Large magnetic gap at the Dirac point in a Mn-induced Bi 2 Te 3 heterostructure
E. D. L. Rienks, S. Wimmer, P. S. Mandal, O. Caha, J. Růžička, A. Ney, H. Steiner, V. V. Volobuev, H. Groiss, M. Albu, S. A. Khan, J. Minár, H. Ebert, G. Bauer, A. Varykhalov, J. Sánchez-Barriga, O. Rader, G. Springholz
LLarge magnetic gap at the Dirac point in a Mn-induced Bi Te heterostructure E. D. L. Rienks , , , ∗ , S. Wimmer , ∗ , P. S. Mandal , , O. Caha , J. R˚uˇziˇcka , A. Ney , H.Steiner , V. V. Volobuev , , , H. Groiss , M. Albu , S. A. Khan , J. Min´ar , H.Ebert , G. Bauer , A. Varykhalov , J. S´anchez-Barriga , O. Rader , G. Springholz Helmholtz-Zentrum Berlin f¨ur Materialien und Energie,Elektronenspeicherring BESSY II, Albert-Einstein-Straße 15, 12489 Berlin, Germany Institut f¨ur Festk¨orperphysik, Technische Universit¨at Dresden, 01062 Dresden, Germany Leibniz-Institut f¨ur Festk¨orper- und Werkstoffforschung Dresden,Helmholtzstraße 20, 01069 Dresden, Germany Institut f¨ur Halbleiter- und Fest¨orperphysik,Johannes Kepler Universit¨at, Altenberger Straße 69, 4040 Linz, Austria Institut f¨ur Physik und Astronomie, Universit¨at Potsdam,Karl-Liebknecht-Straße 24/25, 14476 Potsdam, Germany Department of Condensed Matter Physics, Masaryk University,Kotl´aˇrsk´a 267/2, 61137 Brno, Czech Republic National Technical University ”Kharkiv Polytechnic Institute”,Frunze Street 21, 61002 Kharkiv, Ukraine Institute of Physics, Polish Academy of Sciences,Al. Lotnikow 32/46, 02-668 Warsaw, Poland Zentrum f¨ur Oberfl¨achen- und Nanoanalytik,Johannes Kepler Universit¨at, Linz, 4040 Linz, Austria Graz Center for Electron Microscopy,Steyrergasse 17, 8010 Graz, Austria New Technologies Research Centre,University of West Bohemia, Univerzitni 8,306 14 Pilsen, Czech Republic and Department Chemie, Ludwig-Maximilians-Universit¨at M¨unchen,Butenandtstr. 5-13, 81377 M¨unchen, Germany a r X i v : . [ c ond - m a t . m t r l - s c i ] O c t Dated: October 14, 2018)
Abstract
Magnetically doped topological insulators enable the quantum anomalous Hall effect(QAHE) which provides quantized edge states for lossless charge transport applica-tions [1–9]. The edge states are hosted by a magnetic energy gap at the Dirac point[2] but all attempts to observe it directly have been unsuccessful. The size of thisgap is considered the clue to overcoming the present limitations of the QAHE, whichso far occurs only at temperatures one to two orders of magnitude below its prin-ciple limit set by the ferromagnetic Curie temperature T C [8, 9]. Here, we use lowtemperature photoelectron spectroscopy to unambiguously reveal the magnetic gapof Mn-doped Bi Te films which is present only below T C . Surprisingly, the gap turnsout to be ∼ meV wide, which not only exceeds k B T at room temperature but isalso 5 times larger than predicted by density functional theory [10]. By an exhaus-tive multiscale structure characterization we show that this enhancement is due to aremarkable structure modification induced by Mn doping. Instead of a disordered im-purity system, it forms an alternating sequence of septuple and quintuple layer blocks,where Mn is predominantly incorporated in the center of the septuple layers. Thisself-organized heterostructure substantially enhances the wave-function overlap andthe size of the magnetic gap at the Dirac point, as recently predicted [11]. Mn-dopedBi Se forms a similar heterostructure, however, only a large, albeit nonmagnetic gapis formed. We explain both differences based on the higher spin-orbit interaction inBi Te with the most important consequence of a magnetic anisotropy perpendicularto the films, whereas for Bi Se the spin-orbit interaction it is too weak to over-come the dipole-dipole interaction. Our findings provide crucial insights for pushingthe lossless transport properties of topological insulators towards room-temperatureapplications. ρ xy = h/ ( N e ) where N is an integer number N of gapless 1D edge states and whichdoes not require the presence of an external magnetic field [1, 2]. Magnetically doped 3Dtopological insulators of the tetradymite family [2] have led to the first demonstration of theQAHE in Cr-doped (Bi, Sb) Te [3–7]. Later on, the replacement of Cr by V as magneticdopant delivered the first precise quantized values for ρ xy as well as a vanishing ρ xx at zeromagnetic field [8, 9], which is the key signature for lossless charge transport through edgechannel devices [12]. A crucial issue which would help to understand and develop the QAHEfurther towards applications has, however, remained fundamentally open – the observationand quantification of the magnetic gap at the Dirac point [2].In a magnetic topological insulator the QAHE occurs due to a modification of the bandinversion, in which at the onset of ferromagnetic order the inversion of one of the spinsubbands is released by the exchange splitting and spin orbit coupling [2]. The observationof this exchange splitting has, however, remained elusive. It manifests itself as a magnetic gapat the Dirac point that opens when the system is cooled below the ferromagnetic transitiontemperature. The size of the gap is the crucial parameter for the temperature at which theQAHE can be observed. So far, this temperature is very low, typically around 50 mK [9]to 2 K [13, 14], which is one to two orders of magnitude lower than the ferromagnetic T C ofthese systems. First principles calculations have recently suggested that the magnetic gapcan be enhanced in topological insulator heterostructures [11].Angle resolved photoemission spectroscopy (ARPES) is the method of choice for the directobservation of the magnetic gap and the verification of these predictions. Nevertheless, theexperimental situation appears confusing: Large gaps at the Dirac point of the order of0.1–0.2 eV of Bi Se doped with Mn [15, 16] were explicitly shown to be not of magneticorigin [16]. On the contrary, no gaps are observed for Bi Se when magnetic impuritiesare deposited directly on its surface [16–19]. Also, no gap appears when Mn is doped inthe bulk of Bi Te where the Dirac cone was found to remain intact at temperatures downto 12 K [20]. For V-doped Sb Te a mobility gap of 32 meV was inferred from scanningtunneling Landau level spectroscopy at 1.3 K in comparison to pure Sb Te [21], but dueto the strong overlap with magnetic impurity states, no gap could be observed in the localdensity of states and no correlation to magnetism was reported. For Cr-doped (Bi, Sb) Te an average gap of 56 meV was found by tunneling spectroscopy [22], but again its origin3emained elusive because no temperature dependence was found. In fact, a gap as large as ∼
75 meV was found for Bi Se with 4% Cr by ARPES even at room temperature [23]. Thisclearly suggests a non-magnetic origin of these effects because the ferromagnetic T C is wellbelow 50 K in all of these systems.Interestingly, also the nature of the magnetic doping has remained under debate. Forisovalent doping, it was predicted that Bi Se , Bi Te and Sb Te will form a QAHE state.Thus, this should occur for doping with Cr or Fe but not for Ti or V [2]. The fact that so far,V-doped (Sb,Bi) Te displays the highest QAHE temperatures shows that the situation ismore complex. In particular, non-isovalent magnetic dopants turn out to surprisingly littleaffect the Fermi level and carrier concentration. For example, Mn-doped Bi Se and Bi Te always remain n -type [16, 20] despite the fact that divalent Mn replacing trivalent Bi shouldact as a strong acceptor. These puzzling issues are related to the comparatively complextetradymite lattice structure consisting of quintuple layers separated by van der Waals gapsand the distribution of the dopants over a large number of electrically and magneticallyinequivalent incorporation sites offered by the huge tetradymite unit cell consisting of thirtyindividual atoms. Hence, the actual magnetic dopant distribution is a key for understandingtheir impact on magnetism and band topology of the system.To resolve these issues, we present here a comprehensive study of Mn-doped Bi Te andBi Se films grown under nearly identical conditions. Our data unequivocally reveals a pro-nounced magnetic exchange splitting at the Dirac point in Bi Te , by far exceeding previoustheoretical calculations [10]. It vanishes above the ferromagnetic Curie temperature, beingclear cut evidence for its magnetic origin. On the other hand, no such gap could be identifiedfor Mn-doped Bi Se even at 1 K. By multiscale characterization, we find that the actuallattice structure is very different from the anticipated random impurity system: Mn dopinginduces the formation of self-organized heterostructures consisting of stacked quintuple andseptuple layers. This turns out to be very efficient for obtaining large magnetic gaps. Asfurther crucial factors that distinguish the telluride and selenide systems, we identify thespin-orbit interaction and the way the heterostructures evolve with the Mn concentration. Temperature-dependent band gap and magnetism
Figure 1 shows for Mn-doped Bi Te and Bi Se ARPES dispersions of the Dirac cone mea-sured above and below the ferromagnetic phase transition ( T C = 10 and 6 K, respectively)4or the same 6% Mn concentration. For Mn-doped Bi Te , the photoemission spectrum fromthe center of the surface Brillouin zone shows an intensity maximum due to bulk transitions(50 eV photon energy), while the Dirac point ( E D ) of the surface state contributes a smallerpeak at ∼ T C downto 1 K, the low-binding energy flank of the peak develops a pronounced shoulder, forminga plateau around 0.2 eV, as can be seen in Fig. 1(a–c). We have quantified this change bylinear fits to small sections of the spectrum, indicated in Fig. 1(c), with the condition thatthe slopes at 20 and 1 K are the same. The obtained shifts (S1 ∼
21 meV > S2 ∼
12 meV)are compatible with the scenario in which a single component for the topological surfacestate at 20 K is split into two equally intense components at 1 K. A simulation of this sce-nario (Fig. 1(d)) shows that, for a reasonable parameter range, the gap that opens at theDirac point is 2.5–3 times larger than the sum of shifts (S1 + S2). We therefore arrive at anestimate of the gap ∆ of 90 ±
10 meV at low temperature. Because the ferromagnetic T C amounts to ∼
10 K in this sample, this is the clear and unambiguous proof of the magneticorigin of this gap. This is the central result of the present work.What is probed by the gap at the Dirac point is the exchange splitting of p-electrons ofthe Bi Te host material which ferromagnetically couple the localized magnetic moments ofthe Mn ions [10]. The magnitude of the gap at the Dirac point depends on the exchangecoupling J and the magnetization along the [0001] surface normal [24]. This behavior isprincipally similar to that of the magnetic gap of Mn-doped multiferroic GeTe [25] (althoughthat system is of Rashba type and topologically trivial). Returning to Fig. 1, we see thatthis criterion is not fulfilled for Mn-doped Bi Se with 6% Mn, where we find a large gapat the Dirac point of ∼
200 meV at all temperatures from 1 to 300 K [16]. The gap sizedoes not increase when we cool down to 1 K, i.e., well below T C ∼ Se , contraryto the case of Bi Te , and serves as an additional cross-check for the magnetic gap opening.Figure 2 shows magnetization measurements for Mn-doped Bi Te and Bi Se sampleswith comparable Mn concentrations. The Bi Te sample shows an easy axis magnetization M along the c axis normal to the surface, i.e., M ⊥ > M (cid:107) . This perpendicular anisotropy isrobust since it does not depend on the Mn concentration (see Supplementary Information)and is observed also for bulk single crystals [26, 27]. In contrast, for Mn-doped Bi Se theeasy axis is parallel to the surface plane – also stable in a large concentration range (see5upplementary Information). This opposite behavior is also revealed by magnetotransportmeasurements shown in Fig. 2(c,d), where with magnetic fields applied perpendicular tothe films only Mn-doped Bi Te displays a pronounced anomalous Hall effect (AHE) uponcooling below T C whereas it is negligible in Bi Se (Fig. 2(d)).While an in-plane magnetization merely shifts the Dirac cone in momentum space par-allel to the surface [10, 28], the perpendicular anisotropy in Mn-doped Bi Te is preciselythe precondition for the magnetic band gap opening and for the QAHE. Density functionaltheory (DFT) has predicted the resulting magnetic Dirac gap as 16 meV for 10% Mn sub-stitutionally incorporated in the topmost quintuple layer of Bi Te [10], but this gap has sofar not been experimentally demonstrated. More astonishingly, the magnetic gap of 90 ± × as large as the theoretical prediction.To resolve this discrepancy, we return to Fig. 2, where besides the obvious differencein magnetic anisotropy, there are a several other interesting differences between the twosystems: Firstly, the coercive field of Mn-doped Bi Te is significantly larger than for Bi Se ,which only shows a very narrow opening of the hysteresis loop. Secondly, at the same timethe anisotropy field, at which in-plane and out-of-plane magnetizations are equal is twotimes higher for Bi Te (see Supplementary Information). Finally, the ferromagnetic T C ofMn-doped Bi Te is considerably larger (7–15 K) than for Bi Se (5–7 K) (see inserts in Fig.2(a,b)) and depends more strongly on the Mn concentration. Altogether this demonstratesthat Mn-doped Bi Te is the more robust and anisotropic ferromagnet. Multiscale structure analysis
To clarify how Mn is actually incorporated in Bi Te and Bi Se a systematic multiscalestructure analysis was performed for both types of samples. Figure 3(a) shows Mn-dopedBi Te in high-resolution scanning transmission electron microscopy (HRSTEM), measuredalong the [1100] direction for 10% Mn. Strikingly, we observe upon Mn doping instead ofthe expected periodic sequence of Te-Bi-Te-Bi-Te quintuple layers the emergence of a novelstructure consisting of septuple and quintuple layers that does not exist for stoichiometricBi Te . The septuple layers consist of the sequence Te-Bi-Te-Mn-Te-Bi-Te, where the Mnatoms occupy the central septuple atomic layer as found in Bi MnTe crystals [29]. Thisself-organized heterostructure formation obviously disagrees with the common notion ofsubstitutional Mn incorporation in Bi Te assumed in most previous studies [10, 26, 30].6n is not isoeletronic to Bi due to the different number of valence electrons. Therefore,substitutional Mn on Bi sites should be a strong acceptor inducing a strong p-type doping ofthe system. This is neither observed for Mn-doped Bi Te nor Bi Se which always remainn-type even at high Mn concentrations [16, 20, 27, 31]. On the other hand, Mn incorporatedin Bi MnTe septuple layers is not electrically active because the septuple is formed byaddition of a charge compensated MnTe double layer to a quintuple layer. Apart fromcompensation effects, this explains the surprisingly small effect of Mn-doping on carrierconcentration and Fermi level of the system. According to Fig. 3(b), the formation ofMn-induced septuple/quintuple heterostructures also occurs in Bi Se and the formation ofseptuple layers was also recently seen for Mn-doped Bi Se films [32].To obtain element specific information on the Mn incorporation sites, x-ray absorptionnear-edge spectroscopy (XANES) and extended x-ray absorption fine structure spectroscopy(EXAFS) were performed at the Mn K -edge as summarized in Fig. 4. The absorption spectrawere analyzed by simulations for all possible Mn incorporation sites, ranging from Mn inthe center of the Bi MnTe (Bi MnSe ) septuple layers, substitutional Mn on Bi sites in thequintuple layers, interstitial Mn in the van der Waals gap in either octahedral or tetrahedralcoordination (see Fig. 4(e–g)). In addition, we considered also Mn on anion Te (Se) antisitesi.e., on Te1 (and Se1) sites at the outer layers and on Te2 (and Se2) sites in the center ofthe quintuple layers. Contrary to most theoretical investigations based on substitutionalMn incorporation [10], our analysis shows that Mn in Bi Te prefers to be incorporated inseptuple layers and only a minority as substitutional Mn in the quintuple layers. Whilethe EXAFS data does not rule out Mn on octrahedral sites in the van der Waals gap, thefact that septuples are never seen in undoped Bi Te clearly suggests that the Mn sites areclosely linked to the septuple layers.Turning to Mn-doped Bi Se shown in Figs. 4(b,d), we do not observe as intense EX-AFS oscillations as for Bi Te . This indicates stronger cancellation effects caused by Mndistributed over different lattice sites, including a larger amount of substitutional Mn and alesser fraction within the septuple layers. This is highlighted by the XANES spectra at theMn K -edge which exhibit a characteristic double peak structure at higher and lower photonenergy, attributed respectively to Mn in the center of the septuple and to substitutional Mnin the quintuple layers, where again for Bi Se the signal from Mn in the septuple layers isweaker as compared to Mn in Bi Te . For tetrahedrally coordinated interstitial Mn, as well7s for Mn on Te (Se) antisites, the simulations do not agree with the experiments, indicatingthat these are not favorable for Mn incorporation. Overall, we conclude that for Bi Te thevast majority of Mn is incorporated within the septuple layers and that substitutional Mnis more readily formed in Bi Se , especially at lower Mn concentrations, with an overallbroader distribution of Mn over various other lattice sites.Our results so far suggest a unique heterostructure formation upon Mn-doping but theHRSTEM, XANES, and EXAFS data deliver only a local picture. To systematically char-acterize its evolution on a larger length scale and its dependence on the Mn concentration,x-ray diffraction investigations were performed as summarized in Fig. 5. For both systemswe indeed find a pronounced change of the diffraction spectra with increasing Mn content.This is evidenced by the appearance of additional diffraction peaks (see Fig. 5(a,b)) thatsignify the emergence of septuple layers in the structure. However, the substantial broad-ening of the peaks reveal that the septuple layers are not incorporated periodically at fixeddistances, but rather stochastically after a varying number N QL of quintuple layers as seen inthe STEM cross-sections where N QL varies between one to seven. This requires us to developa one-dimensional paracrystal model to describe and evaluate the experimental diffractiondata, as detailed in the Supplementary Information. In this model, the overall structure isdescribed as a statistically varying sequence of quintuple segments alternating with singleseptuple layers that is characterized by the average number (cid:104) N QL (cid:105) between subsequent sep-tuples and by the randomness of the statistical distribution of the N QL , i.e., their root meansquare (RMS) deviation from the average value.The model fits displayed by the black lines in Figs. 5(a,b) show a remarkably good agree-ment with the diffraction spectra for all Mn concentrations. This impressively corroboratesthe formation of self-organized quintuple/septuple layer heterostructures in both the Bi Te and Bi Se systems. From the fits, the average (cid:104) N QL (cid:105) between the septuple layers (and, thus,the density of septuple layers) as a function of Mn content is obtained, which is displayed inFig. 5(c) together with the statistical variation of N QL . Apparently, in Bi Te the formationof septuple layers starts at lower Mn concentration and the average separation between theseptuple layers is substantially smaller than in Bi Se . This evidences the higher probabilityof septuple layer formation for Bi Te , in agreement with the XANES and EXAFS result.This difference is further highlighted by Fig. 5(d), where the derived number of available Mnsites in the septuples is plotted versus the actual Mn concentration, revealing that in Bi Te Se the density ofseptuple layers at low Mn concentrations is too small to accommodate all Mn atoms, i.e., asignificant Mn fraction must be incorporated on other sites as well. Discussion
The electronic structure of transition metal impurities at the surface and in the bulk of Bi Te and Bi Se has been studied extensively by density functional theory (DFT) calculations.A magnetic band gap of ∼
10 meV has been predicted for Co-doped Bi Se [30] and of 16meV for Mn-doped Bi Te [10]. By the splitting of the Dirac point we probe the exchangeinteraction at the Te sites. This has been confirmed by DFT, where the spectral densityof the split Dirac point is nine times more strongly localized at the Te atoms than at theother sites [10]. The calculated gap value of 16 meV for substitutionally Mn-doped Bi Te by Henk et al. [10] for a Mn concentration of 10% is, however, substantially smaller thatthe magnetic gap of 90 meV revealed by our experiments. For Mn in Bi Se , a nonmagneticband gap of the measured size ( ∼
200 meV) does not appear in any DFT calculation. Atleast, DFT reveals in principle that, depending on orbital symmetry, small gaps in the Diraccone may open due to hybridization with transition metal impurity states. Accordingly, ahybridization gap of ∼ Se for an in-plane ( sic! ) magnetization [33], which is obviously much less than what weexperimentally observe. The only prediction of a such a nonmagnetic gap which also hasthe magnitude seen in our experiments is from calculations assuming an on-site Coulombinteraction U at the impurity site [34].The structural information gained in the present study helps to clarify the question ofthe origin of this nonmagnetic gap: Apparently, Mn forms more substitutional sites inBi Se than in Bi Te where Mn is preferentially incorporated into septuple layers. Mn inthe substitutional site will lead to a larger Coulomb U than in the central Mn monolayerof the septuple layer, where Mn 3 d levels can delocalize in the plane. We could recentlydemonstrate experimentally that U , termed previously as impurity strength [34], indeedinfluences the size of the nonmagnetic gap strongly. For example, indium impurities areknown to enhance the spacing across which surface-surface coupling opens a gap at theDirac point [35]. When we compare Mn doping with In doping in Bi Se , we find that toreach the same gap size as for 8% Mn, only 2% In is required [16, 36]. However, the effect of9mpurities on the nonmagnetic gap decreases with higher spin-orbit interaction of the hostmaterial as shown by our recent work [36]. Thus, Bi Te is principally less susceptible toopening of a nonmagnetic gap than Bi Se , regardless of the structural differences inducedby Mn doping.To explain the marked difference in the magnetic anisotropy of Mn-doped Bi Te andBi Se including the structural motif of the septuple layers, we compute the magneticanisotropy using ab initio calculations (see Supplementary Information) for unit cells con-sisting of one Bi MnX septuple layer and one Bi X quintuple layer (X=Te, Se). We findthat the magnetocrystalline anisotropy inducing the out-of-plane spin orientation is 3.5 timeslarger in the telluride than in the selenide system. This is due to the higher spin-orbit inter-action in Bi Te and is related to warping effects in the Dirac cone, which turn the spins outof the plane [37]. The magnetocrystalline anisotropy is counteracted by the dipole-dipoleinteraction (shape anisotropy) that tends to align the magnetic moments in the plane. Theshape anisotropy comes out to be very similar for the two heterostructure systems, but es-sentially cancels the magnetocrystalline anisotropy in Bi Se , whereas it is superseded bythe magnetocrystalline anisotropy in Bi Te . Thus, the out-of-plane anisotropy persists andis nearly one order of magnitude larger than for the selenide system, where the anisotropyenergy almost changes sign towards in-plane magnetization. In the real samples, the in-plane magnetization for the selenide structures may be additionally supported by the Mnatoms on substitutional sites which favor the magnetic moments to be in plane [33]. For thetelluride system, the preferred perpendicular magnetization agrees well with recent modelcalculations by Otrokov et al. [11] who considered similar types of Bi MnTe /Bi Te het-erostructures in different septuple and quintuple combinations. We conclude that the higherspin-orbit interaction in the telluride system thus overcomes the dipole-dipole interactionand enables the formation of the magnetic gap at the Dirac point.Finally, as mentioned above, our measured magnetic gap size of 90 meV for Mn-dopedBi Te is five times as large as predicted for substitutional Mn incorporation (16 meV)[10]. This represents a huge enhancement that is obviously related to the naturally formedquintuple/septuple layer heterostructures. As pointed out by Otrokov et al. [11] the Mnmonolayer in the center of Bi MnTe septuples enhances the wave function overlap strongly,supporting magnetic gaps as high as 38 – 87 meV, depending on the chosen Bi MnTe /Bi Te combination. This is in excellent agreement with the enhancement found in our experiments.10his demonstrates the great potential of such structures for stabilizing edge transport inQAHE devices. Theory [11] also suggest that the nontrivial topology is retained, by thecalculation of the Chern number C = − MnTe septuple and two Bi Te quintuple layers, and by the persistence of the Diraccone surface state. This is confirmed by our ARPES measurements above and below T C .In conclusion, we have demonstrated unambiguously and for the first time the opening ofa magnetic gap in a topological insulator below the ferromagnetic phase transition and itsclosure for T > T C . The magnetic gap in Mn-doped Bi Te is remarkably large (90 ±
10 meV)as a result of the formation of a natural heterostructure in which Mn is incorporated withinseptuple layers instead of simple substitutional incorporation. Our results thus supportrecent theoretical predictions that magnetic gaps in topological insulators can be significantlyenhanced in multi-layered systems [11]. These are considered as a basis for the realization ofnew topological phases such as the axion insulator state exhibiting quantized magnetoelectriceffects [14, 38] and the chiral Majorana fermion [39]. No magnetic gap is detected for Mn-doped Bi Se within the experimental resolution but instead, a very large non-magnetic gapthat does not increase even when cooling down to 1 K, well below T C , and thus does nothave a magnetic contribution. We correlate this with the difference in magnetic anisotropydue to the much larger spin-orbit interaction in Bi Te and offer a unifed picture for bothobservations. Returning to the question of enhanced QAHE devices, up to now the focus hasbeen on increasing the Curie temperatures of the systems, e.g., by obtaining a high densityof st ates at the Fermi level to increase the exchange integrals. Instead, the magnetic gapsize may turn out to be the more decisive factor for pushing up the operation temperature.Due to the large magnetic gap size, Mn-doping seems to be most promising in this respectand will open up new perspectives for device realization. Data availability
The data sets generated and analysed during the current study are available from the cor-responding authors on reasonable request.
Code availability
The code for the paracrystal model is available from the corresponding authors upon request.The employed electronic structure codes Wien2K and SPR-KKR and x-ray absorption fine11tructure codes FDMNES and FEFF9 can be downloaded after the corresponding licencerequirements given on the respective webpages are fulfilled.
Acknowledgements
We thank B. Henne, F. Wilhelm, and A. Rogalev for support of the XANES and EX-AFS measurements at ID 12 and BM23 beam lines of the ESRF, V. Hol´y for advices onthe structure model, W. Grafeneder for the TEM sample preparation and G. Bihlmayerand A. Ernst for helpful discussions. S.A.K and J.M. are grateful for support fromCEDAMNF (CZ.02.1.01/0.0/0.0/15 003/0000358) of Czech ministry MSMT. This work waspartially supported by CEITEC Nano RI (MEYS CR, 20162019), by SPP1666 of DeutscheForschungsgemeinschaft, and by Impuls- und Vernetzungsfonds der Helmholtz-Gemeinschaft(Helmholtz-Russia Joint Research Group HRJRG-408 and Helmholtz Virtual Institute “Newstates of matter and their excitations”).Corresponding authors: G. Springholz, email: [email protected], O. Rader, email:[email protected]. ∗ These authors contributed equally to the present work. [1] M. Onoda, N. Nagaosa, Quantized Anomalous Hall Effect in Two-Dimensional Ferromagnets:Quantum Hall Effect in Metals, Phys. Rev. Lett. 90, 206601 (2003).[2] R. Yu et al., Quantized anomalous Hall effect in magnetic topological insulators, Science 329,61 (2010).[3] C.-Z. Chang et al., Experimental observation of the quantum anomalous Hall effect in amagnetic topological insulator, Science 340, 167 (2013).[4] J. G. Checkelsky, R. Yoshimi, A. Tsukazaki, K. S. Takahashi, Y. Kozuka, J. Falson, M.Kawasaki, Y. Tokura, Trajectory of the anomalous Hall effect toward the quantized state ina ferromagnetic topological insulator, Nature Phys. 10, 731 (2014).[5] X. Kou, S.-T. Guo, Y. Fan, L. Pan, M. Lang, Y. Jiang, Q. Shao, T. Nie, K. Murata, J. Tang,Y. Wang, L. He, T.-K. Lee, W.-L. Lee, K. L. Wang, Scale-Invariant Quantum AnomalousHall Effect in Magnetic Topological Insulators beyond the Two-Dimensional Limit, Phys. ev. Lett. 113, 137201 (2014).[6] A. J. Bestwick, E. J. Fox, X. Kou, L. Pan, K. L. Wang, D. Goldhaber-Gordon, PreciseQuantization of the Anomalous Hall Effect near Zero Magnetic Field, Phys. Rev. Lett. 114,187201 (2015).[7] Abhinav Kandala, Anthony Richardella, Susan Kempinger, Chao-Xing Liu, and NitinSamarth, Giant anisotropic magnetoresistance in a quantum anomalous Hall insulator, NatureCommun. 6, 7434 (2015).[8] C.-Z. Chang, W. Zhao, D. Y. Kim, H. Zhang, B. A. Assaf, D. Heiman, S.-C. Zhang, C. Liu,M. H. W. Chan, J. S. Moodera, High-precision realization of robust quantum anomalous Hallstate in a hard ferromagnetic topological insulator, Nat. Mater. 14, 473 (2015).[9] S. Grauer, S. Schreyeck, M. Winnerlein, K. Brunner, C. Gould, L. W. Molenkamp, Coincidenceof superparamagnetism and perfect quantization in the quantum anomalous Hall state, Phys.Rev. B 92, 201304(R) (2015).[10] J. Henk, M. Flieger, I. V. Maznichenko, I. Mertig, A. Ernst, S. V. Eremeev, E. V. Chulkov,Topological Character and Magnetism of the Dirac State in Mn-Doped Bi Te , Phys. Rev.Lett. 109, 076801 (2012).[11] M. M. Otrokov, T. V. Menshchikova, M. G. Vergniory, I. P. Rusinov, A. Yu. Vyazovskaya,Yu. M. Koroteev, G. Bihlmayer, A. Ernst, P. M. Echenique, A. Arnau, E. V. Chulkov, Highly-ordered wide bandgap materials for quantized anomalous Hall and magnetoelectric effects, 2DMater. 4, 025082 (2017).[12] X. Zhang and S.-C. Zhang, Chiral interconnects based on topological insulators, Proc. SPIEInt. Soc. Opt. Eng. 8373, 837309 (2012).[13] M. Mogi, R. Yoshimi, A. Tsukazaki, K. Yasuda, Y. Kozuka, K. S. Takahashi, M. Kawasaki,Y. Tokura, Magnetic modulation doping in topological insulators toward higher-temperaturequantum anomalous Hall effect, Appl. Phys. Lett. 107, 182401 (2015).[14] Di Xiao, Jue Jiang, Jae-Ho Shin, Wenbo Wang, Fei Wang, Yi-Fan Zhao, Chaoxing Liu, WeidaWu, Moses H.W. Chan, Nitin Samarth, and Cui-Zu Chang, Realization of the Axion InsulatorState in Quantum Anomalous Hall Sandwich Heterostructures, Phys. Rev. Lett. 120, 056801(2018).[15] D. Zhang, A. Richardella, D. W. Rench, S.-Y. Xu, A. Kandala, T. C. Flanagan, H. Bei-denkopf, A. L. Yeats, B. B. Buckley, P. V. Klimov, D. D. Awschalom, A. Yazdani, P. Schiffer, . Z. Hasan, N. Samarth, Interplay between ferromagnetism, surface states, and quantumcorrections in a magnetically doped topological insulator, Phys. Rev. B 86, 205127 (2012).[16] J. S´anchez-Barriga, A. Varykhalov, G. Springholz, H. Steiner, R. Kirchschlager, G. Bauer, O.Caha, E. Schierle, E. Weschke, A. A. ¨Unal, S. Valencia, M. Dunst, J. Braun, H. Ebert, J.Min´ar, E. Golias, L. V. Yashina, A. Ney, V. Hol´y, O. Rader, Nonmagnetic band gap at theDirac point of the magnetic topological insulator (Bi − x Mn x ) Se , Nat. Commun. 7, 10559(2016).[17] T. Valla, Z.-H. Pan, D. Gardner, Y. S. Lee, S. Chu, Photoemission Spectroscopy of magneticand nonmagnetic impurities on the surface of the Bi Se topological insulator, Phys. Rev.Lett. 108, 117601 (2012).[18] M. R. Scholz, J. S´anchez-Barriga, D. Marchenko, A. Varykhalov, A. Volykhov, L. V. Yashina,O. Rader, Tolerance of Topological Surface States towards Magnetic Moments: Fe on Bi Se ,Phys. Rev. Lett. 108, 256810 (2012).[19] J. Honolka, A. A. Khajetoorians, V. Sessi, T. O. Wehling, S. Stepanow, J.-L. Mi, B. B.Iversen, T. Schlenk, J. Wiebe, N. B. Brookes, A. I. Lichtenstein, Ph. Hofmann, K. Kern, R.Wiesendanger, In-Plane Magnetic Anisotropy of Fe Atoms on Bi Se (111), Phys. Rev. Lett.108, 256811 (2012).[20] J. Ruˇziˇcka, O. Caha, V. Hol´y, H. Steiner, A. Ney, G. Bauer, T. Duchoˇn, K. Veltruska, I.Khalakhan, V. Matolin, E. F. Schwier, H. Iwasawa, K. Shimada, G. Springholz, Structuraland electronic properties of manganese-doped Bi Te epitaxial layers, New J. Phys. 17, 013028(2015).[21] P. Sessi, R. R. Biswas, T. Bathon, O. Storz, S. Wilfert, A. Barla, K. A. Kokh, O. E.Tereshchenko, K. Fauth, M. Bode, A. V. Balatsky, Dual nature of magnetic dopants andcompeting trends in topological insulators, Nat. Commun. 7, 12027 (2016).[22] I. Lee, C. K. Kim, J. Lee, S. J. L. Billinge, R. Zhong, J. A. Schneeloch, T. Liu, T. Valla, J. M.Tranquada, G. Gu, J. C. S. Davis, Imaging Dirac-mass disorder from magnetic dopant atomsin the ferromagnetic topological insulator Cr x (Bi . Sb . ) − x Te , Proc. Natl. Acad. Sci. U. S.A. 112, 1316 (2015).[23] Cui-Zu Chang, Peizhe Tang, Yi-Lin Wang, Xiao Feng, Kang Li, Zuocheng Zhang, Yayu Wang,Li-Li Wang, Xi Chen, Chaoxing Liu, Wenhui Duan, Ke He, Xu-Cun Ma, and Qi-Kun Xue,Chemical-Potential-Dependent Gap Opening at the Dirac Surface States of Bi Se Induced y Aggregated Substitutional Cr Atoms, Phys. Rev. Lett. 112, 056801 (2014).[24] G. Rosenberg, M. Franz, Surface magnetic ordering in topological insulators with bulk mag-netic dopants, Phys. Rev. B 85, 195119 (2012).[25] J. Krempask´y, S. Muff, F. Bisti, M. Fanciulli, H. Volfov´a, A. P. Weber, N. Pilet, P. Warnicke,H. Ebert, J Braun, F. Bertran, V. V. Volobuev, J. Min´ar, G. Springholz, J.H. Dil, V. N.Strocov, Entanglement and manipulation of the magnetic and spinorbit order in multiferroicRashba semiconductors, Nat. Commun. 7, 13071 (2016).[26] Y. S. Hor, P. Roushan, H. Beidenkopf, J. Seo, D. Qu, J. G. Checkelsky, L. A. Wray, D. Hsieh,Y. Xia, S.-Y. Xu, D. Qian, M. Z. Hasan, N. P. Ong, A. Yazdani, R. J. Cava, Developmentof ferromagnetism in the doped topological insulator Bi − x Fe x Te , Phys. Rev. B 81, 195203(2010).[27] M. D. Watson, L. J. Collins-McIntyre, A. I. Coldea, D. Prabhakaran, L. R. Shelford, S. C.Speller, T. Mousavi, C. Grovenor, Z. Salman, S. R. Giblin, G. van der Laan, T. Hesjedal,Study of the structural, electric and magnetic properties of Mn-doped Bi Te single crystals,New J. Phys. 15, 103016 (2013).[28] M. Kharitonov, Interaction-enhanced magnetically ordered insulating state at the edge of atwo-dimensional topological insulator, Phys. Rev. B 86, 165121 (2012).[29] D. S. Lee, T. H. Kim, C.-H. Park, C.-Y. Chung, Y. S. Lim, W.-S. Seoa, H.-H. Park, Crys-tal structure, properties and nanostructuring of a new layered chalcogenide semiconductor,Bi MnTe , Cryst. Eng. Comm. 15, 5532 (2013).[30] T. M. Schmidt, R. H. Miwa, A. Fazzio, Spin texture and magnetic anisotropy of Co impuritiesin Bi Se topological insulators, Phys. Rev. B 84, 245418 (2011).[31] Joon Sue Lee, A. Richardella, D. W. Rench, R. D. Fraleigh, T. C. Flanagan, J. A. Borchers,Jing Tao, N. Samarth, Ferromagnetism and spin-dependent transport in n-type Mn-dopedbismuth telluride thin films, Phys. Rev. B 89, 174425 (2014).[32] J. A. Hagmann, Xiang Li, S. Chowdhury, S.-N. Dong, S. Rouvimov, S. J. Pookpanratana,K. M. Yu, T. A. Orlova, T. B. Bolin, C. U. Segre, D. G. Seiler, C. A. Richter, XinyuLiu, M. Dobrowolska, J. K. Furdyna, Molecular beam growth and structure of self-assembledBi Se /Bi MnSe multilayer heterostructures, New J. Phys. 19, 085002 (2017).[33] L. B. Abdalla, L. Seixas, T. M. Schmidt, R. H. Miwa, A. Fazzio, Topological insulatorBi Se (111) surface doped with transition metals: an ab-initio investigation, Phys. Rev. B
8, 045312 (2013).[34] A. M. Black-Schaffer, A. V. Balatsky, Strong potential impurities on the surface of a topolog-ical insulator, Phys. Rev. B 85, 121103(R) (2012).[35] L. Wu, M. Brahlek, R. V. Aguilar, A. V. Stier, C. M. Morris, Y. Lubashevsky, L. S. Bilbro,N. Bansal, S. Oh, N. P. Armitage, A sudden collapse in the transport lifetime across thetopological phase transition in (Bi − x In x ) Se, Nature Phys. 9, 410 (2013).[36] J. S´anchez-Barriga, I. Aguilera, D. Y. Tsukanova, P. S. Mandal, L. V. Yashina, A. M. Abaku-mov, A. N. Chaika, A. Varykhalov, G. Bihlmayer, S. Bl¨ugel, O. Rader (unpublished)[37] Liang Fu, Hexagonal Warping Effects in the Surface States of the Topological Insulator Bi Te ,Phys. Rev. Lett. 103, 266801 (2009)[38] M. Mogi, M. Kawamura, A. Tsukazaki, R. Yoshimi, K. S. Takahashi, M. Kawasaki, andY. Tokura, Tailoring tricolor structure of magnetic topological insulator for robust axioninsulator, Science Advances 10, eaao1669 (2017).[39] Q. L. He, L. Pan, A. L. Stern, E. C. Burks, Xiaoyu Che, Gen Yin Jing Wang et el. ChiralMajorana fermion modes in a quantum anomalous Hall insulator-superconductor structure,Science 357, 294 (2017). igures n-doped Bi Te I n t en s i t y ( a r b . un i t s ) Bulk VB 20 K Δ S1 S21 K1 K
Bulk VB E k || Binding energy (eV)Simulation0.4 0.3 0.2 0.1 0.0 S1
21 meV S2
12 meV Δ Mn-doped Bi Se K . . (a)(b) (c) (d) Δ I n t en s i t y ( a r b . un i t s ) I n t en s i t y ( a r b . un i t s ) Binding energy (eV)0.4 0.2 0.00.6 Binding energy (eV)0.20.50.8
20 K1 K D E F (e) (g) Δ (f) B i nd i ng ene r g y ( e V ) || (Å –1 ) 0.20.0–0.2 Δ ( e V ) || (Å –1 )–0.21 K IG. 1:
Magnetic gap of Mn-doped Bi Te derived by ARPES. (a–d) Measurements forBi Te with 6% Mn performed above and below the Curie temperature T C ∼
10 K. (The spectra in(c,d,g) and those marked by thick lines in (a,b,d) correspond to the center of the surface Brillouinzone, i. e., electron wave vector component k (cid:107) = 0 ˚A − .) Linear fits to the regions indicated in (c)yield shifts of 21 and 12 meV between these sections of the 20 K and 1 K spectra. (d) Simulationshowing that this corresponds to a magnetic gap ∆ = 90 ±
10 meV. (e–g) Same analysis for Mn-doped Bi Se with 6% Mn and a T C of 6 K, revealing only a nonmagnetic gap of 220 ± ± k (cid:107) = 0 ˚A − . - 4 0 0 - 2 0 0 0 2 0 0 4 0 0- 1 . 0- 0 . 50 . 00 . 51 . 0 - 4 0 0 - 2 0 0 0 2 0 0 4 0 0- 1 . 0- 0 . 50 . 00 . 51 . 0
051 01 52 0
M n ( 3 % ) ( d )( c )
C u r i e T e m p e r a t u r e
M n : B i T e (cid:1) M (cid:1) M ( a ) T = 2 K
M n - d o p e d B i T e Magnetization M (kA/m)
M a g n e t i c f i e l d m H ( m T )
M a g n e t i z a t i o n o u t - o f - p l a n e i n - p l a n e
M n ( 4 % )
C u r i e T e m p e r a t u r e ( b )
T = 2 K
M n - d o p e d B i S e Magnetization M (kA/m)
M a g n e t i c f i e l d m H ( m T )
M a g n e t i z a t i o n o u t - o f - p l a n e i n - p l a n e M (cid:1) M (cid:1) M n : B i S e M ^ (cid:1) M || TC (K)
M n - c o n t e n t ( % )
M n : B i T e AHE (10-1 W ) M a g n e t i c f i e l d m H ( m T )
4 K 5 K 1 0 K 2 0 K M ^ (cid:1) M || M n ( 8 % )
A n o m a l o u s H a l l E f f e c t
M n ( 6 % ) o r d i n a r y H a l l c o n t r i b u t i o n s u b t r a c t e d
A n o m a l o u s H a l l E f f e c t
M n : B i S e AHE (10-1 W ) M a g n e t i c f i e l d m H ( m T )
2 K 3 K 5 K 1 0 K 2 0 K
I B V H TC (K)
M n - c o n t e n t ( % )
FIG. 2:
Magnetic properties.
In-plane and out-of-plane magnetization M ( H ) of Bi Te (a) andBi Se (b) films with Mn concentrations of 3 and 4 % measured at 2 K by SQUID with the magneticfield either parallel or perpendicular to the surface, evidencing a perpendicular anisotropy (easyaxis) for Bi Te and an in-plane easy axis for Bi Se . The Curie temperature as a function of Mnconcentration is depicted in the inserts, evidencing that T C is significantly higher in the telluridesystem. (c,d) Anomalous Hall effect (AHE) measurements of the samples with the contribution ofthe ordinary Hall effect extracted from the high field data subtracted (see Supplementary Informa-tion). Due to the perpendicular magnetic anisotropy, only Mn-doped Bi Te displays a pronouncedanomalous Hall effect appearing when the sample is cooled below T C .
800 -400 0 400 800-20-1001020 -100 -50 0 50 100-10-50510 -400 -200 0 200 400-1.0-0.50.00.51.0 -400 -200 0 200 400-1.0-0.50.00.51.0
Mn(3%) (d)(c)
Curie Temperature
Mn:Bi Te ǁ M ┴ M (a) T = 2 K
Mn-doped Bi Te M agne t i z a t i on M ( k A / m ) Magnetic field m H (mT)
Magnetization out-of-plane in-plane
Mn(4%)
Curie Temperature (b)
T = 2 K
Mn-doped Bi Se M agne t i z a t i on M ( k A / m ) Magnetic field m H (mT)
Magnetization out-of-plane in-plane M ┴ M ǁ Mn:Bi Se M ^^^ ^ M || T C ( K ) Mn-content (%)
Mn:Bi Te A H E ( - W ) Magnetic field m H (mT) M ^^^ ^ M || Mn(8%)
Anomalous Hall Effect
Mn(6%) inear contribution subtracted
Anomalous Hall Effect
Mn:Bi Se A H E ( - W ) Magnetic field m H (mT) I T C ( K ) Mn-content (%)
Figure 2:
Magnetic characterization.
In-plane and out-of-plane magnetization M ||, ┴ (H) of Mn-doped Bi Te (a) and Bi Se (b) films measured at 2 K by SQUID applying the magnetic field either in-plane or out-of-plane (i.e., along the c- axis) as indicated. The magnetic anisotropy is perpendicular for the telluride and in-plane for the selenide system. Hence, only Mn-doped Bi Te displays an anomalous Hall effect in the FM state (b) but not Bi Se (f). Note that the contribution of the normal Hall effect has been subtracted in the AHE traces (see Supplemental figure S3 for details). The insets in (a,b) reveal that the Curie temperature is substantially higher in the telluride system. Figure 3 . HRSTEM cross sections of Mn-doped (a) Bi Te and (b) Bi Se with Mn concentration of 6%, recorded along the [-1010] and [-1-120] zone axes, respectively. The images reveal a layered structure of quintuple (QL) and septuple layers (SL) separated by van der Waals gaps. Heavy atoms such as Bi appear brighter due to the atomic-number contrast. The septuple layers appear darker in the STEM images due to the incorporation of the lighter Mn atoms. Note the different scales. SL QL
10 nm 10 nm
Mn-doped Bi Te Mn-doped Bi Se (a) (b) SL QL
FIG. 3:
HR-STEM cross sections of Mn-doped Bi Te and Bi Se recorded along the [1100] and[1210] zone axis, respectively. The STEM cross sections reveal the natural formation of a layeredheterostructure consisting of Bi MnTe (Bi MnSe ) septuple layers (SL) inserted between Bi Te (Bi Se ) quintuple (QL) layers adjoined by van der Waals gaps. Due to the atomic-number contrast,the heavy atoms (Bi) appear brighter in the high angle annular dark field (HAADF) images,and the septuple layers in the overview images darker due to the lighter Mn atoms preferentiallyincorporated. Note the different scales. The Mn concentration in (a) was 10% and in (b) locally9% and on average 6% according to x-ray diffraction. (a)(c)
6% Mn in Bi Te EXAFS c ( a r b . u . ) Photon energy (keV) measurementcalculation XA N ES ( no r m a li z ed ) Photon energy (keV)
Mn-doped Bi Te Experiment % Mn % Mn Simulation: substitutional Mn in QL Mn in septuple layer
XANES
Mn K-edge
Mn(6%) in Bi Se XANES
Mn K-edge (b)
Photon energy (keV) XA N ES ( no r m a li z ed ) Experiment: % Mn % Mn Simulation: substitutional Mn in QL Mn in septuple layer (d)
EXAFS c ( a r b . u . ) Photon energy (keV) measurementcalculation
Mn-doped Bi Se Figure 4:
Mn-incorporation sites in Bi Te and Bi Se derived by XANES (a,b) and EXAFS (c,d) measured at the Mn K-edge (symbols: measurements, solid lines: simulations). The XANES spectra display distinct contributions, which are fitted assuming substitutional Mn sites (orange lines) and Mn positioned in the central SL layer (green lines). The septuple layer has a higher weight in Bi Te than in Bi Se independently of the Mn concentration. The EXAFS data (red symbols) shown for 9% Mn is compared to simulations (green lines) for different incorporation sites shown in (e-g), as well as on substitutional Te,Se(1) and (2) in the middle, respectively, edge of the QL. The septuple position shows the best agreement in Bi Te . EXAFS oscillations are less pronounced in Bi Se indicating a more pronounced distribution of Mn over the different lattice sites for all Mn concentrations (see supplemental note 2). (e) Mn in septuple layer (f)
Substitutional Mn (g)
Interstitial Mn octahedral site (h)
Interstitial Mn tetrahedral site (1)(2)
Mn-doped Bi Te Mn-doped Bi Se FIG. 4:
Spectroscopic determination of the Mn incorporation sites in Bi Te andBi Se derived from x-ray absorption spectroscopy (XANES, EXAFS) at the Mn K-edge. Thesymbols represent the experimental spectra, the solid lines the simulation performed for differentincorporation sites including substitutional Mn on Bi sites in quintuple layers, Mn in the centerof septuple layers, as well as interstitial Mn in the van der Waals gaps as shown in (e-h). Thetwo contributions seen in the XANES spectra (a,b) are associated with substitutional Mn sitesand Mn in the center of the septuple layers, having a higher weight in Bi Te than in Bi Se .The comparison of the EXAFS data (red lines in (c,d)) recorded for 6% Mn to the simulations(green lines) shows best agreement for Mn in the center of the septuple layers in Bi Te . EXAFSoscillations are less pronounced in Bi Se indicating a more pronounced distribution of Mn overthe different lattice sites for all Mn concentrations (see Supplementary Information). IG. 5:
X-ray diffraction analysis of the septuple/quintuple heterostructures formedin Bi Te and Bi Se upon Mn doping as a function of Mn concentration ranging from 0 to 11%.The measured diffraction spectra (red and blue lines in (a,b)) are fitted using a random stackingparacrystal model consisting of a statistically varying alternation of Bi X quintuple and Bi Mn X septuple layers as described in the Supplementary Information, providing an excellent fit (blacklines) of the experimental data for both the telluride and selenide system. The average numberof quintuples (cid:104) N QL (cid:105) between subsequent septuples and the root mean square (RMS) width of therandom distribution derived from the fit is plotted in (c) versus Mn content (open, respectively,full symbols). A smaller average distance (cid:104) N QL (cid:105) , i.e., higher concentrations of septuples, is foundfor Bi Te as compared to Bi Se . The number of available Mn sites in the center of the septuplelayers relative to the total number n tot of (Bi and Mn) atoms is shown in (d) versus nominal Mncontent. The number expected for unity occupancy is indicated by the dashed line. Experimentalpoints below the line indicate that a significant fraction of Mn atoms resides in other lattice sites.This applies to Bi Se but not to Bi Te ..