# 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.

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## 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.

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## 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.

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## 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.

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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

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• ### Topological Electronic Structure and Intrinsic Magnetization in MnBi4Te7 : A Bi2Te3 Derivative with a Periodic Mn Sublattice

• Raphael C. Vidal
• , Alexander Zeugner
• , Jorge I. Facio
• , Rajyavardhan Ray
• , M. Hossein Haghighi
• , Anja U. B. Wolter
• , Laura T. Corredor Bohorquez
• , Federico Caglieris
• , Simon Moser
• , Tim Figgemeier
• , Thiago R. F. Peixoto
• , Hari Babu Vasili
• , Manuel Valvidares
• , Sungwon Jung
• , Cephise Cacho
• , Alexey Alfonsov
• , Kavita Mehlawat
• , Vladislav Kataev
• , Christian Hess
• , Manuel Richter
• , Bernd Büchner
• , Jeroen van den Brink
• , Michael Ruck
• , Friedrich Reinert
• , Hendrik Bentmann
•  & Anna Isaeva

Physical Review X (2019)