in momentum space. The QAH insulator harbours dissipation-free chiral edge states in the absence of an external magnetic field. However, the topological Hall (TH) effect, a hallmark of chiral spin textures, is a consequence of real-space Berry curvature. Here, by inserting a topological insulator (TI) layer between two magnetic TI layers, we realized the concurrence of the TH effect and the QAH effect through electric-field gating. The TH effect is probed by bulk carriers, whereas the QAH effect is characterized by chiral edge states. The appearance of the TH effect in the QAH insulating regime is a consequence of chiral magnetic domain walls that result from the gate-induced Dzyaloshinskii–Moriya interaction and occurs during the magnetization reversal process in the magnetic TI sandwich samples. The coexistence of chiral edge states and chiral spin textures provides a platform for proof-of-concept dissipationless spin-textured spintronic applications.

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Fig. 1: QAH effect in TI sandwich heterostructures.
Fig. 2: Gate-induced TH effect in TI sandwich heterostructures.
Fig. 3: Concurrence of the QAH and TH effects in TI sandwich heterostructures.
Fig. 4: Chiral domain walls and theoretical interpretations of the appearance of the TH effect.

Data availability

The data that support the findings of this study are available from C.-Z.C. on reasonable request.

Code availability

The code for theoretical calculations of spin susceptibility and DM interaction and simulations of the quantum transport simulation through a single chiral magnetic domain wall from C.L. and J.Zang on reasonable request.


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

    Article  CAS  Google Scholar 

  2. Qi, X. L. & Zhang, S. C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).

    Article  CAS  Google Scholar 

  3. Nagaosa, N. & Tokura, Y. Topological properties and dynamics of magnetic skyrmions. Nat. Nanotechnol. 8, 899–911 (2013).

    Article  CAS  Google Scholar 

  4. Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539–1592 (2010).

    Article  Google Scholar 

  5. Haldane, F. D. M. Model for a Quantum Hall effect without Landau levels: condensed-matter realization of the ‘parity anomaly’. Phys. Rev. Lett. 61, 2015–2018 (1988).

    Article  CAS  Google Scholar 

  6. Liu, C. X., Qi, X. L., Dai, X., Fang, Z. & Zhang, S. C. Quantum anomalous Hall effect in Hg1–yMnyTe quantum wells. Phys. Rev. Lett. 101, 146802 (2008).

    Article  Google Scholar 

  7. Qi, X. L., Hughes, T. L. & Zhang, S. C. Topological field theory of time-reversal invariant insulators. Phys. Rev. B 78, 195424 (2008).

    Article  Google Scholar 

  8. Yu, R. et al. Quantized anomalous Hall effect in magnetic topological insulators. Science 329, 61–64 (2010).

    Article  CAS  Google Scholar 

  9. Chang, C. Z. et al. Experimental observation of the quantum anomalous hall effect in a magnetic topological insulator. Science 340, 167–170 (2013).

    Article  CAS  Google Scholar 

  10. Chang, C. Z. et al. High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator. Nat. Mater. 14, 473–477 (2015).

    Article  CAS  Google Scholar 

  11. Checkelsky, J. G. et al. Trajectory of the anomalous Hall effect towards the quantized state in a ferromagnetic topological insulator. Nat. Phys. 10, 731–736 (2014).

    Article  CAS  Google Scholar 

  12. Kou, X. F. et al. Scale-invariant quantum anomalous Hall effect in magnetic topological insulators beyond the two-dimensional limit. Phys. Rev. Lett. 113, 137201 (2014).

    Article  Google Scholar 

  13. Mogi, M. et al. Magnetic modulation doping in topological insulators toward higher-temperature quantum anomalous Hall effect. Appl. Phys. Lett. 107, 182401 (2015).

    Article  Google Scholar 

  14. Neubauer, A. et al. Topological Hall effect in the A phase of MnSi. Phys. Rev. Lett. 102, 186602 (2009).

    Article  CAS  Google Scholar 

  15. Lee, M., Kang, W., Onose, Y., Tokura, Y. & Ong, N. P. Unusual Hall effect anomaly in MnSi under pressure. Phys. Rev. Lett. 102, 186601 (2009).

    Article  Google Scholar 

  16. Kanazawa, N. et al. Large topological Hall effect in a short-period helimagnet MnGe. Phys. Rev. Lett. 106, 156603 (2011).

    Article  CAS  Google Scholar 

  17. Huang, S. X. & Chien, C. L. Extended skyrmion phase in epitaxial FeGe(111) thin films. Phys. Rev. Lett. 108, 267201 (2012).

    Article  CAS  Google Scholar 

  18. Matsuno, J. et al. Interface-driven topological Hall effect in SrRuO3–SrIrO3 bilayer. Sci. Adv. 2, e1600304 (2016).

    Article  Google Scholar 

  19. Ohuchi, Y. et al. Electric-field control of anomalous and topological Hall effects in oxide bilayer thin films. Nat. Commun. 9, 213 (2018).

    Article  Google Scholar 

  20. Yasuda, K. et al. Geometric Hall effects in topological insulator heterostructures. Nat. Phys. 12, 555–559 (2016).

    Article  CAS  Google Scholar 

  21. Liu, C. et al. Dimensional crossover-induced topological Hall effect in a magnetic topological insulator. Phys. Rev. Lett. 119, 176809 (2017).

    Article  Google Scholar 

  22. Chen, Y. L. et al. Experimental realization of a three-dimensional topological insulator, Bi2Te3. Science 325, 178–181 (2009).

    Article  CAS  Google Scholar 

  23. Zhang, J. S. et al. Band structure engineering in (Bi1–xSbx)2Te3 ternary topological insulators. Nat. Commun. 2, 574 (2011).

    Article  Google Scholar 

  24. Zhu, J. J., Yao, D. X., Zhang, S. C. & Chang, K. Electrically controllable surface magnetism on the surface of topological insulators. Phys. Rev. Lett. 106, 097201 (2011).

    Article  Google Scholar 

  25. Ye, F., Ding, G. H., Zhai, H. & Su, Z. B. Spin helix of magnetic impurities in two-dimensional helical metal. Eur. Phys. Lett. 90, 47001 (2010).

    Article  Google Scholar 

  26. Xiao, D. et al. Realization of the axion insulator state in quantum anomalous Hall sandwich heterostructures. Phys. Rev. Lett. 120, 056801 (2018).

    Article  CAS  Google Scholar 

  27. Mogi, M. et al. A magnetic heterostructure of topological insulators as a candidate for an axion insulator. Nat. Mater. 16, 516–521 (2017).

    Article  CAS  Google Scholar 

  28. Mogi, M. et al. Tailoring tricolor structure of magnetic topological insulator for robust axion insulator. Sci. Adv. 3, eaao1669 (2017).

    Article  Google Scholar 

  29. Zhang, Y. et al. Crossover of the three-dimensional topological insulator Bi2Se3 to the two-dimensional limit. Nat. Phys. 6, 584–588 (2010).

    Article  Google Scholar 

  30. Chang, C. Z. et al. Thin films of magnetically doped topological insulator with carrier-independent long-range ferromagnetic order. Adv. Mater. 25, 1065–1070 (2013).

    Article  CAS  Google Scholar 

  31. Zhang, Z. C. et al. Electrically tuned magnetic order and magnetoresistance in a topological insulator. Nat. Commun. 5, 4915 (2014).

    Article  CAS  Google Scholar 

  32. Chang, C. Z. et al. Zero-field dissipationless chiral edge transport and the nature of dissipation in the quantum anomalous Hall state. Phys. Rev. Lett. 115, 057206 (2015).

    Article  Google Scholar 

  33. Wang, W. B. et al. Direct evidence of ferromagnetism in a quantum anomalous Hall system. Nat. Phys. 14, 791–795 (2018).

    Article  CAS  Google Scholar 

  34. Jiang, W. J. et al. Skyrmions in magnetic multilayers. Phys. Rep. 704, 1–49 (2017).

    Article  Google Scholar 

  35. Hou, W. T., Yu, J. X., Daly, M. & Zang, J. D. Thermally driven topology in chiral magnets. Phys. Rev. B 96, 140403(R) (2017).

    Article  Google Scholar 

  36. Bottcher, M., Heinze, S., Egorov, S., Sinova, J. & Dupe, B. BT phase diagram of Pd/Fe/Ir(111) computed with parallel tempering Monte Carlo. N. J. Phys. 20, 103014 (2018).

    Article  Google Scholar 

  37. Wang, W. B. et al. Spin chirality fluctuation in two-dimensional ferromagnets with perpendicular magnetic anisotropy. Nat. Mater. 18, 1054–1059 (2019).

    Article  CAS  Google Scholar 

  38. Liu, C. X. et al. Oscillatory crossover from two-dimensional to three-dimensional topological insulators. Phys. Rev. B 81, 041307 (2010).

    Article  Google Scholar 

  39. Li, W. et al. Origin of the low critical observing temperature of the quantum anomalous Hall effect in V-doped (Bi,Sb)2Te3 film. Sci. Rep. 6, 32732 (2016).

    Article  CAS  Google Scholar 

  40. Moriya, T. Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91–98 (1960).

    Article  CAS  Google Scholar 

  41. Groenendijk D. J. et al. Berry phase engineering at oxide interfaces. Preprint at http://arXiv/abs/1810.05619 (2018).

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The authors thank X. D. Xu, B. H. Yan, H. Z. Lu and W. D. Wu for helpful discussions. D.X. and N.S. acknowledge support from an ONR grant (N-000141512370) and Penn State 2DCC-MIP under NSF grant DMR-1539916. J.-H.S. and M.H.W.C. acknowledge the support from NSF grant DMR-1707340. C.L. acknowledges the support from an ONR grant (N00014-15-1-2675 and renewal No. N00014-18-1-2793). D.A. and J.Zang acknowledge the support from DOE grants (DE-SC0016424 and DE-SC0020221). C.-Z.C. acknowledges the support from the Gordon and Betty Moore Foundation’s EPiQS Initiative (Grant GBMF9063) and an ARO Young Investigator Program Award (W911NF1810198). Support for transport measurements and data analysis was provided by DOE grant (DE-SC0019064).

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Authors and Affiliations



N.S., M.H.W.C. and C.-Z.C. conceived and designed the experiment. D.X. grew the sandwich heterostructure samples with the help of N.S. and C.-Z.C. F.W., K.W. and J.J. performed characterizations of the samples with the help of C.-Z.C. J.J., F.W., J.-H.S., R.X. and M.K. performed the dilution refrigerator measurements with the help of M.H.W.C. and C.-Z.C. J.J., F.W., Y.-F.Z. and L.Z. carried out the PPMS transport measurement with the help M.H.W.C. and C.-Z.C. D.A., J.Zhang, J. Zang and C. L. provided theoretical support and did all the theoretical calculations. J.J., J.Zang, C.L., N.S., M.H.W.C. and C.-Z.C. analysed the data and wrote the manuscript with contributions from all authors.

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Correspondence to Nitin Samarth, Moses H. W. Chan or Cui-Zu Chang.

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Supplementary information

Supplementary Information

I. Characterizations of the TI sandwich heterostructure. II. Determining the Curie temperature of the TI sandwich heterostructure. III. Additional transport results of the TI sandwich heterostructure (3-5-3 sample 1). IV. Transport results of the second 3-5-3 TI sandwich heterostructure (3-5-3 sample 2). V. Transport results of TI sandwich heterostructures with different sample configurations. VI. Theoretical calculations for the spin susceptibility in magnetic TI. VII. Simulation of the quantum transport through a single chiral magnetic domain wall in magnetic TI.

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Jiang, J., Xiao, D., Wang, F. et al. Concurrence of quantum anomalous Hall and topological Hall effects in magnetic topological insulator sandwich heterostructures. Nat. Mater. 19, 732–737 (2020).

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