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prediction and observation of an antiferromagnetic topological insulator | nature

prediction and observation of an antiferromagnetic topological insulator | nature

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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 insulatora stoichiometric well ordered magnetic compoundcould be an ideal solution to these problems, but no such material has been observed so far. Here we predict by abinitio calculations and further confirm using various experimental techniques the realization of an antiferromagnetic topological insulator in the layered van der Waals compound MnBi2Te4. Theantiferromagnetic 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=1forMnBi2Te4, 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.

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.

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).

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, 15051509 (1998).

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, 864875 (1981).

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).

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

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, 15071517 (2016).

M.M.O. and E.V.C. thank A. Arnau and J. I. Cerd 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 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 thecalculations 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 EF-BGM-4-RFTF-1/2017-21/04/1-M-02) is also acknowledged. M.M.O. acknowledges support by the Diputacin 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 Wrzburg-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.

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.., 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.

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 1070shells were calculated. The vertical dashed line shows the final Nel temperature of 25.4K, estimated from the calculation for 70shells. Note that the simulations revealed the onset of the AFM ground state only above 20shells.

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.

a, Temperature- and field-dependent resistivity data. b, Hall voltage as a function of the applied magnetic field for MnBi2Te4 at 5K. 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 21019cm3 and 100cm2V1s1, respectively. The measurements were performed on Bsamples.

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

a, ARPES map of MnBi2Te4 taken at 10K with a photon energy of 6.3eV. In this case, the photoelectrons have a kinetic energy of about 1.5eV 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 Bsamples.

Septuple-layer resolved (0001) surface electronic structure of MnBi2Te4 calculated for the SOC constant value =0.550. The size of the colour circles that comprise the datareflects 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.

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 18K. Absence of any hdependence confirms the surface-state character of the upper cone. The measurements were performed on Dsamples.

a, Dispersion of MnBi2Te4(0001) measured at 18K with a photon energy of 21.5eV 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 18K (blue) and 80K (red). c, Linear dichroism (IrightIleft), 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 Dsamples. d, Upper part of the MnBi2Te4(0001) gapped Dirac cone as calculated abinitio. 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 d,e 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. SeeMethods for more information on the dichroic ARPES measurements.

a, ARPES EDC profiles taken at the \(\bar{\Gamma }\)-point of MnBi2Te4(0001) at 10.5K and 35K. 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 35K and 10.5K, respectively. The peaks of the bulk bands at 35K (10.5K) 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 6.4eV and T=10.5K (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 10K and 35K with a temperature step T0.9K and two sweep directions (10K 35K 10K). Because the measurements upon heating and cooling reveal essentiallythe 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 andthe intensity dependencieson temperature in bd were acquired from two differentB samples, showing slightly different binding energy of the Dirac point gap centres (0.28eV and 0.25eV, respectively). d, Intensity integrated within the energy window E marked by the dashed black lines in c. The average intensity in the plateau-like region above approximately 24K was set to 1. E 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 TN24K 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.

a, Spin-integrated ARPES spectrum taken at 6eV 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. c,d, 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=+0.11 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=300K.

Otrokov, M.M., Klimovskikh, I.I., Bentmann, H. et al. Prediction and observation of an antiferromagnetic topological insulator. Nature 576, 416422 (2019). https://doi.org/10.1038/s41586-019-1840-9

buckyballs tricks : how to make a pyramid with buckyballs

buckyballs tricks : how to make a pyramid with buckyballs

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