Prediction and observation of an antiferromagnetic topological insulator

Abstract

Magnetic topological insulators are narrow-gap semiconductor materials that combine non-trivial band topology and magnetic order1. Unlike their nonmagnetic counterparts, magnetic topological insulators may have some of the surfaces gapped, which enables a number of exotic phenomena that have potential applications in spintronics1, such as the quantum anomalous Hall effect2 and chiral Majorana fermions3. So far, magnetic topological insulators have only been created by means of doping nonmagnetic topological insulators with 3d transition-metal elements; however, such an approach leads to strongly inhomogeneous magnetic4 and electronic5 properties of these materials, restricting the observation of important effects to very low temperatures2,3. An intrinsic magnetic topological insulator—a stoichiometric well ordered magnetic compound—could be an ideal solution to these problems, but no such material has been observed so far. Here we predict by ab initio calculations and further confirm using various experimental techniques the realization of an antiferromagnetic topological insulator in the layered van der Waals compound MnBi2Te4. The antiferromagnetic ordering  that MnBi2Te4 shows makes it invariant with respect to the combination of the time-reversal and primitive-lattice translation symmetries, giving rise to a 2 topological classification; 2 = 1 for MnBi2Te4, confirming its topologically nontrivial nature. Our experiments indicate that the symmetry-breaking (0001) surface of MnBi2Te4 exhibits a large bandgap in the topological surface state. We expect this property to eventually enable the observation of a number of fundamental phenomena, among them quantized magnetoelectric coupling6,7,8 and axion electrodynamics9,10. Other exotic phenomena could become accessible at much higher temperatures than those reached so far, such as the quantum anomalous Hall effect2 and chiral Majorana fermions3.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Theoretical insights into the crystal, magnetic and electronic structure of MnBi2Te4.
Fig. 2: MnBi2Te4 single crystals and their magnetic properties.
Fig. 3: Photoemission spectroscopy insight into the surface and bulk bandstructure of MnBi2Te4.
Fig. 4: Spin characterization of bulk and surface electronic structure of MnBi2Te4.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request. The crystal structure is available in the joint Cambridge Crystallographic Data Centre/FIZ Karlsruhe (https://www.ccdc.cam.ac.uk/structures/) under the depository number CSD-1867581.

References

  1. 1.

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

  2. 2.

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

  3. 3.

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

  4. 4.

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

  5. 5.

    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).

  6. 6.

    Mong, R. S. K., Essin, A. M. & Moore, J. E. Antiferromagnetic topological insulators. Phys. Rev. B 81, 245209 (2010).

  7. 7.

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

  8. 8.

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

  9. 9.

    Li, R., Wang, J., Qi, X.-L. & Zhang, S.-C. Dynamical axion field in topological magnetic insulators. Nat. Phys. 6, 284–288 (2010).

  10. 10.

    Wang, J., Lian, B. & Zhang, S.-C. Dynamical axion field in a magnetic topological insulator superlattice. Phys. Rev. B 93, 045115 (2016).

  11. 11.

    Lee, D. S. et al. Crystal structure, properties and nanostructuring of a new layered chalcogenide semiconductor, Bi2MnTe4. CrystEngComm 15, 5532–5538 (2013).

  12. 12.

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

  13. 13.

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

  14. 14.

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

  15. 15.

    Sánchez-Barriga, J. et al. Nonmagnetic band gap at the Dirac point of the magnetic topological insulator (Bi1−xMnx)2Se3. Nat. Commun. 7, 10559 (2016).

  16. 16.

    Vaknin, D., Davidov, D., Zevin, V. & Selig, H. Anisotropy and two-dimensional effects in the ESR properties of OsF6-graphite intercalation compounds. Phys. Rev. B 35, 6423–6431 (1987).

  17. 17.

    Vithayathil, J. P., MacLaughlin, D. E., Koster, E., Williams, D. L. & Bucher, E. Spin fluctuations and anisotropic nuclear relaxation in single-crystal UPt3. Phys. Rev. B 44, 4705–4708 (1991).

  18. 18.

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

  19. 19.

    Eremeev, S. V., Otrokov, M. M. & Chulkov, E. V. Competing rhombohedral and monoclinic crystal structures in MnPn2Ch4 compounds: an ab-initio study. J. Alloys Compd. 709, 172–178 (2017).

  20. 20.

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

  21. 21.

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

  22. 22.

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

  23. 23.

    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).

  24. 24.

    Otrokov, M. M. et al. Magnetic extension as an efficient method for realizing the quantum anomalous Hall state in topological insulators. JETP Lett. 105, 297–302 (2017).

  25. 25.

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

  26. 26.

    Hirahara, T. et al. Large-gap magnetic topological heterostructure formed by subsurface incorporation of a ferromagnetic layer. Nano Lett. 17, 3493–3500 (2017).

  27. 27.

    Hagmann, J. A. et al. Molecular beam epitaxy growth and structure of self-assembled Bi2Se3/Bi2MnSe4 multilayer heterostructures. New J. Phys. 19, 085002 (2017).

  28. 28.

    Rienks, E. D. L. et al. Large magnetic gap at the Dirac point in a Mn-induced Bi2Te3 heterostructure. Preprint at https://arxiv.org/abs/1810.06238 (2018).

  29. 29.

    Eremeev, S. V., Otrokov, M. M. & Chulkov, E. V. New universal type of interface in the magnetic insulator/topological insulator heterostructures. Nano Lett. 18, 6521–6529 (2018).

  30. 30.

    Gong, C. et al. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals. Nature 546, 265–269 (2017).

  31. 31.

    Huang, B. et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 546, 270–273 (2017).

  32. 32.

    Baltz, V. et al. Antiferromagnetic spintronics. Rev. Mod. Phys. 90, 015005 (2018).

  33. 33.

    Šmejkal, L., Mokrousov, Y., Yan, B. & MacDonald, A. H. Topological antiferromagnetic spintronics. Nat. Phys. 14, 242–251 (2018).

  34. 34.

    Zhang, D. et al. Topological axion states in magnetic insulator MnBi2Te4 with the quantized magnetoelectric effect. Phys. Rev. Lett. 122, 206401 (2019).

  35. 35.

    Li, J. et al. Intrinsic magnetic topological insulators in van der Waals layered MnBi2Te4-family materials. Sci. Adv. 5, eaaw5685 (2019).

  36. 36.

    Gong, Y. et al. Experimental realization of an intrinsic magnetic topological insulator. Chin. Phys. Lett. 36, 076801 (2019).

  37. 37.

    Lee, S. H. et al. Spin scattering and noncollinear spin structure-induced intrinsic anomalous Hall effect in antiferromagnetic topological insulator MnBi2Te4. Phys. Rev. Res. 1, 012011(R) (2019).

  38. 38.

    Yan, J.-Q. et al. Crystal growth and magnetic structure of MnBi2Te4. Phys. Rev. Mater. 3, 064202 (2019).

  39. 39.

    Chen, B. et al. Intrinsic magnetic topological insulator phases in the Sb doped MnBi2Te4 bulks and thin flakes. Nat. Commun. 10, 4469 (2019).

  40. 40.

    Deng, Y. et al. Magnetic-field-induced quantized anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4. Preprint at https://arxiv.org/abs/1904.11468 (2019).

  41. 41.

    Liu, C. et al. Quantum phase transition from axion insulator to Chern insulator in MnBi2Te4. Preprint at https://arxiv.org/abs/1905.00715 (2019).

  42. 42.

    Ge, J. et al. High-Chern-number and high-temperature quantum Hall effect without Landau levels. Preprint at https://arxiv.org/abs/1907.09947 (2019).

  43. 43.

    Otrokov, M. M. et al. Unique thickness-dependent properties of the van der Waals interlayer antiferromagnet MnBi2Te4 films. Phys. Rev. Lett. 122, 107202 (2019).

  44. 44.

    Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

  45. 45.

    Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

  46. 46.

    Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).

  47. 47.

    Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

  48. 48.

    Koelling, D. D. & Harmon, B. N. A technique for relativistic spin-polarised calculations. J. Phys. C 10, 3107 (1977).

  49. 49.

    Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 27, 1787–1799 (2006).

  50. 50.

    Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104 (2010).

  51. 51.

    Grimme, S., Ehrlich, S. & Goerigk, L. Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem. 32, 1456–1465 (2011).

  52. 52.

    Anisimov, V. I., Zaanen, J. & Andersen, O. K. Band theory and Mott insulators: Hubbard U instead of Stoner I. Phys. Rev. B 44, 943–954 (1991).

  53. 53.

    Dudarev, S. L., Botton, G. A., Savrasov, S. Y., Humphreys, C. J. & Sutton, A. P. Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study. Phys. Rev. B 57, 1505–1509 (1998).

  54. 54.

    Becke, A. D. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 38, 3098 (1988).

  55. 55.

    Perdew, J. P., Ernzerhof, M. & Burke, K. Rationale for mixing exact exchange with density functional approximations. J. Chem. Phys. 105, 9982–9985 (1996).

  56. 56.

    Heyd, J., Scuseria, G. E. & Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 8207–8215 (2003).

  57. 57.

    Fang, C., Gilbert, M. J. & Bernevig, B. A. Topological insulators with commensurate antiferromagnetism. Phys. Rev. B 88, 085406 (2013).

  58. 58.

    Wimmer, E., Krakauer, H., Weinert, M. & Freeman, A. J. Full-potential self-consistent linearized-augmented-plane-wave-method for calculating the electronic structure of molecules and surfaces: O2 molecule. Phys. Rev. B 24, 864–875 (1981).

  59. 59.

    FLEUR http://www.flapw.de, version fleur.26e (2017).

  60. 60.

    Anisimov, V. I., Aryasetiawan, F. & Lichtenstein, A. I. First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA+U method. J. Phys. Condens. Matter 9, 767 (1997).

  61. 61.

    Shick, A. B., Liechtenstein, A. I. & Pickett, W. E. Implementation of the LDA+U method using the full-potential linearized augmented plane-wave basis. Phys. Rev. B 60, 10763–10769 (1999).

  62. 62.

    Anisimov, V. I., Solovyev, I. V., Korotin, M. A., Czyżyk, M. T. & Sawatzky, G. A. Density-functional theory and NiO photoemission spectra. Phys. Rev. B 48, 16929–16934 (1993).

  63. 63.

    Sandratskii, L. M. & Bruno, P. Exchange interactions and Curie temperature in (Ga,Mn)As. Phys. Rev. B 66, 134435 (2002).

  64. 64.

    Ležaić, M., Mavropoulos, P., Enkovaara, J., Bihlmayer, G. & Blügel, S. Thermal collapse of spin polarization in half-metallic ferromagnets. Phys. Rev. Lett. 97, 026404 (2006).

  65. 65.

    Kurz, P., Förster, F., Nordström, L., Bihlmayer, G. & Blügel, S. Ab initio treatment of noncollinear magnets with the full-potential linearized augmented plane wave method. Phys. Rev. B 69, 024415 (2004).

  66. 66.

    Soven, P. Coherent-potential model of substitutional disordered alloys. Phys. Rev. 156, 809 (1967).

  67. 67.

    Gyorffy, B. L. Coherent-potential approximation for a nonoverlapping-muffin-tin-potential model of random substitutional alloys. Phys. Rev. B 5, 2382 (1972).

  68. 68.

    Lüders, M., Ernst, A., Temmerman, W. M., Szotek, Z. & Durham, P. J. Ab initio angle-resolved photoemission in multiple-scattering formulation. J. Phys. Condens. Matter 13, 8587 (2001).

  69. 69.

    Geilhufe, M. et al. Numerical solution of the relativistic single-site scattering problem for the Coulomb and the Mathieu potential. J. Phys. Condens. Matter 27, 435202 (2015).

  70. 70.

    Gyorffy, B. L., Pindor, A. J., Staunton, J., Stocks, G. M. & Winter, H. A first-principles theory of ferromagnetic phase transitions in metals. J. Phys. F 15, 1337 (1985).

  71. 71.

    Staunton, J., Gyorffy, B. L., Pindor, A. J., Stocks, G. M. & Winter, H. Electronic structure of metallic ferromagnets above the Curie temperature. J. Phys. F 15, 1387 (1985).

  72. 72.

    Marzari, N. & Vanderbilt, D. Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B 56, 12847 (1997).

  73. 73.

    Mostofi, A. A. et al. wannier90: A tool for obtaining maximally-localized Wannier functions. Comput. Phys. Commun. 178, 685–699 (2008).

  74. 74.

    Lopez Sancho, M. P., Lopez Sancho, J. M., Sancho, J. M. L. & Rubio, J. Highly convergent schemes for the calculation of bulk and surface Green functions. J. Phys. F 15, 851–858 (1985).

  75. 75.

    Henk, J. & Schattke, W. A subroutine package for computing Green’s functions of relaxed surfaces by the renormalization method. Comput. Phys. Commun. 77, 69–83 (1993).

  76. 76.

    Zeugner, A. et al. Chemical aspects of the candidate antiferromagnetic topological insulator MnBi2Te4. Chem. Mater. 31, 2795–2806 (2019).

  77. 77.

    X-Shape, Crystal Optimization for Numerical Absorption Correction Program Version 2.12.2, https://www.stoe.com/product/software-x-area/ (Stoe & Cie, 2009).

  78. 78.

    Petricek, V., Dusek, M. & Palatinus, L. Jana2006 http://jana.fzu.cz (Institute of Physics, 2011).

  79. 79.

    Sheldrick, G. M. SHELXL Version 2014/7 https://shelx.uni-goettingen.de (Georg-August-Universität Göttingen, 2014).

  80. 80.

    Sheldrick, G. M. A short history of SHELX. Acta Crystallogr. A 64, 112–122 (2008).

  81. 81.

    Aliev, Z. S. et al. Novel ternary layered manganese bismuth tellurides of the MnTe-Bi2Te3 system: synthesis and crystal structure. J. Alloys Compd. 789, 443–450 (2019).

  82. 82.

    Abragam, A. & Bleaney, B. Electron Paramagnetic Resonance of Transition Ions (Oxford University Press, 2012).

  83. 83.

    Benner, H. & Boucher, J. In Magnetic Properties of Layered Transition Metal Compounds 323–378 (Kluwer, 1990).

  84. 84.

    Turov, E. A. Physical Properties of Magnetically Ordered Crystals (Academic Press, 1965).

  85. 85.

    Petaccia, L. et al. BaD ElPh: a 4-m normal-incidence monochromator beamline at Elettra. Nucl. Instrum. Methods Phys. Res. A 606, 780–784 (2009).

  86. 86.

    Iwasawa, H. et al. Rotatable high-resolution ARPES system for tunable linear-polarization geometry. J. Synchrotron Radiat. 24, 836–841 (2017).

  87. 87.

    Iwasawa, H. et al. Development of laser-based scanning µ-ARPES system with ultimate energy and momentum resolutions. Ultramicroscopy 182, 85–91 (2017).

  88. 88.

    Bentmann, H. et al. Strong linear dichroism in spin-polarized photoemission from spin–orbit-coupled surface states. Phys. Rev. Lett. 119, 106401 (2017).

  89. 89.

    Chernov, S. V. et al. Anomalous d-like surface resonances on Mo(110) analyzed by time-of-flight momentum microscopy. Ultramicroscopy 159, 453–463 (2015).

  90. 90.

    Tusche, C. et al. Multi-MHz time-of-flight electronic bandstructure imaging of graphene on Ir(111). Appl. Phys. Lett. 108, 261602 (2016).

  91. 91.

    Schönhense, G. et al. Spin-filtered time-of-flight k-space microscopy of Ir towards the complete photoemission experiment. Ultramicroscopy 183, 19–29 (2017).

  92. 92.

    Krupin, O. et al. Rashba effect at magnetic metal surfaces. Phys. Rev. B 71, 201403 (2005).

  93. 93.

    Rybkin, A. G. et al. Magneto-spin–orbit graphene: interplay between exchange and spin–orbit couplings. Nano Lett. 18, 1564–1574 (2018).

  94. 94.

    Sánchez-Barriga, J. et al. Subpicosecond spin dynamics of excited states in the topological insulator Bi2Te3. Phys. Rev. B 95, 125405 (2017).

  95. 95.

    Abbate, M. et al. Probing depth of soft X-ray absorption spectroscopy measured in total-electron-yield mode. Surf. Interface Anal. 18, 65–69 (1992).

  96. 96.

    Barla, A. et al. Design and performance of BOREAS, the beamline for resonant X-ray absorption and scattering experiments at the ALBA synchrotron light source. J. Synchrotron Radiat. 23, 1507–1517 (2016).

Download references

Acknowledgements

M.M.O. and E.V.C. thank A. Arnau and J. I. Cerdá for discussions. We acknowledge support by the Basque Departamento de Educacion, UPV/EHU (grant number IT-756-13), the Spanish Ministerio de Economia y Competitividad (MINECO grant number FIS2016-75862-P), and the Academic D.I. Mendeleev Fund Program of Tomsk State University (project number 8.1.01.2018). Support from the Saint Petersburg State University grant for scientific investigations (grant ID 40990069), the Russian Science Foundation (grants number 18-12-00062  for part of the photoemission measurements and 18-12-00169 for part of the calculations of topological invariants and tight-binding bandstructure calculations), the Russian Foundation for Basic Research (grant number 18-52-06009), and the Science Development Foundation under the President of the Republic of Azerbaijan (grant number EİF-BGM-4-RFTF-1/2017-21/04/1-M-02) is also acknowledged. M.M.O. acknowledges support by the Diputación Foral de Gipuzkoa (project number 2018-CIEN-000025-01). I.I.K. and A.M.S. acknowledge partial support from the CERIC-ERIC consortium for the stay at the Elettra synchrotron. The ARPES measurements at HiSOR were performed with the approval of the Proposal Assessing Committee (proposal numbers 18AG020, 18BU005). The support of the German Research Foundation (DFG) is acknowledged by A.U.B.W., A.I. and B.B. within Collaborative Research Center 1143 (SFB 1143, project ID 247310070); by A.Z., A.E. and A.I. within Special Priority Program 1666 Topological Insulators; by H.B. and F.R. within Collaborative Research Center 1170; and by A.Z. and A.I. within the ERANET-Chemistry Program (RU 776/15-1). H.B., A.U.B.W., A.A., V.K., B.B., F.R. and A.I. acknowledge financial support from the DFG through the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter – ct.qmat (EXC 2147, project ID 39085490). A.E. acknowledges support by the OeAD grant numbers HR 07/2018 and PL 03/2018. This work was also supported by the Fundamental Research Program of the State Academies of Sciences, line of research III.23. A.K. was financially supported by KAKENHI number 17H06138 and 18H03683. I.P.R. acknowledges support by the Ministry of Education and Science of the Russian Federation within the framework of the governmental program Megagrants (state task number 3.8895.2017/P220). E.V.C. acknowledges financial support by the Gobierno Vasco-UPV/EHU project (IT1246-19). S.K. acknowledges financial support from an Overseas Postdoctoral Fellowship, SERB-India (OPDF award number SB/OS/PDF-060/2015-16). J.S.-B.acknowledges financial support from the Impuls-und Vernetzungsfonds der Helmholtz-Gemeinschaft under grant number HRSF-0067 (Helmholtz-Russia Joint Research Group). The calculations were performed in Donostia International Physics Center, in the research park of Saint Petersburg State University Computing Center (http://cc.spbu.ru), and at Tomsk State University.

Author information

The bandstructure calculations were performed by M.M.O., M.B.-R., S.V.E. and A.Yu.V. The exchange-coupling constants calculations were performed by M.B.-R., Yu.M.K, M.M.O. and A.E. The paramagnons calculations were performed by A.E. The magnetic anisotropy studies were performed by M.M.O. The Monte Carlo simulations were performed by M.H. The topological invariant calculations were done by S.V.E. Tight-binding calculations were performed by I.P.R. and V.M.K. Crystals were grown by A.Z., A.I., Z.S.A. and M.B.B. X-ray diffraction measurements and structure determination were performed by A.Z. and I.R.A. The resistivity and Hall measurements, as well as contact preparation, were done by N.T.M., N.A.A. and V.N.Z. XMCD and resonant photoemission experiments were performed by R.C.V., T.R.F.P., C.H.M., K.K., S.S. and H.B. Magnetization experiments and their analysis were mainly performed by S.G., B.B. and A.U.B.W. with contributions by A.V.K. ARPES measurements were done by I.I.K., D.E., A.M.S., E.F.S., S.K., A.K., L.P., G.D.S.,   R.C.V., K.K., M.Ü., S.M. and H.B. The analysis of the ARPES data was done by I.I.K., D.E.,  R.C.V. and H.B. Spin-ARPES measurements were performed by I.I.K., D.E., A.M.S., F.F. and J.S.-B. ESR measurements were done by A.A. and V.K. The project was planned by M.M.O., A.I., H.B., A.M.S., N.T.M., F.R., P.M.E. and E.V.C. The supervision of the project was executed by E.V.C. All authors contributed to the discussion and manuscript editing. The paper was written by M.M.O. with contributions from A.I., H.B., V.K. and A.U.B.W.

Correspondence to M. M. Otrokov or E. V. Chulkov.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Monte Carlo simulations for bulk MnBi2Te4.

The temperature-dependent magnetic susceptibility of bulk MnBi2Te4 calculated for various numbers of magnetic shells j up to which the exchange-coupling constants Ji,j were considered in the classical Heisenberg Hamiltonian. In increments of 10, results for 10–70 shells were calculated. The vertical dashed line shows the final Néel temperature of 25.4 K, estimated from the calculation for 70 shells. Note that the simulations revealed the onset of the AFM ground state only above 20 shells.

Extended Data Fig. 2 Electronic structure of the S-breaking and S-preserving surfaces of MnBi2Te4.

a, b, Surface electronic bandstructure of MnBi2Te4 calculated for the (0001) (S-breaking; a), and \((10\bar{1}1)\) (S-preserving; b) terminations using the ab-initio-based tight-binding approach. The regions with a continuous spectrum correspond to the three-dimensional bulk states projected onto a two-dimensional Brillouin zone.

Extended Data Fig. 3 Resistivity and Hall measurements of bulk MnBi2Te4.

a, Temperature- and field-dependent resistivity data. b, Hall voltage as a function of the applied magnetic field for MnBi2Te4 at 5 K. The Hall-effect measurements unambiguously indicate n-type conductivity for our MnBi2Te4 samples that show a negative Hall voltage for positive values of the applied magnetic field. The estimated electron concentration and Hall mobility are around 2 × 1019 cm−3 and 100 cm2 V−1 s−1, respectively. The measurements were performed on B samples.

Extended Data Fig. 4 D-sample ARPES.

a, Dispersion of MnBi2Te4(0001) measured at 12 K with a photon energy of 28 eV. b, EDC representation of the data in a. The red curve marks the EDC at the \(\bar{\Gamma }\)-point. c, ARPES image acquired at 300 K ( = 28 eV). d, Dispersion of MnBi2Te4(0001) measured at a temperature of 12 K with a photon energy of 9 eV (which is more bulk sensitive). e, The second derivative d2N(E)/dE2 of the data in d. f, ARPES image acquired at 300 K ( = 9 eV). The measurements were performed on D samples.

Extended Data Fig. 5 Laser-based ARPES.

a, ARPES map of MnBi2Te4 taken at 10 K with a photon energy of 6.3 eV. In this case, the photoelectrons have a kinetic energy of about 1.5 eV and, subsequently, a large mean free path in the sample, corresponding to a high bulk sensitivity of this experiment. b, The second derivative d2N(E)/dE2 of the data in a. c, Fitting results for the EDC spectrum at the \(\bar{\Gamma }\)-point. The raw data, the resulting fitting curve and its decomposition with Voigt peaks are shown by blue symbols, a black solid line and the grey dashed and red solid lines, respectively. Red (grey) lines indicate the peaks attributed to the gapped Dirac cone state (bulk bands). The measurements were performed on B samples.

Extended Data Fig. 6 Surface electronic structure of MnBi2Te4 in the artificial topologically trivial phase.

Septuple-layer resolved (0001) surface electronic structure of MnBi2Te4 calculated for the SOC constant value λ = 0.55λ0. The size of the colour circles that comprise the data reflects the state localization in a particular septuple-layer block of the eight-septuple-layer-thick slab. a, First septuple layer (that is, the surface layer; red). b, Second septuple layer (subsurface; blue). c, Third septuple layer (bulk-like; green). d, Fourth septuple layer (bulk-like; black). The grey areas correspond to the bulk bandstructure projected onto the surface Brillouin zone. We see that near the \(\bar{\Gamma }\)-point there are (1) no surface states in the bulk bandgap and (2) no resonance states near the bandgap edges. The first quantum-well states of both the valence and conduction bands are strongly localized in the inner parts of the slab.

Extended Data Fig. 7 Photon-energy-dependent ARPES data.

Photon-energy-dependent ARPES data measured near the Brillouin zone centre along the \(\bar{{\rm{K}}}\mbox{--}\bar{\Gamma }\mbox{--}\bar{{\rm{K}}}\) direction at a temperature of 18 K. Absence of any  dependence confirms the surface-state character of the upper cone. The measurements were performed on D samples.

Extended Data Fig. 8 Temperature-dependent linear dichroism in the Dirac cone photoemission intensity.

a, Dispersion of MnBi2Te4(0001) measured at 18 K with a photon energy of 21.5 eV and p-polarized light along the \(\bar{{\rm{K}}}\mbox{--}\bar{\Gamma }\mbox{--}\bar{{\rm{K}}}\) direction. b, Momentum distribution curves representation of the data acquired at 18 K (blue) and 80 K (red). c, Linear dichroism (Iright − Ileft), where Iright and Ileft are the intensities of the right and left branches of the upper and lower cone corresponding to positive and negative k, respectively. The measurements were performed on D samples. d, Upper part of the MnBi2Te4(0001) gapped Dirac cone as calculated ab initio. The size of the coloured circles reflects the value and sign of the spin vector Cartesian projections, with red (blue) corresponding to the positive (negative) sy components (perpendicular to kz), and yellow (cyan) to the out-of-plane components +sz (−sz). e, As in d, but with the size of the purple circles reflecting the weight of the px orbitals of all Bi and Te atoms of the topmost septuple-layer block at each k. Note that in de the bulk-like bands of the slab are omitted. The magnetic moment of the topmost Mn layer points towards vacuum, but in Fig. 1e and Extended Data Fig. 6 it points in the opposite direction. f, The weight of the s, px, py and pz orbitals of all Bi and Te atoms of the topmost septuple-layer block for the left (triangles) and right (squares) branches as a function of energy. See Methods for more information on the dichroic ARPES measurements.

Extended Data Fig. 9 Temperature-dependent laser ARPES measurements.

a, ARPES EDC profiles taken at the \(\bar{\Gamma }\)-point of MnBi2Te4(0001) at 10.5 K and 35 K. The raw data, resulting fitted curves, and their decompositions with Voigt peaks are shown by the coloured symbols, the black dashed lines, and the coloured lines and grey symbols, respectively. Red and blue lines (red circles and blue squares) indicate the peaks (EDCs) of the Dirac cone state at 35 K and 10.5 K, respectively. The peaks of the bulk bands at 35 K (10.5 K) are shown by grey circles (squares). b, Integrated intensity of the first two bulk conduction-band states (those analysed in detail in Extended Data Fig. 5c) as a function of temperature. Inset, The ARPES MnBi2Te4(0001) map measured with a laser photon energy of 6.4 eV and T = 10.5 K (as in Fig. 3d). The green rectangle marks the region of the map where the first two bulk conduction-band states are located. The average intensity in the shown temperature interval was set to 1. c, EDC profiles, N(E), taken at the \(\bar{\Gamma }\)-point between 10 K and 35 K with a temperature step ΔT ≈ 0.9 K and two sweep directions (10 K → 35 K→ 10 K). Because the measurements upon heating and cooling reveal essentially the same behaviour, in c we show the data averaged over these two sets of the EDC profiles at each temperature point. Note that the data in a and the intensity dependencies on temperature in bd were acquired from two different B samples, showing slightly different binding energy of the Dirac point gap centres (0.28 eV and 0.25 eV, respectively). d, Intensity integrated within the energy window ΔE marked by the dashed black lines in c. The average intensity in the plateau-like region above approximately 24 K was set to 1. ΔE contains both the lower and upper parts of the Dirac cone at the \(\bar{\Gamma }\)-point and corresponds to the energy interval in which the contribution of the cone is dominant and that of the bulk states is almost negligible. The vertical cyan line approximately shows the start of the intensity increase, which roughly corresponds to TN ≈ 24 K for MnBi2Te4. e, The second derivative, d2N(E)/dE2, of the EDC profiles in c, shown for a clearer visualization of the Dirac point gap behaviour.

Extended Data Fig. 10 Spin-resolved ARPES data.

a, Spin-integrated ARPES spectrum taken at 6 eV photon energy along the \(\bar{{\rm{K}}}\mbox{--}\bar{\Gamma }\mbox{--}\bar{{\rm{K}}}\) direction. Yellow and cyan curves show the location of the gapped TSS. b, Spin-resolved ARPES spectra taken at the \(\bar{\Gamma }\)-point with respect to the out-of-plane spin quantization axis. The out-of-plane spin polarization is shown below the corresponding spin-up and spin-down spectra. cd, Measured out-of-plane (c) and in-plane (d) spin polarization at different momentum values. The in-plane spin polarization changes its sign with k, as expected for the TSS. The change of the out-of-plane spin polarization sign at k = +0.1 Å–1 near the Fermi level in c (bottom) is discussed in the Methods section ‘Dichroic ARPES measurements’. The data in a, b and c, d were acquired on B and D samples, respectively. The measurements were performed at T = 300 K.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Otrokov, M.M., Klimovskikh, I.I., Bentmann, H. et al. Prediction and observation of an antiferromagnetic topological insulator. Nature 576, 416–422 (2019). https://doi.org/10.1038/s41586-019-1840-9

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.