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1 In the format provided by the authors and unedited. DOI:.38/NMAT4855 A magnetic heterostructure of topological insulators as a candidate for axion insulator M. Mogi, M. Kawamura, R. Yoshimi, A. Tsukazaki, Y. Kozuka, N. Shirakawa, K. S. Takahashi, M. Kawasaki and Y. Tokura Supplementary Note High-quality magnetic heterostructure of TI with Cr modulation doping. a b c. Cr(%)-(Bi,Sb) Te 3 nm (Bi,Sb) Te 3 nm Cr(%)-(Bi,Sb) Te 3 nm (Bi,Sb) Te 3 nm σ (e /h) - - T = 5 mk V G =.6 V Figure S Quantum anomalous Hall effect at 5 mk and quantization of σ xy at T 3 K in a MTI heterostructure. a, Schematic layout of a MTI heterostructure device studied in b and c. b, Magnetic field dependence of σ xy and σ xx at T = 5 mk. Gate voltage (V G ) is applied to tune the chemical potential to the charge neutral point (.6 V). c, Temperature dependence of σ xy and σ xx at B =. T. Magnetic field is applied for magnetic training. QAH regime (σ xy = e /h) is achieved below T = 3 K. σ xx σ xy σ (e /h) σ xy σ xx B =. T V G =.6 V T (K) As reported in Supplementary Ref., we can increase the observable temperature of QAH effect up to several Kelvin by modulation-doping of Cr to (Bi,Sb) Te 3 grown by molecular beam epitaxy (MBE). The selective Cr doping in the vicinity to the surface can enhance exchange interaction between topological surface states and bulk ferromagnetism while maintaining topologically nontrivial bulk insulation and strong perpendicular magnetic anisotropy. Notably, Cr doping kept apart from the outermost surfaces by about nm may improve the spatial homogeneity of magnetization gap as judged by the enhanced temperature stability of QAH state. Figure NATURE MATERIALS

2 Sb shows the near ideal QAH effect observed at T = 5 mk for the MTI heterostructure shown in Fig. Sa. The quantized σ xy can subsist up to T = 3 K as shown in Fig. Sc. Note that the observed σ xy quantized at ±e /h asserts that the topological surface state is formed at the outermost surfaces of the heterostructure film, but not at the interface between magnetic and non-magnetic TI layers. Supplementary Note Cross-sectional structure and elemental distribution in a MTI heterostructure. a b ADF-STEM Cr c Cr Cr(%)-(Bi,Sb)Te3 nm (Bi,Sb)Te3 5 nm Cr(%)-(Bi,Sb)Te3 nm (Bi,Sb)Te3 nm 5 nm InP d Bi e Sb f Te 5 nm 5 nm 5 nm 5 nm Figure S Cross-sectional analysis of a MTI heterostructure. a, Schematic layout of a MTI heterostructure studied here. Dotted lines are the guide to the eyes for the annular dark field scanning transmission electron microscopy (ADF-STEM) image shown in b. b, ADF-STEM image of a MTI heterostructure shown in a and a line profile of Cr distribution. Red shaded regions are the layers where we intended to dope Cr. The red arrows indicate the peaks of the line profile of Cr. c-f, Distribution maps of each element, Cr (c), Bi (d), Sb (e) and Te (f) studied by an energy dispersive x-ray spectroscopy (EDX). Figure Sb displays an annular dark field scanning transmission electron microscope image for a vertically asymmetric MTI heterostructure (Fig. Sa) having NATURE MATERIALS

3 similar structure as the film studied in the main text (Fig. e) with a total thickness of nm. Distribution of elements: Cr, Bi, Sb and Te are analyzed by energy dispersive x-ray spectroscopy (EDX) mappings in Fig. Sc-f respectively. Bi, Sb and Te appear to be distributed uniformly in the whole of the thin films. In contrast, Cr is separately distributed to upper and lower of the thin films. For more detail, we analyzed a line profile of Cr distribution shown in Fig. Sb. The line profile has peaks consistent with the layers where we intend to dope Cr. The 5-nm-thick separation layer clearly disconnects the Cr distribution along the growth direction. In addition to the two peaks, we observe another peak at the interface between the MTI film and the InP substrate. Supplementary Note 3 Magneto-resistivity of magnetic heterostructures of TIs and stabilization of ZHP state by vertical asymmetry. a b c d Cr(5%)-(Bi,Sb)Te3 8 nm (Bi,Sb)Te3 nm Cr(%)-(Bi,Sb)Te3 nm (Bi,Sb)Te3 nm Cr(%)-(Bi,Sb)Te3 nm (Bi,Sb)Te3 nm Cr(%)-(Bi,Sb)Te3 nm (Bi,Sb)Te3 3 nm Cr(%)-(Bi,Sb)Te3 nm (Bi,Sb)Te3 nm Cr(%)-(Bi,Sb)Te3 nm (Bi,Sb)Te3 5 nm Cr(%)-(Bi,Sb)Te3 nm (Bi,Sb)Te3 nm e f g ρ yx (h/e ) - T = 5 mk V G =V ρ yx (h/e ) T = 4 mk V G =8V - ρ yx (h/e ) - T = 4 mk V G =V h ρ yx (h/e ) - T = 4 mk V G =-V ρ xx (h/e ) 3 ρ xx (h/e ) 3 ρ xx (h/e ) 3 ρ xx (h/e ) Figure S3 Magnetotransport properties of various MTI heterostructures. a-d, Schematic of MTI heterostructures. a, b and d were studied in the main text (also shown in Fig. ). e-h, Magnetic field dependence of Hall resistivity (ρ yx ) and longitudinal resistivity (ρ xx ) of the samples shown in a-d respectively, at temperatures of T = 4-5 mk. Gate voltage (V G ) is applied so as to tune the Fermi energy to the charge neutral point. 3 NATURE MATERIALS 3

4 In Fig.S3 we show magnetic field dependence of Hall resistivity (ρ yx ) and longitudinal resistivity (ρ xx ) of the MTI devices studied in the main text. The Hall conductivity (σ xy ) and the longitudinal conductivity (σ xx ) in the main text are calculated from these data. As for the single layer film shown in Fig. S3a and Supplementary Ref., a sharp rectangle hysteresis curve in ρ yx is observed (Fig. S3e). Accordingly, the peak of ρ xx during the magnetization reversal stays as low as ~. h/e. Similar jumping behavior of magnetization reversal has also been reported in Supplementary Ref., 3 and can be observed in relatively thick (> 8 QL) magnetically doped (Bi,Sb) Te 3 thin films due to even stronger magnetic anisotropy compared to that of thin ones (typically 3~6 QLs). In addition to these devices, we studied a totally 8-nm-thick MTI heterostructure with vertical asymmetry shown in Fig. S3c. Compared with the vertically symmetric MTI heterostructure with the same thickness (shown in Fig. S3b and also in Fig. d in the main text), the magnetotransport exhibits extremely high resistivity (~5 h/e ) during the reversal of magnetization (Fig. S3g). [The observed peculiar peaks of ρ yx around the coercive fields probably came from unintentional capacitive couplings between the lead wires. High longitudinal voltage ρ xx (>> h/e ) caused to induce extra voltage on the Hall voltage probes.] When the high resistivity is converted to conductivity by tensor calculation, ZHPs show up. Interlayer coupling between two separated magnetic layers would be weakened in this heterostructure as compared with the devices shown in Fig. S3a and S3b. In addition, because of the difference between upper and lower magnetic layers where top of the upper magnetic layer contacts with vacuum (here, AlO x capping layer) and lower magnetic layer is sandwiched by BST layers, the vertical asymmetry would give a slight difference of magnetic anisotropy or 4 NATURE MATERIALS 4

5 B c between the two magnetic layers, and hence gives rise to the anti-parallel magnetization configuration. In the MTI heterostructure with thicker separation layer shown in Fig. S3d (also shown in Fig. e), the more stable ZHP (higher ρ xx ) can be obtained (Fig. S3e). It would appear counter-intuitive that plateau-like features are not seen in the ρ yx -B curves of Fig. S3g and S3h, while the ZHP are seen clearly in the σ xy -B curves of the same sample (Fig. h in the main text and Fig. S7c shown later). This may be related to a broadening of magnetization reversal. If the inhomogeneous broadening in the magnetization reversal of each layer is much smaller than the difference in the coercive fields, the magnetization does not change at all between the coercive fields. Then, a plateau-like structure is expected in the ρ yx -B curves. In reality, however, the magnetization reversal occurs rather gradually. In our magnetization measurement (shown later in Fig. S4), a broad magnetization reversal (gentle slope in M-B curve) was observed, suggesting the presence of minor domains. Therefore, even in the magnetic field range between the coercive fields, the magnetization changes gradually resulting in the smooth change in the ρ yx -B curves. Nevertheless, under a magnetic field between the two coercive fields, the major domain can form the anti-parallel magnetization between the upper and the lower magnetic layers. This anti-parallel magnetization of the major domain is responsible for the zero Hall plateau in σ xy. 5 NATURE MATERIALS 5

6 Supplementary Note 4 Magnetization versus Hall conductivity and resistivity. a b c M ( -6 emu/cm ) σ xy (e /h) ρ yx (h/e ) T =.6 K T =.5 K T =.5 K Figure S4 Hysteresis curves of magnetization, Hall conductivity and Hall resistivity. Magnetic field (B) dependence of magnetization (M) measured by SQUID at T =.6 K (a), Hall conductivity (σ xy ) (b) and Hall resistivity (ρ yx ) (c) at T =.5 K. The magnetic heterostructure of the sample is schematically drawn in the inset of a. σ xx (e /h) ρ xx (h/e ) Cr(%)-(Bi,Sb)Te3 nm - (Bi,Sb)Te3 3 nm Cr(%)-(Bi,Sb)Te3 nm (Bi,Sb)Te3 nm - To confirm that magnetization is directly reflected to Hall conductivity, we compare the hysteresis curves of magnetization (M), Hall conductivity (σ xy ) and Hall resistivity (ρ yx ) at T =.5-.6 K in a MTI heterostructure (Fig. S4a, inset). In this film, the signature of ZHP is observed at T =.5 K (Fig.S4b). The MTI heterostructure has two magnetic layers where Cr-concentration and thickness are the same, therefore, magnetic moments is expected to be zero (M = ) when the magnetizations become anti-parallel. 6 NATURE MATERIALS 6

7 Magnetization measurement was conducted using a superconducting quantum interference device (SQUID) magnetometer in Quantum Design, Magnetic Property Measurement System (MPMS) at.6 K, reached with a higher-conductance pumping line than usual. To obtain the magnetic moments of the MTI film, we subtracted diamagnetic contribution of the InP substrate (~ µemu/cm at B = T) which was measured at T = 5 K well above the Curie temperature of the MTI film. The hysteresis curve of the magnetization in Fig. S4a shows a ferromagnetic behavior with perpendicular magnetic anisotropy, which is consistent with the transport measurement. In the M-B curve, kinks (changes in the slope) are seen during the magnetization reversal at around the M =. Similar kinks can be observed in σ xy -B curves at around σ xy = which develops into ZHP with further decreasing temperature. Although gradual changes in the slope are seen in the ρ yx -B curves, they are well apart from ρ yx =. At this temperature (.5-.6 K), the transition at the B c is sharp and that at B c is burred in the magnetization. This is well reflected in σ xy. The values of B c in M-B and σ xy -B show a good agreement with each other. The similarity between the M-B curves and the σ xy -B curves ensures the picture that the change of magnetization is intrinsically reflected in σ xy, rather than in ρ yx. Additionally, we point out that the hysteresis curve of magnetization, unlike that of σ xy, does not close at around ±.3 T, which rather resembles that of ρ yx which closes at around ±.4 T. This is not contradictory to the above discussion because the QAH state emerges even if the magnetic moments do not perfectly align. Quantization of σ xy is possible when a finite magnetization-gap exists. The not-fully aligned magnetic moments may lead to residual dissipation at this temperature (σ xx shown in Fig. S4b inset), of which hysteresis curve does not close until ± T. 7 NATURE MATERIALS 7

8 Supplementary Note 5 Zero-field ZHP state in four-terminal measurement. σ xy (e /h) - - ' 3 T = 4 mk V G = - V.8 σ xx (e /h) Figure S5 Minor loop in four-terminal conductivity of a MTI heterostructure under ZHP state. Four-terminal Hall conductivity (σ xy ) and longitudinal conductivity (σ xx ) of the MTI heterostructure device shown in Fig. e in the main text as a function of magnetic field for a minor loop (from red to blue lines) and a major loop (from red to gray lines). Magnetic field scan for the respective loops is the same as shown in Fig. 3 in the main text.. ' In Fig. 3 in the main text, we show two-terminal conductance measured in Hall-bar and Corbino-disk for minor loops. We observe zero σ xx with -µv excitation voltages. In Fig.S4 we show the minor loop in four-terminal measurement with a fixed excitation current ( na). In ZHP state at B = B (B is defined in the main text) and at B = T in the process of minor loop, exactly zero σ xx is not observed due to current-induced breakdown of the insulating state as argued in the main text, although the resistance of the sample becomes larger than MΩ. When the applied current is na, at least V appears between the ends of the sample. Comparing between the 8 NATURE MATERIALS 8

9 ZHP states at B = B and at B = T, the value of σ xx at B = T is lower than that at B = B. The ZHP state is stabilized at zero magnetic fields, which is consistent with the discussion for the temperature dependence of ZHP state in the main text (Fig. 4c). A slightly smaller coercive field in the minor loop than that in major loop possibly indicates the presence of residual small minor domains with parallel magnetization configuration in the upper and lower magnetic layers. Although such small magnetic domains may remain, it appears that most of magnetizations between the two magnetic layers point oppositely to generate the magnetization gap. Supplementary Note 6 Single semi-circle relations in vertically symmetric MTI heterostructures. a σ xx (e /h). B-driven mk mk T = 5 mk σ xy (e /h) b σ xx (e /h) T = 4 mk B-driven - - σ xy (e /h) Figure S6 Semi-circle relation in vertically symmetric MTIs. a,b, (σ xy, σ xx )-plots from the results of magnetic field dependent σ xy and σ xx of the homogenously Cr-doped film (a) shown in Fig. f and of the symmetric MTI heterostructure (b) shown in Fig. g in the main text. In the vertically asymmetric MTI heterostructure (Fig. e in the main text), external magnetic field induced topological phase transition between QAH and ZHP states traces double semicircles in (σ xy, σ xx ) space with centers at (, ±e /h) as shown in Fig. 4b in the main text 4,5,6. We also plotted the magnetic field dependence of σ xy and 9 NATURE MATERIALS 9

10 σ xx of the samples shown in Fig. c (single-layer of MTI) and d (symmetric MTI heterostructure) on the (σ xy, σ xx )-plane shown in Fig. S6a and S6b respectively. In contrast to the asymmetric MTI heterostructure exhibiting the ZHP state, these show single semicircles centered at (, ). These results indicate that the magnetization reversal occur at once in the both films without experiencing the anti-parallel magnetization configuration. Moreover, an insulating phase originating from the hybridization gap is not observed even near the coercive field in these films. Supplementary Note 7 Thickness dependence on hybridization effect via tilted magnetic-field measurements. a c σ xy (e /h) σ xx (e /h) t = 8 or nm - Cr(%)-(Bi,Sb) Te 3 nm (Bi,Sb) Te 3 3 or 5 nm Cr(%)-(Bi,Sb) Te 3 nm (Bi,Sb) Te 3 nm T = 4 mk V G =V 8-nm-thick film b d t = nm nm t = nm Figure S7 Tilted magnetic-field measurements in 8- and -nm-thick heterostructure films. a, Schematic layout of MTI heterostructures studied in (b), (c) σ xx (e /h) σ xx (e /h) T = 4 mk B // in-plane 8 nm 8 nm nm B (= T) // in-plane B = -B (ZHP) 5 /T (K - ) 5 3 NATURE MATERIALS

11 and (d). b, In-plane magnetic field (B) dependence of 8- (blue) and - (red) nm-thick film measured at T = 4 mk. c, Perpendicular magnetic field (B) dependence of Hall conductivity (σ xy ) and longitudinal conductivity (σ xx ) in the 8-nm-thick film derived from the data shown in Fig. S3g. d, Temperature (T) dependence of σ xx for the two samples measured in Corbino-disks under in-plane magnetic field (B = T) and under ZHP states (B = B ) on a logarithmic scale as a function of /T. Solid squares show the data of 8- (blue) and - (red) nm-thick films under in-plane magnetic field. Open circles show the data of 8- (blue) and - (red) nm-thick films under ZHP state. We conducted a field-tilted measurement in a thinner (8 nm) film which is the same one shown in Fig. S3g to examine the thickness dependence on the hybridization effect. In the 8-nm-thick film, Cr is modulation doped in a similar asymmetric structure as adopted for the -nm-thick film studied in the main text, and the thickness of the separation layer is reduced to 3 nm (Fig. S7a). Figure S7b shows the in-plane magnetic field dependence of σ xx of the two films. By thinning film, σ xx in the 8-nm-thick film becomes smaller than that in the -nm-thick film perhaps due to the larger hybridization effect as expected. Besides, σ xx takes almost constant values as a function of in-plane magnetic field at least within ± T. A slight increase in σ xx with the in-plane field may be related to the orbital effect that reduces the hybridization by opposite shift of top and bottom surface dispersion in the momentum space but is not so significant within ± T. In the asymmetric heterostructures of 8- and -nm-thick films, both of them show zero Hall plateaus (Fig. h in the main text and Fig. S7c) with similar thermal activated conduction, despite of the possible difference in the hybridization gap energies, as shown in Fig. S7d. This result ensures again that the hybridization gap cannot be the main origin of the observed zero Hall plateau. In addition, as described in the main text, the 8-nm-thick film with a symmetric structure does not show the zero Hall plateau (Fig. NATURE MATERIALS

12 f and g). This contrasts to the observation of the zero Hall plateau in the asymmetric 8-nm-thick film (Fig. S7c). Given that the hybridization gap is dominated by the film thickness, the appearance or absence of the zero Hall plateau in the films with the same thickness again suggests irrelevance of the hybridization gap to the zero Hall plateau observed in the present study. The fact that the emergence of the zero Hall plateau is sensitive to the magnetic-layer structure, i.e. symmetric or asymmetric, supports our assignment of the zero Hall plateau to the anti-parallel magnetization configuration. Supplementary Note 8 Temperature dependence of QAH and ZHP states in a Corbino-disk device of a vertically asymmetric MTI heterostructure..6 σ xx (e /h) T = 53 mk 47 mk 38 mk 3 mk mk 3 mk 9 mk 7 mk 4 mk Figure S8 Minor loop measurement of ZHP state in a Corbino-disk under various temperatures. Magnetic field dependence of longitudinal conductivity (σ xx ) for Corbino-disk device shown in Fig. 3b in the main text measured at various temperatures (T = 4, 7, 9, 3,, 3, 38, 47 and 53 mk). Temperature dependence of σ xx for QAH and ZHP states is taken from the results and is shown in Fig. 4c in the main text. NATURE MATERIALS

13 In Fig. 4c in the main text, we exhibit temperature dependence of σ xx for QAH and ZHP states in a Corbino-disk of a vertically asymmetric MTI heterostructure. The dependence is clearly different from that of in-plane magnetization state. The data is taken from the magnetic field dependence of σ xx at various temperatures as shown in Fig. S6. The decrease of σ xx as a function of B around B = B subsists at even T = 53 mk or more. At B = B, σ xx decreases with time at T < 3 mk, on the other hand, at T > mk σ xx increases with time. The value of σ xx in Fig. 4c in the main text is taken the value of after sufficiently waiting. Supplementary References. Mogi, M. et al. Magnetic modulation doping in topological insulators toward higher-temperature quantum anomalous Hall effect. Appl. Phys. Lett. 7, 84 (5).. Kou, X. et al. Scale-Invariant Quantum Anomalous Hall Effect in Magnetic Topological Insulators beyond the Two-Dimensional Limit. Phys. Rev. Lett. 3, 37 (4). 3. Liu, M. et al. Large discrete jumps observed in the transition between Chern states in a ferromagnetic Topological Insulator. Sci. Adv., e667 (6). 4. Kivelson, S., Lee, D-H. & Zhang, S-C. Global phase diagram in the quantum Hall effect. Phys. Rev. B 46, 3-38 (99). 5. Burgess, C. P., Dib, R. & Dolan, B. P. Derivation of the semicircle law from the law of corresponding states. Phys. Rev. B 6, (). 6. Nomura, K. & Nagaosa, N. Surface-Quantized Anomalous Hall Current and the Magnetoelectric Effect in Magnetically Disordered Topological Insulators. Phys. Rev. Lett. 6, 668 (). 3 NATURE MATERIALS 3