Abstract
Magnetically doped topological insulators enable the quantum anomalous Hall effect (QAHE), which provides quantized edge states for lossless charge-transport applications1,2,3,4,5,6,7,8. The edge states are hosted by a magnetic energy gap at the Dirac point2, but hitherto all attempts to observe this gap directly have been unsuccessful. Observing the gap is considered to be essential to overcoming the limitations of the QAHE, which so far occurs only at temperatures that are one to two orders of magnitude below the ferromagnetic Curie temperature, TC (ref. 8). Here we use low-temperature photoelectron spectroscopy to unambiguously reveal the magnetic gap of Mn-doped Bi2Te3, which displays ferromagnetic out-of-plane spin texture and opens up only below TC. Surprisingly, our analysis reveals large gap sizes at 1 kelvin of up to 90 millielectronvolts, which is five times larger than theoretically predicted9. Using multiscale analysis we show that this enhancement is due to a remarkable structure modification induced by Mn doping: instead of a disordered impurity system, a self-organized alternating sequence of MnBi2Te4 septuple and Bi2Te3 quintuple layers is formed. This enhances the wavefunction overlap and size of the magnetic gap10. Mn-doped Bi2Se3 (ref. 11) and Mn-doped Sb2Te3 form similar heterostructures, but for Bi2Se3 only a nonmagnetic gap is formed and the magnetization is in the surface plane. This is explained by the smaller spin–orbit interaction by comparison with Mn-doped Bi2Te3. Our findings provide insights that will be crucial in pushing lossless transport in topological insulators towards room-temperature applications.
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Data availability
The data sets generated and analysed here are available from the corresponding authors on reasonable request.
Code availability
The code for the paracrystal model is available from the corresponding authors upon request. The electronic structure codes Wien2K and SPR-KKR and X-ray absorption fine structure codes FDMNES and FEFF9 can be downloaded after the corresponding licence requirements given on the respective webpages are fulfilled.
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Acknowledgements
ARPES experiments were performed at BESSY II of Helmholtz-Zentrum Berlin and the EXAFS and XANES experiments at the European Synchrotron Radiation Facility. We thank B. Henne, F. Wilhelm and A. Rogalev for support with XANES and EXAFS measurements; W. Grafeneder and G. Hesser for TEM sample preparation; V. Holý for advice on the paracrystal model; and G. Bihlmayer and A. Ernst for helpful discussions. This project was supported by the Austrian Science Fund (FWF, project P30969-N27 and P28185-N27); the Austrian Federal Ministry for Digital and Economic Affairs, the National Foundation for Research, Technology and Development in the frame of the Christian Doppler Laboratory for Nanoscale Phase Transformations; the Deutsche Forschungsgemeinschaft (grants SPP 1666, SFB 1143 project C4, SFB 1277 project A2); the Central European Institute of Technology (CEITEC) Nano research infrastructure (ID LM2015041, MEYS CR, 2016-2019) and Computational and Experimental Design of Advanced Materials with New Functionalities (CEDAMNF; grant CZ.02.1.01/0.0/0.0/15_003/0000358) of the Czech Ministerstvo Školství Mládeže a Telovýchovy (MSMT); the Impuls- und Vernetzungsfonds der Helmholtz-Gemeinschaft (Virtual Institute New States of Matter and their Excitations and Helmholtz-Russia Joint Research Group no. HRSF-0067); and the European Union Horizon 2020 programme (grant 823717–ESTEEM3).
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Samples were grown by S.W., H.S., V.V.V. and G.S. X-ray analysis was carried out by S.W., H.S., G.S., J.R. and O.C. O.C. performed paracrystal modelling and magnetotransport measurements. XANES and EXAFS measurements were made by A.N., O.C., H.S. and G.S., and the simulations by O.C., A.N., J.R. and J. Minár. SQUID was carried out by A.N., and HR-STEM by M.A., H.G., S.W., G.K., O.C. and J. Michalička. DFT calculations were done by S.A.K., J. Minár and H.E. ARPES was carried out by E.D.L.R. and P.S.M., and spin-resolved ARPES by J.S.-B., F.F. and A.V. The work was coordinated by G.S., G.B. and O.R. The manuscript was written by O.R. and G.S. with input from all authors.
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Extended data figures and tables
Extended Data Fig. 1 ARPES measurements.
a, Data for an additional Mn-doped Bi2Te3 film with Mn concentration of 10%. The normal emission spectra shown on the left, recorded at 1 K and 30 K, show a substantial redistribution of spectral weight around the binding energy of approximately 180 meV when crossing the ferromagnetic transition at TC = 12 K. The shifts in the regions marked S1 and S2, shown on the right on a magnified scale, are of similar magnitude to that seen for the 6% Mn-doped case in Fig. 1. The shifts marked by arrows are compatible with a 100 meV gap opening at the Dirac point. ARPES was measured with p-polarized light and hν = 50 eV. b, c, ARPES measurements, showing that the gap in 6%-Mn-doped Bi2Se3 is independent of temperature. b, ARPES E(k) map recorded at 1 K, with the angle-dependent binding energies of the upper Dirac cone and bulk valence band indicated with blue and orange lines, obtained from Lorentzian fits to energy-distribution curves. c, Temperature dependence of the binding energies of the upper Dirac cone minimum (blue circles), the bulk valence band at \(\bar{\Gamma }\) (orange squares) and their difference (black diamonds). The ferromagnetic Curie temperature is 6 K as obtained by SQUID. This analysis represents an alternative to that in Fig. 1g, which was based on fits of the upper and lower Dirac cones. In both cases, the data do not provide any indication of a relative or absolute shift of the band edges, or of a gap of the order seen in Mn-doped Bi2Te3 when crossing the ferromagnetic transition temperature.
Extended Data Fig. 2 Spin-resolved ARPES of Mn-doped Bi2Te3.
a, Geometry of the spin-resolved ARPES experiments, including the magnetization directions indicated by M+ and M−. Hor. Pol., horizontal light polarization. b, Plot of the fit results from spin-up and spin-down spectra of the topological surface state (TSS) at the Dirac point (ED), and determination of the magnetic exchange splitting, Δ = 56 ± 4 meV, at 6.5 K. c, d, Fit to the spin-resolved spectra at 6.5 K, including a transition from the bulk conduction band (BCB). e, Demonstration that the spin polarization reverses when the magnetization, M, is reversed. This reversal was achieved by field cooling in an applied field of 10 mT. f, Temperature-dependent magnetization, M(T), measured by SQUID on a reference sample that was identical to that used to determine the magnetic field necessary for field cooling and magnetization reversal. g, h, Before the spin-resolved ARPES measurement, the reversible temperature-dependent broadening in ARPES was verified by cooling from 14 K to 6.5 K and warming up again to 14 K. At a photon energy of 30 eV, most of the intensity near the Fermi energy stems from the bulk conduction band. i, Reversible broadening of the energy-dispersion curves upon cooling from above to below TC and warming up again. j, TSS gap at the Dirac point Δ derived by ARPES and spin-resolved ARPES (red squares), plotted against temperature, together with the temperature-dependent out-of-plane magnetization (blue crosses), showing that the magnetic exchange splitting at the Dirac point Δ faithfully follows the magnetization perpendicular to the sample surface. Data at 1 K and 20 K are from Fig. 1c, d. Data from spin-resolved photoemission (at 6.5 K and 300 K) have the smallest error. Data for 14 K were derived from i, taking the spin-resolved data from 6.5 K as a reference point.
Extended Data Fig. 3 Magnetic properties of Mn-doped Bi2Se3 and Bi2Te3.
a, d, Temperature-dependent magnetization, M(T), used to determine the ferromagnetic Curie temperature, TC, Mn-doped Bi2Se3 (a) and Bi2Te3 (d). The magnetization was measured after field cooling (FC) at 10 mT. As indicated, below TC the magnetization of the samples rises steeply by more than two orders of magnitude. b, e, In-plane (ip) versus out-of-plane (oop) hysteresis loops at 300 K and 2 K, showing the absence of ferromagnetism at room temperature. c, f, Magnetization versus applied field, M(H), for samples with different Mn concentrations, xMn, as indicated. For all Mn-doped Bi2Se3 films, the easy axis of magnetization is found to be in plane, whereas for all Mn-doped Bi2Te3 films it is perpendicular to the surface. The insets show the Curie temperature, TC, plotted against Mn concentration. For all measurements, the diamagnetic contribution of the substrate measured at 300 K was subtracted. g, Magnetocrystalline anisotropy energy, EMCA, obtained through DFT for Bi2Se3/MnBi2Se4 and Bi2Te3/MnBi2Te4 by subtracting band energies for two orientations of the magnetization. Shown are magnetocrystalline anisotropy EMCA = E(M∥x) − E(M∥z), shape anisotropy Eshape and total magnetic anisotropy Eaniso = EMCA + Eshape.
Extended Data Fig. 4 STEM of pure and Mn-doped Bi2Se3 and EDX maps of Mn-doped Bi2Te3.
a, b, Comparison of HR-STEM HAADF cross-sections of Bi2Se3 (a) and Mn-doped Bi2Se3 (xMn = 6%) (b) films grown under identical growth conditions, showing the high structural perfection and that additional septuple layers are formed only with Mn doping, whereas the pure Bi2Se3 film consists only of quintuple layers. These STEM cross-sections were recorded along two different zone axes. c, Atomic-layer-resolved distribution of the Bi, Te and Mn atoms of a Mn-doped Bi2Te3 film (xMn = 10%) obtained by STEM-EDX mapping. The Mn atoms are predominantly incorporated in the centre of the septuple layers and to a lesser extent in the outer layers of the septuple units. No Mn is seen in the van der Waals gaps. Note that in this sample, because of the higher Mn concentration, two subsequent septuples are observed in the STEM cross-section.
Extended Data Fig. 5 Anomalous Hall effect.
Data for Mn-doped Bi2Te3 and Bi2Se3 with respectively 6% and 8% Mn. a, b, Raw data for Hall resistance as a function of magnetic field applied perpendicularly to the surface, measured at different temperatures above and below TC as indicated. c, d, Temperature dependence of the carrier concentration and Hall mobility. Note that above TC the contribution of the anomalous Hall effect to the Hall voltage is negligible and therefore does not affect the carrier concentration and mobility measurements.
Extended Data Fig. 6 Possible Mn-incorporation sites in Bi2Te3 and Bi2Se3.
a, Structure models for, left to right: Mn in the centre of septuple layers; Mn substituting for Bi in quintuple layers; and interstitial Mn in the van der Waals gaps on octrahedal sites and tetrahedral sites. b, Nominal nearest-neighbour (NN) distances of Mn atoms located in various positions as derived by EXAFS analysis, including also possible Mn on Te (Se) antisites in the quintuples. Index ‘1’ refers to Te (Se) sites next to the van der Waals gaps, index ‘2’ to those in the centre of the quintuple.
Extended Data Fig. 7 Fits of EXAFS oscillations for different amounts of Mn doping.
a, b, Bi2Te3; c, d, Bi2Se3. Experimental data points are represented by the red or blue circles; black lines denote fitted curves (unlike the simulations in Fig. 3). a, c are plotted with respect to the wavevector k and the background-subtracted EXAFS absorption χ(k) is k-weighted; b, d show the magnitude, that is, the absolute value of χ(R) after Fourier transformation. e, EXAFS-fitted nearest-neighbour distances of Mn atoms in Bi2Te3 and Bi2Se3 as a function of Mn concentration.
Extended Data Fig. 8 Simulated diffraction patterns.
a–d, Varying paracrystal parameters of the septuple/quintuple heterostructures of: a, c, Mn-doped Bi2Te3 and b, d, Mn-doped Bi2Se3. a, b depict the influence of different average numbers of quintuples, \(\langle {N}_{{\rm{QL}}}\rangle \), between the septuples with a fixed relative r.m.s. deviation (r.m.s.d.) of its distribution, set to 0.5. At high \(\langle {N}_{{\rm{QL}}}\rangle \), the system approaches the pure Bi2Y3 (Y = Te, Se) phase. c, d show simulations for different r.m.s.d. of the statistical distribution of the number of quintuples between the septuples but constant average separation, \(\langle {N}_{{\rm{QL}}}\rangle \) = 5. The limit of r.m.s.d. = 0 corresponds to a perfectly periodic multilayer of five quintuples alternating with one septuple; the additional maxima are the resulting superlattice satellite peaks. A larger r.m.s.d. means a more disordered multilayer. Dashed lines are plotted at positions of the (000.\({\rm{\ell }}\)) peaks of the pure Bi2Y3 structure. e shows the average vertical (0001) lattice plane spacing ⟨d⟩ as a function of Mn concentration determined by the fit of the experimental diffraction spectra presented in Fig. 4a,b, and panel f the corresponding in-plane lattice constants determined from reciprocal space maps around the (101.20) reciprocal lattice point.
Extended Data Fig. 9 RHEED.
a–f, Comparison of RHEED patterns for: a Mn-doped Bi2Te3; b, Mn-doped Bi2Se3; c, Mn-doped Sb2Te3; d, Pb-doped Bi2Te3; e, Sn-doped Bi2Te3; and f, Ge-doped Bi2Te3, recorded during epitaxial growth, showing perfect two-dimensional growth in all cases. The layer thickness was 200 nm and the dopant concentration was around 10% in all cases. The corresponding X-ray diffraction curves of the samples are shown in Fig. 4, and the values derived from the fits using the septuple/quintuple paracrystal stacking model are listed in g. \(\langle {N}_{{\rm{QL}}}\rangle \) is the average number of quintuples between consecutive XBi2Te4 septuple layers; σQL is the relative r.m.s.d. of the distribution; and %SL is the occupancy of Mn sites in the septuple layers.
Extended Data Fig. 10 Electronic and magnetic properties of Mn-doped Sb2Te3.
a, Angle-resolved photoemission spectrum recorded at a temperature of 38 K and a photon energy of 23 eV photon energy, showing p-type behaviour and that the Fermi level, EF, is close to the Dirac point, the latter being only slightly above the top of the valence band. b, In-plane and out-of-plane hysteresis curves, M(H), recorded through SQUID at 2 K (blue) and 300 K (red), showing the same perpendicular magnetic anisotropy with easy axis normal to the surface as for Mn-doped Bi2Te3 (Fig. 2 and Extended Data Fig. 3).
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Rienks, E.D.L., Wimmer, S., Sánchez-Barriga, J. et al. Large magnetic gap at the Dirac point in Bi2Te3/MnBi2Te4 heterostructures. Nature 576, 423–428 (2019). https://doi.org/10.1038/s41586-019-1826-7
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DOI: https://doi.org/10.1038/s41586-019-1826-7
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