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Direct evidence of ferromagnetism in a quantum anomalous Hall system


Quantum anomalous Hall (QAH) systems are of great fundamental interest and potential application because of their dissipationless conduction without the need for an external magnetic field1,2,3,4,5,6,7,8,9. The QAH effect has been realized in magnetically doped topological insulator thin films10,11,12,13,14. However, full quantization requires extremely low temperature (T < 50 mK) in the earliest works, athough it has been significantly improved by modulation doping or co-doping of magnetic elements15,16. Improved ferromagnetism has been shown in these thin films, yet direct evidence of long-range ferromagnetic order is lacking. Herein, we present direct visualization of long-range ferromagnetic order in thin films of Cr and V co-doped (Bi,Sb)2Te3 using low-temperature magnetic force microscopy with in situ transport. The magnetization reversal process reveals typical ferromagnetic domain behaviour—that is, domain nucleation and possibly domain wall propagation—in contrast to much weaker magnetic signals observed in the endmembers, possibly due to superparamagnetic behaviour17,18,19. The observed long-range ferromagnetic order resolves one of the major challenges in QAH systems, and paves the way towards high-temperature dissipationless conduction by exploring magnetic topological insulators.

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Fig. 1: Schematic of the in situ transport set-up and the Cr concentration (y) dependence of σxy and Hc/FWHMMR.
Fig. 2: The magnetization reversal process at 5 K at the neutral point \({{\bf{\it V}}}_{{\bf{g}}}^{{\bf{0}}}\).
Fig. 3: Gate dependence of ferromagnetic behaviour.
Fig. 4: Gate dependence of ρyx and Hc and schematic band structure.


  1. 1.

    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).

    ADS  Article  Google Scholar 

  2. 2.

    Onoda, M. & Nagaosa, N. Quantized anomalous Hall effect in two-dimensional ferromagnets: Quantum Hall effect in metals. Phys. Rev. Lett. 90, 206601 (2003).

    ADS  Article  Google Scholar 

  3. 3.

    Liu, C. X., Qi, X. L., Dai, X., Fang, Z. & Zhang, S. C. Quantum anomalous Hall effect in Hg1−yMn1−yTe quantum wells. Phys. Rev. Lett. 101, 146802 (2008).

    ADS  Article  Google Scholar 

  4. 4.

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

    ADS  Article  Google Scholar 

  5. 5.

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

    ADS  Article  Google Scholar 

  6. 6.

    Qiao, Z. H. et al. Quantum anomalous Hall effect in graphene from Rashba and exchange effects. Phys. Rev. B 82, 161414 (2010).

    ADS  Article  Google Scholar 

  7. 7.

    Nomura, K. & Nagaosa, N. Surface-quantized anomalous Hall current and the magnetoelectric effect in magnetically disordered topological insulators. Phys. Rev. Lett. 106, 166802 (2011).

    ADS  Article  Google Scholar 

  8. 8.

    Zhang, H., Lazo, C., Bluegel, S., Heinze, S. & Mokrousov, Y. Electrically tunable quantum anomalous Hall effect in graphene decorated by 5d transition-metal adatoms. Phys. Rev. Lett. 108, 056802 (2012).

    ADS  Article  Google Scholar 

  9. 9.

    Ezawa, M. Valley-polarized metals and quantum anomalous Hall effect in silicene. Phys. Rev. Lett. 109, 055502 (2012).

    ADS  Article  Google Scholar 

  10. 10.

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

    ADS  Article  Google Scholar 

  11. 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  Google Scholar 

  12. 12.

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

    ADS  Article  Google Scholar 

  13. 13.

    Kou, X. et al. Metal-to-insulator switching in quantum anomalous Hall states. Nat. Commun. 6, 8474 (2015).

    Article  Google Scholar 

  14. 14.

    Feng, Y. et al. Observation of the zero Hall plateau in a quantum anomalous Hall insulator. Phys. Rev. Lett. 115, 126801 (2015).

    ADS  Article  Google Scholar 

  15. 15.

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

    ADS  Article  Google Scholar 

  16. 16.

    Ou, Y. et al. Enhancing the quantum anomalous Hall effect by magnetic codoping in a topological insulator. Adv. Mater. 30, 1703062 (2018).

    Article  Google Scholar 

  17. 17.

    Lachman, E. O. et al. Visualization of superparamagnetic dynamics in magnetic topological insulators. Sci. Adv. 1, e1500740 (2015).

    ADS  Article  Google Scholar 

  18. 18.

    Grauer, S. et al. Coincidence of superparamagnetism and perfect quantization in the quantum anomalous Hall state. Phys. Rev. B 92, 201304 (2015).

    ADS  Article  Google Scholar 

  19. 19.

    Lee, I. et al. Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Crx(Bi0.1Sb0.9)2−xTe3. Proc. Natl Acad. Sci. USA 112, 1316–1321 (2015).

    ADS  Article  Google Scholar 

  20. 20.

    Bednorz, J. G. & Muller, K. A. Possible high T c superconductivity in the Ba–La–Cu–O system. Z. Phys. B 64, 189–193 (1986).

    ADS  Article  Google Scholar 

  21. 21.

    Wu, M. K. et al. Superconductivity at 93 K in a new mixed-phase Y–Ba–Cu–O compound system at ambient pressure. Phys. Rev. Lett. 58, 908–910 (1987).

    ADS  Article  Google Scholar 

  22. 22.

    Maeda, H., Tanaka, Y., Fukutomi, M. & Asano, T. A new high-Tc oxide superconductor without a rare earth element. Jpn J. Appl. Phys. 27, L209–L210 (1988).

    ADS  Article  Google Scholar 

  23. 23.

    Schilling, A., Cantoni, M., Guo, J. D. & Ott, H. R. Superconductivity above 130 K in the Hg–Ba–Ca–Cu–O system. Nature 363, 56–58 (1993).

    ADS  Article  Google Scholar 

  24. 24.

    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).

    ADS  Article  Google Scholar 

  25. 25.

    Grauer, S. et al. Scaling of the quantum anomalous Hall effect as an indicator of axion electrodynamics. Phys. Rev. Lett. 118, 246801 (2017).

    ADS  Article  Google Scholar 

  26. 26.

    Chang, C.-Z. et al. Chemical-potential-dependent gap opening at the Dirac surface states of Bi2Se3 induced by aggregated substitutional Cr atoms. Phys. Rev. Lett. 112, 056801 (2014).

    ADS  Article  Google Scholar 

  27. 27.

    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).

    ADS  Article  Google Scholar 

  28. 28.

    Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492–1505 (1958).

    ADS  Article  Google Scholar 

  29. 29.

    Andriotis, A. N. & Menon, M. Defect-induced magnetism: Codoping and a prescription for enhanced magnetism. Phys. Rev. B 87, 155309 (2013).

    ADS  Article  Google Scholar 

  30. 30.

    Qi, S. F. et al. High-temperature quantum anomalous Hall effect in n–p codoped topological insulators. Phys. Rev. Lett. 117, 056804 (2016).

    ADS  Article  Google Scholar 

  31. 31.

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

    ADS  Article  Google Scholar 

  32. 32.

    Ruderman, M. A. & Kittel, C. Indirect exchange coupling of nuclear magnetic moments by conduction electrons. Phys. Rev. 96, 99–102 (1954).

    ADS  Article  Google Scholar 

  33. 33.

    Kou, X. F. et al. Interplay between different magnetisms in Cr-doped topological insulators. ACS Nano 7, 9205–9212 (2013).

    Article  Google Scholar 

  34. 34.

    Wang, W., Chang, C.-Z., Moodera, J. S. & Wu, W. Visualizing ferromagnetic domain behavior of magnetic topological insulator thin films. npj Quant. Mater. 1, 16023 (2016).

    Article  Google Scholar 

  35. 35.

    Li, M. et al. Experimental verification of the Van Vleck nature of long-range ferromagnetic order in the vanadium-doped three-dimensional topological insulator Sb2Te3. Phys. Rev. Lett. 114, 146802 (2015).

    ADS  Article  Google Scholar 

  36. 36.

    Li, H. et al. Carriers dependence of the magnetic properties in magnetic topological insulator Sb1.95−xBixCr0.05Te3. Appl. Phys. Lett. 101, 072406 (2012).

    ADS  Article  Google Scholar 

  37. 37.

    Checkelsky, J. G., Ye, J., Onose, Y., Iwasa, Y. & Tokura, Y. Dirac-fermion-mediated ferromagnetism in a topological insulator. Nat. Phys. 8, 729–733 (2012).

    Article  Google Scholar 

  38. 38.

    Sessi, P. et al. Signatures of Dirac fermion-mediated magnetic order. Nat. Commun. 5, 5349 (2014).

    Article  Google Scholar 

  39. 39.

    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).

    ADS  Article  Google Scholar 

  40. 40.

    Wang, W. et al. Visualizing weak ferromagnetic domains in multiferroic hexagonal ferrite thin film. Phys. Rev. B 95, 134443 (2017).

    ADS  Article  Google Scholar 

  41. 41.

    Wang, W. et al. Visualizing ferromagnetic domains in magnetic topological insulators. APL Mater. 3, 083301 (2015).

    ADS  Article  Google Scholar 

  42. 42.

    Rugar, D. et al. Magnetic force microscopy: General principles and application to longitudinal recording media. J. Appl. Phys. 68, 1169–1183 (1990).

    ADS  Article  Google Scholar 

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We thank C. Chang for helpful discussions and P. Sass for proofreading the manuscript. This work at Rutgers is supported by the Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, US Department of Energy under Award numbers DE-SC0008147 and DE-SC0018153. The work at Tsinghua University is supported by the National Natural Science Foundation of China and the Ministry of Science and Technology of China.

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W.Wu, K.H. and Y.W. conceived the project. W.Wu and W.Wa designed the MFM experiment. W.Wa performed MFM experiments with in situ transport measurements, and analysed the data. Y.O. synthesized the MBE films under the supervision of K.H. and Q.X. C.L. and Y.W. carried out transport characterization of the films. W.Wu and W.Wa wrote the manuscript with inputs from all authors.

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Correspondence to Weida Wu.

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Wang, W., Ou, Y., Liu, C. et al. Direct evidence of ferromagnetism in a quantum anomalous Hall system. Nature Phys 14, 791–795 (2018).

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