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Magnetic topological insulators


The importance of global band topology is unequivocally recognized in condensed matter physics, and new states of matter, such as topological insulators, have been discovered. Owing to their bulk band topology, 3D topological insulators possess a massless Dirac dispersion with spin–momentum locking at the surface. Although 3D topological insulators were originally proposed in time-reversal invariant systems, the onset of a spontaneous magnetization or, equivalently, a broken time-reversal symmetry leads to the formation of an exchange gap in the Dirac band dispersion. In such magnetic topological insulators, tuning of the Fermi level in the exchange gap results in the emergence of a quantum Hall effect at zero magnetic field, that is, of a quantum anomalous Hall effect. Here, we review the basic concepts of magnetic topological insulators and their experimental realization, together with the discovery and verification of their emergent properties. In particular, we discuss how the development of tailored materials through heterostructure engineering has made it possible to access the quantum anomalous Hall effect, the topological magnetoelectric effect, the physics related to the chiral edge states that appear in these materials and various spintronic phenomena. Further theoretical and experimental research on magnetic topological insulators will provide fertile ground for the development of new concepts for next-generation electronic devices for applications such as spintronics with low energy consumption, dissipationless topological electronics and topological quantum computation.

Key points

  • The chemical doping of topological insulators with transition metal elements induces a spontaneous magnetization that interacts with the topological surface state to open a mass gap at the Dirac point.

  • The precise tuning of the Fermi level at the mass gap enables the observation of the quantum anomalous Hall effect — a zero-magnetic-field quantum Hall effect arising in the presence of a spontaneous magnetization — which is further stabilized by heterostructure engineering.

  • Chiral edge conduction associated with the quantum anomalous Hall effect is manipulated by magnetic domain walls, and the edge modes can be turned into chiral Majorana edge modes via proximity coupling with a superconductor.

  • Heterostructure engineering and terahertz measurements enable the observation of the quantized topological magnetoelectric effect.

  • The spin–momentum-locked conduction electrons in the surface state lead to versatile spintronic functionalities, such as an efficient generation of spin transfer torque, as a result of charge-to-spin conversion.

  • The further development of materials design and engineering will realize the quantum anomalous Hall effect at higher temperatures, the control of this state with external fields and exotic topological states of matter.

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Fig. 1: The electronic structure of a topological insulator and of a magnetic topological insulator.
Fig. 2: Two possible mechanisms for the ferromagnetism in magnetic topological insulators.
Fig. 3: Exchange gap formation by magnetization.
Fig. 4: Experimental observations of the quantum anomalous Hall effect.
Fig. 5: Chiral edge conductions.
Fig. 6: Topological magneto-optical effect and magnetoelectric axion insulator.
Fig. 7: Spintronic functionalities.
Fig. 8: Future perspectives for magnetic topological insulators.


  1. 1.

    Stewart, G. R. Heavy-fermion systems. Rev. Mod. Phys. 56, 755–787 (1984).

    ADS  Google Scholar 

  2. 2.

    Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).

    ADS  Google Scholar 

  3. 3.

    Fert, A. Nobel lecture: origin, development, and future of spintronics. Rev. Mod. Phys. 80, 1517–1530 (2008).

    ADS  Google Scholar 

  4. 4.

    Tokura, Y. Critical features of colossal magnetoresistive manganites. Rep. Prog. Phys. 69, 797–851 (2006).

    ADS  Google Scholar 

  5. 5.

    Dietl, T. & Ohno, H. Dilute ferromagnetic semiconductors: physics and spintronic structures. Rev. Mod. Phys. 86, 187–251 (2014).

    ADS  Google Scholar 

  6. 6.

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

    ADS  Google Scholar 

  7. 7.

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

    ADS  Google Scholar 

  8. 8.

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

    ADS  Google Scholar 

  9. 9.

    Klitzing, Kv, Dorda, G. & Pepper, M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45, 494 (1980).

    ADS  Google Scholar 

  10. 10.

    Thouless, D. J., Kohmoto, M., Nightingale, M. P. & den Nijs, M. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405 (1982).

    ADS  Google Scholar 

  11. 11.

    Kohmoto, M. Topological invariant and the quantization of the Hall conductance. Ann. Phys. 160, 343 (1985).

    ADS  MathSciNet  Google Scholar 

  12. 12.

    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 (1988).

    ADS  Google Scholar 

  13. 13.

    Ohgushi, K., Murakami, S. & Nagaosa, N. Spin anisotropy and quantum Hall effect in the kagomé lattice: chiral spin state based on a ferromagnet. Phys. Rev. B 62, R6065 (2000).

    ADS  Google Scholar 

  14. 14.

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

    ADS  Google Scholar 

  15. 15.

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

    ADS  Google Scholar 

  16. 16.

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

    ADS  Google Scholar 

  17. 17.

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

    ADS  Google Scholar 

  18. 18.

    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  Google Scholar 

  19. 19.

    Kane, C. L. & Mele, E. J. Z2 topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005).

    ADS  Google Scholar 

  20. 20.

    Kane, C. L. & Mele, E. J. Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005).

    ADS  Google Scholar 

  21. 21.

    Fu, L. & Kane, C. L. Topological insulators with inversion symmetry. Phys. Rev. B 76, 045302 (2007).

    ADS  Google Scholar 

  22. 22.

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

    ADS  Google Scholar 

  23. 23.

    Ando, Y. Topological insulator materials. J. Phys. Soc. Jpn. 82, 102001 (2013).

    ADS  Google Scholar 

  24. 24.

    Cava, R. J., Ji, H., Fuccillo, M. K., Gibson, Q. D. & Hor, Y. S. Crystal structure and chemistry of topological insulators. J. Mater. Chem. C. 1, 3176–3189 (2013).

    Google Scholar 

  25. 25.

    Zhang, H. et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nat. Phys. 5, 438–442 (2009).

    Google Scholar 

  26. 26.

    Murakami, S. Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase. New J. Phys. 9, 356 (2007).

    ADS  Google Scholar 

  27. 27.

    Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011).

    ADS  Google Scholar 

  28. 28.

    Hasan, M. Z., Xu, S. Y., Belopolski, I. & Huang, S. M. Discovery of Weyl fermion semimetals and topological Fermi arc states. Annu. Rev. Condens. Matter Phys. 8, 289–309 (2017).

    ADS  Google Scholar 

  29. 29.

    Fang, Z. et al. The anomalous Hall effect and magnetic monopoles in momentum space. Science 302, 92–95 (2003).

    ADS  Google Scholar 

  30. 30.

    Heremans, J. P., Cava, R. J. & Samarth, N. Tetradymites as thermoelectrics and topological insulators. Nat. Rev. Mater. 2, 17049 (2017).

    ADS  Google Scholar 

  31. 31.

    Kou, X., Fan, Y., Lang, M., Upadhyaya, P. & Wang, K. L. Magnetic topological insulators and quantum anomalous hall effect. Sol. St. Commun. 215, 34–53 (2015).

    ADS  Google Scholar 

  32. 32.

    Chang, C.-Z. & Li, M. Quantum anomalous Hall effect in time-reversal-symmetry breaking topological insulators. J. Phys. Condens. Matter 28, 123002 (2016).

    ADS  Google Scholar 

  33. 33.

    Ke, H., Wang, Y. & Xue, Q.-K. Topological materials: quantum anomalous Hall system. Annu. Rev. Cond. Mat. Phys. 9, 329–344 (2018).

    ADS  Google Scholar 

  34. 34.

    Biswas, R. R. & Balatsky, A. V. Impurity-induced states on the surface of three-dimensional topological insulators. Phys. Rev. B 81, 233405 (2010).

    ADS  Google Scholar 

  35. 35.

    Rosenberg, G. & Franz, M. Surface magnetic ordering in topological insulators with bulk magnetic dopants. Phys. Rev. B 85, 195119 (2012).

    ADS  Google Scholar 

  36. 36.

    Henk, J. et al. Complex spin texture in the pure and Mn-doped topological insulator Bi2Te3. Phys. Rev. Lett. 108, 206801 (2012).

    ADS  Google Scholar 

  37. 37.

    Zhang, J.-M., Zhu, W., Zhang, Y., Xiao, D. & Yao, Y. Tailoring magnetic doping in the topological insulator Bi2Se3. Phys. Rev. Lett. 109, 266405 (2012).

    ADS  Google Scholar 

  38. 38.

    Kacman, P. Spin interactions in diluted magnetic semiconductors and magnetic semiconductors. Semicond. Sci. Technol. 16, R25–R39 (2001).

    ADS  Google Scholar 

  39. 39.

    Dietl, T., Ohno, H. & Matsukura, F. Hole-mediated ferromagnetism in tetrahedrally coordinated semiconductors. Phys. Rev. B 63, 195205 (2001).

    ADS  Google Scholar 

  40. 40.

    Dietl, T. & Ohno, H. Ferromagnetic III-V and II-VI semiconductors. MRS Bull. 28, 714–719 (2003).

    Google Scholar 

  41. 41.

    Liu, Q., Liu, C.-X., Xu, C., Qi, X.-L. & Zhang, S.-C. Magnetic impurities on the surface of a topological insulator. Phys. Rev. Lett. 102, 156603 (2009).

    ADS  Google Scholar 

  42. 42.

    Abanin, D. A. & Pesin, D. A. Ordering of magnetic impurities and tunable electronic properties of topological insulators. Phys. Rev. Lett. 106, 136802 (2011).

    ADS  Google Scholar 

  43. 43.

    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).

    ADS  Google Scholar 

  44. 44.

    Hor, Y. S. et al. Development of ferromagnetism in the doped topological insulator Bi2-xMnxTe3. Phys. Rev. B 81, 195203 (2010).

    ADS  Google Scholar 

  45. 45.

    Checkelsky, J. G. et al. Dirac-fermion-mediated ferromagnetism in a topological insulator. Nat. Phys. 8, 729–733 (2012).

    Google Scholar 

  46. 46.

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

    Google Scholar 

  47. 47.

    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).

    ADS  Google Scholar 

  48. 48.

    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  Google Scholar 

  49. 49.

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

    Google Scholar 

  50. 50.

    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  Google Scholar 

  51. 51.

    Chen, Y. L. et al. Massive Dirac fermion on the surface of a magnetically doped topological insulator. Science 329, 659–662 (2010).

    ADS  Google Scholar 

  52. 52.

    Wray, L. A. et al. A topological insulator surface under strong Coulomb, magnetic and disorder perturbations. Nat. Phys. 7, 32–37 (2011).

    Google Scholar 

  53. 53.

    Xu, S.-Y. et al. Hedgehog spin texture and Berry’s phase tuning in a magnetic topological insulator. Nat. Phys. 8, 616–622 (2012).

    Google Scholar 

  54. 54.

    Sessi, P. et al. Dual nature of magnetic dopants and competing trends in topological insulators. Nat. Commun. 7, 12027 (2016).

    ADS  Google Scholar 

  55. 55.

    Krieger, J. A. et al. Spectroscopic perspective on the interplay between electronic and magnetic properties of magnetically doped topological insulators. Phys. Rev. B 96, 184402 (2017).

    ADS  Google Scholar 

  56. 56.

    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  Google Scholar 

  57. 57.

    Wang, J., Lian, B., Zhang, H. & Zhang, S. C. Anomalous edge transport in the quantum anomalous Hall state. Phys. Rev. Lett. 111, 086803 (2013).

    ADS  Google Scholar 

  58. 58.

    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  Google Scholar 

  59. 59.

    Bestwick, A. J. et al. Precise quantization of the anomalous Hall effect near zero magnetic field. Phys. Rev. Lett. 114, 187201 (2015).

    ADS  Google Scholar 

  60. 60.

    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  Google Scholar 

  61. 61.

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

    ADS  Google Scholar 

  62. 62.

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

    Google Scholar 

  63. 63.

    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).

    Google Scholar 

  64. 64.

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

    Google Scholar 

  65. 65.

    Chang, C.-Z. et al. Observation of the quantum anomalous Hall insulator to Anderson insulator quantum phase transition and its scaling behavior. Phys. Rev. Lett. 117, 126802 (2016).

    ADS  Google Scholar 

  66. 66.

    Kawamura, M. et al. Current-driven instability of the quantum anomalous Hall effect in ferromagnetic topological insulators. Phys. Rev. Lett. 119, 016803 (2017).

    ADS  Google Scholar 

  67. 67.

    Fox, E. J. et al. Part-per-million quantization and current-induced breakdown of the quantum anomalous Hall effect. Phys. Rev. B 98, 075145 (2018).

    ADS  Google Scholar 

  68. 68.

    Kawamura, M. et al. Topological quantum phase transition in magnetic topological insulator upon magnetization rotation. Phys. Rev. B 98, 140404 (2018).

    ADS  Google Scholar 

  69. 69.

    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).

    ADS  Google Scholar 

  70. 70.

    Jeckelmann, B. & Jeanneret, B. The quantum Hall effect as an electrical resistance standard. Rep. Prog. Phys. 64, 1603–1655 (2001).

    ADS  Google Scholar 

  71. 71.

    Scherer, H. & Camarota, B. Quantum metrology triangle experiments: a status review. Meas. Sci. Technol. 23, 124010 (2012).

    ADS  Google Scholar 

  72. 72.

    Gotz, M. et al. Precision measurement of the quantized anomalous Hall resistance at zero magnetic field. Appl. Phys. Lett. 112, 072102 (2018).

    ADS  Google Scholar 

  73. 73.

    Kaneko, N. Review of quantum electrical standards and benefits and effects of the implementation of the ‘Revised SI’. IEEJ Trans. 12, 627–637 (2017).

    Google Scholar 

  74. 74.

    Ribeiro-Palau, R. et al. Quantum Hall resistance standard in graphene devices under relaxed experimental conditions. Nat. Nanotechnol. 10, 965–972 (2015).

    ADS  Google Scholar 

  75. 75.

    Upadhyaya, P. & Tserkovnyak, Y. Domain wall in a quantum anomalous Hall insulator as a magnetoelectric piston. Phys. Rev. B 94, 020411 (2016).

    ADS  Google Scholar 

  76. 76.

    Liu, M. et al. Large discrete jumps observed in the transition between Chern states in a ferromagnetic topological insulator. Sci. Adv. 2, e1600167 (2016).

    ADS  Google Scholar 

  77. 77.

    Yasuda, K. et al. Quantized chiral edge conduction on domain walls of a magnetic topological insulator. Science 358, 1311–1314 (2017).

    ADS  Google Scholar 

  78. 78.

    Büttiker, M. Absence of backscattering in the quantum Hall effect in multiprobe conductors. Phys. Rev. B 38, 9375–9389 (1988).

    ADS  Google Scholar 

  79. 79.

    Rosen, I. T. et al. Chiral transport along magnetic domain walls in the quantum anomalous Hall effect. NPJ Quantum Mater. 2, 69 (2017).

    ADS  Google Scholar 

  80. 80.

    Fu, L. & Kane, C. L. Superconducting proximity effect and majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).

    ADS  Google Scholar 

  81. 81.

    Qi, X.-L., Hughes, T. L. & Zhang, S.-C. Chiral topological superconductor from the quantum Hall state. Phys. Rev. B 82, 184516 (2010).

    ADS  Google Scholar 

  82. 82.

    Wang, J., Zhou, Q., Lian, B. & Zhang, S.-C. Chiral topological superconductor and half-integer conductance plateau from quantum anomalous Hall plateau transition. Phys. Rev. B 92, 064520 (2015).

    ADS  Google Scholar 

  83. 83.

    Majorana, E. Teoria simmetrica dell’elettrone e del positrone. Nuovo Cim. 14, 171–184 (1937).

    ADS  MATH  Google Scholar 

  84. 84.

    Kitaev, A. Y. Anyons in an exactly solved model and beyond. Ann. Phys. 321, 2–111 (2006).

    ADS  MathSciNet  MATH  Google Scholar 

  85. 85.

    Wilczek, F. Majorana returns. Nat. Phys. 5, 614–618 (2009).

    Google Scholar 

  86. 86.

    Alicea, J. New directions in the pursuit of Majorana fermions in solid state systems. Rep. Prog. Phys. 75, 076501 (2012).

    ADS  Google Scholar 

  87. 87.

    He, Q. L. et al. Chiral Majorana fermion modes in a quantum anomalous Hall insulator–superconductor structure. Science 357, 294–299 (2017).

    ADS  MathSciNet  MATH  Google Scholar 

  88. 88.

    Wang, J., Lian, B. & Zhang, S.-C. Universal scaling of the quantum anomalous Hall plateau transition. Phys. Rev. B 89, 085106 (2014).

    ADS  Google Scholar 

  89. 89.

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

    ADS  Google Scholar 

  90. 90.

    Huang, Y., Setiawan, F. & Sau, J. D. Disorder-induced half-integer quantized conductance plateau in quantum anomalous Hall insulator-superconductor structures. Phys. Rev. B 97, 100501(R) (2018).

    ADS  Google Scholar 

  91. 91.

    Ji, W. & Wen, X.-G. 1/2(e 2/h) conductance plateau without 1D chiral Majorana fermions. Phys. Rev. Lett. 120, 107002 (2018).

    ADS  Google Scholar 

  92. 92.

    Lian, B., Wang, J., Sun, X.-Q., Vaezi, A. & Zhang, S.-C. Quantum phase transition of chiral Majorana fermions in the presence of disorder. Phys. Rev. B 97, 125408 (2018).

    ADS  Google Scholar 

  93. 93.

    Lian, B., Sun, X.-Q., Vaezi, A., Qi, X.-L. & Zhang, S.-C. Topological quantum computation based on chiral Majorana fermions. Proc. Natl Acad. Sci. USA 115, 10938–10942 (2018).

    ADS  MathSciNet  Google Scholar 

  94. 94.

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

    ADS  Google Scholar 

  95. 95.

    Peccei, R. D. & Quinn, H. R. CP conservation in the presence of pseudoparticles. Phys. Rev. Lett. 38, 1440 (1977).

    ADS  Google Scholar 

  96. 96.

    Essin, A. M., Moore, J. E. & Vanderbilt, D. Magnetoelectric polarizability and axion electrodynamics in crystalline insulators. Phys. Rev. Lett. 102, 146805 (2009).

    ADS  Google Scholar 

  97. 97.

    Tokura, Y., Seki, S. & Nagaosa, N. Mulrtiferroics of spin origin. Rep. Prog. Phys. 77, 076501 (2014).

    ADS  Google Scholar 

  98. 98.

    Freeman, A. J. & Schmid, H. Magnetoelectric interaction phenomena in crystals (Gordon and Breach Science Publishers London, 1975).

  99. 99.

    Kurumaji, T. et al. Optical magnetoelectric resonance in a polar magnet (Fe,Zn)2Mo3O8 with axion-type coupling. Phys. Rev. Lett. 119, 077206 (2017).

    ADS  Google Scholar 

  100. 100.

    Tse, W.-K. & MacDonald, A. H. Giant magneto-optical Kerr effect and universal Faraday effect in thin-film topological insulators. Phys. Rev. Lett. 105, 057401 (2010).

    ADS  Google Scholar 

  101. 101.

    Maciejko, J., Qi, X.-L., Drew, H. D. & Zhang, S.-C. Topological quantization in units of the fine structure constant. Phys. Rev. Lett. 105, 166803 (2010).

    ADS  Google Scholar 

  102. 102.

    Okada, K. N. et al. Terahertz spectroscopy on Faraday and Kerr rotations in a quantum anomalous Hall state. Nat. Commun. 7, 12245 (2016).

    ADS  Google Scholar 

  103. 103.

    Liang., W. et al. Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator. Science 354, 1124–1127 (2016).

    MathSciNet  MATH  Google Scholar 

  104. 104.

    Dziom, V. et al. Observation of the universal magnetoelectric effect in a 3D topological insulator. Nat. Commun. 8, 15197 (2017).

    ADS  Google Scholar 

  105. 105.

    Armitage, N. P. & Wu, L. On the matter of topological insulators as magnetoelectrics. Preprint at (2018).

  106. 106.

    Morimoto, T., Furusaki, A. & Nagaosa, N. Topological magnetoelectric effects in thin films of topological insulators. Phys. Rev. B 92, 085113 (2015).

    ADS  Google Scholar 

  107. 107.

    Wang, J., Lian, B., Qi, X.-L. & Zhang, S.-C. Quantized topological magnetoelectric effect of the zero-plateau quantum anomalous Hall state. Phys. Rev. B 92, 081107(R) (2015).

    ADS  Google Scholar 

  108. 108.

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

    ADS  Google Scholar 

  109. 109.

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

    Google Scholar 

  110. 110.

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

    ADS  Google Scholar 

  111. 111.

    Edelstein, V. M. Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems. Solid State Commun. 73, 233 (1990).

    ADS  Google Scholar 

  112. 112.

    Kondou, K. et al. Fermi-level-dependent charge-to-spin current conversion by Dirac surface states of topological insulators. Nat. Phys. 12, 1027–1031 (2016).

    Google Scholar 

  113. 113.

    Mellnik, A. R. et al. Spin–transfer torque generated by a topological insulator. Nature 511, 449–451 (2014).

    ADS  Google Scholar 

  114. 114.

    Wang, Y. et al. Topological surface states originated spin–orbit torques in Bi2Se3. Phys. Rev. Lett. 114, 257202 (2015).

    ADS  MathSciNet  Google Scholar 

  115. 115.

    Shiomi, Y. et al. Spin-electricity conversion induced by spin injection into topological insulators. Phys. Rev. Lett. 113, 196601 (2014).

    ADS  Google Scholar 

  116. 116.

    Deorani, P. et al. Observation of inverse spin Hall effect in bismuth selenide. Phys. Rev. B 90, 094403 (2014).

    ADS  Google Scholar 

  117. 117.

    Jamali, M. et al. Giant spin pumping and inverse spin Hall effect in the presence of surface and bulk spin–orbit coupling of topological insulator Bi2Se3. Nano Lett. 15, 7126–7132 (2015).

    ADS  Google Scholar 

  118. 118.

    Mendes, J. B. S. et al. Dirac-surface-state-dominated spin to charge current conversion in the topological insulator (Bi0.22Sb0.78)2Te3 films at room temperature. Phys. Rev. B 96, 180415 (2017).

    ADS  Google Scholar 

  119. 119.

    Wang, H. et al. Surface-state-dominated spin–charge current conversion in topological-insulator/ferromagnetic-insulator heterostructures. Phys. Rev. Lett. 117, 076601 (2016).

    ADS  Google Scholar 

  120. 120.

    Liu, L. et al. Spin-polarized tunneling study of spin-momentum locking in topological insulators. Phys. Rev. B 91, 235437 (2015).

    ADS  Google Scholar 

  121. 121.

    Fan, Y. et al. Magnetization switching through giant spin–orbit torque in a magnetically doped topological insulator heterostructure. Nat. Mater. 13, 699–704 (2014).

    ADS  Google Scholar 

  122. 122.

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

    Google Scholar 

  123. 123.

    Han, W., Otani, Y. & Maekawa, S. Quantum materials for spin and charge conversion. NPJ Quantum Mater. 3, 27 (2018).

    ADS  Google Scholar 

  124. 124.

    Yabin, F. et al. Electric-field control of spin–orbit torque in a magnetically doped topological insulator. Nat. Nanotechol. 11, 352–359 (2016).

    ADS  Google Scholar 

  125. 125.

    Jiang., Z. et al. Enhanced spin Seebeck effect signal due to spin-momentum locked topological surface states. Nat. Commun. 7, 11458 (2016).

    ADS  Google Scholar 

  126. 126.

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

    ADS  Google Scholar 

  127. 127.

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

    Google Scholar 

  128. 128.

    Avci, C. O. et al. Magnetoresistance of heavy and light metal/ferromagnet bilayers. Appl. Phys. Lett. 107, 192405 (2015).

    ADS  Google Scholar 

  129. 129.

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

    ADS  Google Scholar 

  130. 130.

    Tokura, Y. & Nagaosa, N. Nonreciprocal responses from non-centrosymmetric quantum materials. Nat. Commun. 9, 3740 (2018).

    ADS  Google Scholar 

  131. 131.

    Baibich, M. N. et al. Giant magnetoresistance of (001) Fe/(001) Cr magnetic superlattices. Phys. Rev. Lett. 61, 2472 (1988).

    ADS  Google Scholar 

  132. 132.

    Binasch, G., Grünberg, P., Saurenbach, F. & ZinnEnhanced, W. magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange. Phys. Rev. B 39, 4828 (1989).

    ADS  Google Scholar 

  133. 133.

    Yoshimi, R. et al. Quantum Hall states stabilized in semi-magnetic bilayers of topological insulators. Nat. Commun. 6, 8530 (2015).

    Google Scholar 

  134. 134.

    Ogawa, N. et al. Zero-bias photocurrent in ferromagnetic topological insulator. Nat. Commun. 7, 12246 (2016).

    ADS  Google Scholar 

  135. 135.

    Grinberg, I. et al. Perovskite oxides for visible-light-absorbing ferroelectric and photovoltaic materials. Nature 503, 509–512 (2013).

    ADS  Google Scholar 

  136. 136.

    Ogawa, N., Sotome, M., Kaneko, Y., Ogino, M. & Tokura, Y. Shift current in the ferroelectric semiconductor SbSI. Phys. Rev. B 96, 241203 (2017).

    ADS  Google Scholar 

  137. 137.

    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  Google Scholar 

  138. 138.

    Okada, K. N. et al. Enhanced photogalvanic current in topological insulators via Fermi energy tuning. Phys. Rev. B 93, 081403 (2016).

    ADS  Google Scholar 

  139. 139.

    Fert, A., Reyren, N. & Cros, V. Magnetic skyrmions: advances in physics and potential applications. Nat. Rev. Mater. 2, 17031 (2017).

    ADS  Google Scholar 

  140. 140.

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

    ADS  Google Scholar 

  141. 141.

    He, Q. L. et al. Exchange-biasing topological charges by antiferromagnetism. Nat. Commun. 9, 2767 (2018).

    ADS  Google Scholar 

  142. 142.

    Miron, I. M. et al. Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection. Nature 476, 189–193 (2011).

    ADS  Google Scholar 

  143. 143.

    Liu, L., Lee, O. J., Gudmundsen, T. J., Ralph, D. C. & Buhrman, R. A. Current-induced switching of perpendicularly magnetized magnetic layers using spin torque from the spin Hall effect. Phys. Rev. Lett. 109, 096602 (2012).

    ADS  Google Scholar 

  144. 144.

    Liu, L. et al. Spin-torque switching with the giant spin Hall effect of tantalum. Science 336, 555–558 (2012).

    ADS  Google Scholar 

  145. 145.

    Pai, C. F. et al. Spin transfer torque devices utilizing the giant spin Hall effect of tungsten. Appl. Phys. Lett. 101, 122404 (2012).

    ADS  Google Scholar 

  146. 146.

    Slonczewski, J. C. Current-driven excitation of magnetic multilayers. J. Magn. Magn. Mat. 159, L1–L7 (1996).

    ADS  Google Scholar 

  147. 147.

    Ralph, D. C. & Stiles, M. D. Spin transfer torques. J. Magn. Magn. Mat. 230, 1190–1216 (2008).

    ADS  Google Scholar 

  148. 148.

    Yasuda, K. et al. Current-nonlinear Hall effect and spin-orbit torque magnetization switching in a magnetic topological insulator. Phys. Rev. Lett. 119, 137204 (2017).

    ADS  Google Scholar 

  149. 149.

    Gupta, S., Kanai, S., Matsukura, F. & Ohno, H. Magnetic and transport properties of Sb2Te3 doped with high concentration of Cr. Appl. Phys. Express 10, 103001 (2017).

    ADS  Google Scholar 

  150. 150.

    Lv, Y. et al. Unidirectional spin-Hall and Rashba−Edelstein magnetoresistance in topological insulator-ferromagnet layer heterostructures. Nat. Commun. 9, 111 (2018).

    ADS  Google Scholar 

  151. 151.

    Han, J. et al. Room-temperature spin–orbit torque switching induced by a topological insulator. Phys. Rev. Lett. 119, 077702 (2017).

    ADS  Google Scholar 

  152. 152.

    Wang, Y. et al. Room temperature magnetization switching in topological insulator–ferromagnet heterostructures by spin–orbit torques. Nat. Commun. 8, 1364 (2017).

    ADS  Google Scholar 

  153. 153.

    Khang, N. H. D., Ueda, Y. & Hai, P. N. A conductive topological insulator with colossal spin Hall effect for ultra-low power spin-orbit-torque switching. Nat. Mater. 17, 808–813 (2018).

    ADS  Google Scholar 

  154. 154.

    DC, M. et al. Room-temperature perpendicular magnetization switching through giant spin-orbit torque from sputtered BixSe(1-x) topological insulator material. Nat. Mater. 17, 800–807 (2018).

    ADS  Google Scholar 

  155. 155.

    Wei, P. et al. Exchange-coupling-induced symmetry breaking in topological insulators. Phys. Rev. Lett. 110, 186807 (2013).

    ADS  Google Scholar 

  156. 156.

    Lee, C., Katmis, F., Jarillo-Herrero, P., Moodera, J. S. & Gedik, N. Direct measurement of proximity-induced magnetism at the interface between a topological insulator and a ferromagnet. Nat. Commun. 7, 12014 (2016).

    ADS  Google Scholar 

  157. 157.

    Katmis, F. et al. A high-temperature ferromagnetic topological insulating phase by proximity coupling. Nature 533, 513–516 (2016).

    ADS  Google Scholar 

  158. 158.

    Alegria, L. D. et al. Large anomalous Hall effect in ferromagnetic insulator-topological insulator heterostructures. Appl. Phys. Lett. 105, 053512 (2014).

    ADS  Google Scholar 

  159. 159.

    Lang, M. et al. Proximity induced high-temperature magnetic order in topological insulator-ferrimagnetic insulator heterostructure. Nano Lett. 14, 3459–3465 (2014).

    ADS  Google Scholar 

  160. 160.

    Jiang, Z. et al. Independent tuning of electronic properties and induced ferromagnetism in topological insulators with heterostructure approach. Nano Lett. 15, 5835–5840 (2015).

    ADS  Google Scholar 

  161. 161.

    Tang, C. et al. Above 400-K robust perpendicular ferromagnetic phase in a topological insulator. Sci. Adv. 3, e1700307 (2017).

    ADS  Google Scholar 

  162. 162.

    Otrokov, M. M. et al. Highly-ordered wide bandgap materials for quantized anomalous Hall and magnetoelectric effects. 2D Mater. 4, 025082 (2017).

    Google Scholar 

  163. 163.

    Zhang, D., Shi, M., Xing, D., Zhang, H. & Wang, J. Topological axion states in magnetic insulator MnBi2Te4 with the quantized magnetoelectric effect. Preprint at (2018).

  164. 164.

    Li, J. et al. Intrinsic magnetic topological insulators in van der Waals layered MnBi2Te4-family materials. Preprint at (2018).

  165. 165.

    Otrokov, M. M. et al. Prediction and observation of the first antiferromagnetic topological insulator. Preprint at (2018).

  166. 166.

    Gong, Y. et al. Experimental realization of an intrinsic magnetic topological insulator. Preprint at (2018).

  167. 167.

    Yeats, A. L. et al. Local optical control of ferromagnetism and chemical potential in a topological insulator. Proc. Natl Acad. Sci. USA 114, 10379–10383 (2017).

    ADS  Google Scholar 

  168. 168.

    Mahoney, A. C. et al. Zero-field edge plasmons in a magnetic topological insulator. Nat. Commun. 8, 1836 (2017).

    ADS  Google Scholar 

  169. 169.

    Fu, L. & Kane, C. L. Probing neutral Majorana fermion edge modes with charge transport. Phys. Rev. Lett. 102, 216403 (2009).

    ADS  Google Scholar 

  170. 170.

    Akhmerov, A. R., Nilsson, J. & Beenakker, C. W. J. Electrically detected interferometry of Majorana fermions in a topological insulator. Phys. Rev. Lett. 102, 216404 (2009).

    ADS  Google Scholar 

  171. 171.

    Schuffelgen, P. et al. Stencil lithography of superconducting contacts on MBE-grown topological insulator thin films. J. Cryst. Growth 477, 183–187 (2017).

    ADS  Google Scholar 

  172. 172.

    He, Q. L. et al. Two-dimensional superconductivity at the interface of a Bi2Te3/FeTe heterostructure. Nat. Commun. 5, 4247 (2014).

    Google Scholar 

  173. 173.

    Burkov, A. A. & Balents, L. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett. 107, 127205 (2011).

    ADS  Google Scholar 

  174. 174.

    Balents, L. Viewpoint: Weyl electrons kiss. Physics 4, 36 (2011).

    Google Scholar 

  175. 175.

    Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).

    ADS  MathSciNet  Google Scholar 

  176. 176.

    Jiang, G. et al. Quantum anomalous Hall multilayers grown by molecular beam epitaxy. Chin. Phys. Lett. 35, 076802 (2018).

    ADS  Google Scholar 

  177. 177.

    Fang, C., Gilbert, M. J. & Bernevig, B. A. Large-Chern-number quantum anomalous Hall effect in thin-film topological crystalline insulators. Phys. Rev. Lett. 112, 046801 (2014).

    ADS  Google Scholar 

  178. 178.

    Assaf, B. A. et al. Inducing magnetism onto the surface of a topological crystalline insulator. Phys. Rev. B 91, 195310 (2015).

    ADS  Google Scholar 

  179. 179.

    Wang, F. et al. Chromium-induced ferromagnetism with perpendicular anisotropy in topological crystalline insulator SnTe (111) thin films. Phys. Rev. B 97, 115414 (2018).

    ADS  Google Scholar 

  180. 180.

    Tang, E., Mei, J. W. & Wen, X. G. High-temperature fractional quantum Hall states. Phys. Rev. Lett. 106, 236802 (2011).

    ADS  Google Scholar 

  181. 181.

    Sun, K., Gu, Z., Katsura, H. & Sarma, S. D. Nearly flatbands with nontrivial topology. Phys. Rev. Lett. 106, 236803 (2011).

    ADS  Google Scholar 

  182. 182.

    Neupert, T., Santos, L., Chamon, C. & Mudry, C. Fractional quantum Hall states at zero magnetic field. Phys. Rev. Lett. 106, 236804 (2011).

    ADS  Google Scholar 

  183. 183.

    Klinovaja, J., Tserkovnyak, Y. & Loss, D. Integer and fractional quantum anomalous Hall effect in a strip of stripes model. Phys. Rev. B 91, 085426 (2015).

    ADS  Google Scholar 

  184. 184.

    Maciejko, J. & Fiete, G. A. Fractionalized topological insulators. Nat. Phys. 11, 385–388 (2015).

    Google Scholar 

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The authors thank R. Yoshimi, M. Mogi, M. Kawamura, N. Nagaosa, M. Kawasaki and T. Dietl for enlightening discussions on magnetic topological insulators. This research was supported in part by the Japan Society for the Promotion of Science (JSPS; no. 16J03476), the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan (no. JP15H05853), and Core Research for Evolutional Science and Technology (CREST), Japanese Science and Technology (JST; no. JPMJCR16F1).

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Tokura, Y., Yasuda, K. & Tsukazaki, A. Magnetic topological insulators. Nat Rev Phys 1, 126–143 (2019).

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