Abstract
Studying the influence of broken timereversal symmetry on topological materials is an important fundamental problem of current interest in condensed matter physics and its understanding could also provide a route toward proofofconcept spintronic devices that exploit spintextured topological states. Here we develop a new model quantum material for studying the effect of breaking timereversal symmetry: a hybrid heterostructure wherein a ferromagnetic semiconductor Ga_{1−x}Mn_{x}As, with an outofplane component of magnetization, is cleanly interfaced with a topological insulator (Bi,Sb)_{2}(Te,Se)_{3} by molecular beam epitaxy. Lateral electrical transport in this bilayer is dominated by conduction through (Bi,Sb)_{2}(Te,Se)_{3} whose conductivity is a few orders of magnitude higher than that of highly resistive Ga_{1−x}Mn_{x}As. Electrical transport measurements in a topgated heterostructure device reveal a crossover from weak antilocalization to weak localization as the temperature is lowered or as the chemical potential approaches the Dirac point. This is accompanied by a systematic emergence of an anomalous Hall effect. These results are interpreted in terms of the opening of a gap at the Dirac point due to exchange coupling between the topological insulator surface state and the ferromagnetic ordering in Ga_{1−x}Mn_{x}As. The experiments described here show that welldeveloped III–V ferromagnetic semiconductors could serve as valuable components of artificially designed quantum materials aimed at exploring the interplay between magnetism and topological phenomena.
Introduction
A threedimensional (3D) topological insulator (TI) is characterized by surface states that are protected by timereversal (TR) symmetry.^{1,2,3,4} The TR symmetry can be broken by doping a TI with magnetic atoms or interfacing a TI surface with a magnetic layer, causing an energy gap to open at the Dirac point.^{5,6,7,8} Unique quantum phenomena resulting from the broken TR symmetry have been proposed: such as a topological magnetoelectric effect,^{5} an image magnetic monopole effect,^{9} topological Kerr and Faraday rotation,^{5} and the quantum anomalous Hall effect (AHE).^{10} Some of these phenomena have been demonstrated experimentally.^{11,12,13,14} The synthesis and characterization of a variety of magnetically doped 3D TIs with transition metals have been reported in this context.^{7,15,16,17,18,19,20} Angleresolved photoemission spectroscopy (ARPES) has suggested evidence for the opening of a gap induced by breaking TR symmetry in magnetically doped TI systems,^{7,8,18,21} although recent studies point out an alternative mechanism for the gap seen in such studies.^{22} In addition, a spinresolved ARPES experiment revealed a hedgehoglike spin texture in the modified surface state of Bi_{2}Se_{3} films by Mn doping.^{23} Manipulating the spin texture of the surface states in a TI could play an important role within the burgeoning field of “topological spintronics.”^{24,25,26,27,28,29}
In this paper, we break TR symmetry in the surface state of a TI by interfacing the surface with a ferromagnetic insulator (FMI) with perpendicular magnetization. The key advantage of a TI/FMI heterostructure over magnetically doped TIs is the selective modification of one surface by an adjacent FMI. Magnetic proximity affects only the interfaced surface; thus magnetic properties or the resulting effects are free from the magnetism of the bulk or other surfaces of the TI layer. So far, several TI/FMI heterostructures have been experimentally reported using FMIs interfaced with TIs where the chemical potential is located in or near the conduction band.^{30,31,32,33,34,35,36,37,38} In many cases, the magnetic anisotropy of the FMI was in plane. Ideally, to induce a magnetic gap, it would be preferable to have an FMI whose magnetization is perpendicular to the TI surface. Weak localization (WL),^{31,38} suppression of weak antilocalization (WAL),^{34} and induced AHE^{33,39} have been observed by interfacing a TI with an FMI or ferrimagnetic insulator with perpendicular magnetic anisotropy.^{39} However, electronic transport evidence of a magnetic gap can be ambiguous when the chemical potential of the TI is fixed as in previous studies, especially in the bulk bands that are away from the Dirac point. Thus there remains an important context for realizing an electrically gated TI/FMI heterostructure with a clean interface, perpendicular magnetic anisotropy, and chemical potential in the bulk band gap. We note also that, to avoid a nonmagnetic gap due to quantum tunneling between opposite surface states, the TI film needs to be thicker than the critical thickness for hybridization.^{40} Here we demonstrate a new approach that meets all these conditions using a TI/FMI heterostructure that uses a highly resistive III–V ferromagnetic semiconductor, (Ga,Mn)As, as the insulating ferromagnetic layer.
Results and discussions
Synthesis of (Bi,Sb)_{2}(Te,Se)_{3}/(Ga,Mn)As heterostructures
The ferromagnetic Curie temperature (T_{C}) and resistivity as well as the magnetic easy axis of (Ga,Mn)As films can be engineered by Mndoping, annealing, and strain.^{41,42,43} Here we desire highly resistive Ga_{1−x}Mn_{x}As with an outofplane magnetization. High resistivity was achieved by using a low Mndoping of x ≈ 0.05 and a perpendicular component of magnetization, with T_{C} ≈ 50 K, by growing the (Ga,Mn)As film (15 nm) on an InP (111)A substrate by molecular beam epitaxy (MBE). (See Supplementary Information S1 for magnetic and structural characterization.) An advantage of using highly resistive (Ga,Mn)As for the TI/FMI heterostructure is the welldefined interface, without an amorphous interfacial layer or secondary phases, as was demonstrated for epitaxial growth of Bichalcogenide TIs on GaAs (111).^{44} After growing the (Ga,Mn)As film, the substrate was transferred to another MBE chamber without breaking vacuum for the growth of the 3D TI (Bi,Sb)_{2}(Te,Se)_{3} thin film (8 nm). The Dirac fermion dynamics in Bi_{2}(Te_{3−x}Se_{x}) can be engineered by varying the composition of Te (3 − x) and Se (x),^{45} and we chose x = 1 (Bi_{2}Te_{2}Se) to place the Dirac point above the top of the valence band. The resulting elemental composition of Te and Se in the (Bi,Sb)_{2}(Te,Se)_{3} film grown on the (Ga,Mn)As layer was Te:Se ≈ 2.1:0.9, as determined by energy dispersive Xray spectroscopy (EDS) in a transmission electron microscope (TEM). Further engineering of the chemical potential was achieved by Sbdoping: with an optimal ratio of Bi and Sb (Bi:Sb ≈ 1.25:0.75), we were able to place the chemical potential in the bulk band gap, as confirmed by electrical transport measurements.
Ambipolar transport
Although the selective modification of one TI surface with an FMI is advantageous, as discussed earlier, the buried interface between TI and FMI restricts direct probing of the modified TI surface state by techniques such as ARPES or scanning tunneling microscopy. However, electrical transport measurements do provide a route to study the modification of the surface states by quantum corrections to the magnetoconductance (MC) and via the AHE. For transport measurements, we fabricated a topgated Hallbar device with highκ dielectric HfO_{2} and Au/Ti gate metal by standard photolithography (Fig. 1a, b). One important question for the electrical transport laterally through the heterostructure is whether a current flows only through the TI layer. The black curve in the Fig. 1c, d represents the resistivity when the current flows through the whole TI/(Ga,Mn)As heterostructure while the red curve shows the resistivity of only the (Ga,Mn)As layer after the TI overlayer was carefully removed by mechanical scratching. Since the resistivity of the (Ga,Mn)As is more than two orders of magnitude higher than that of the bilayer <40 K and not even measurable at lower temperatures by standard direct current methods, we conclude that the current flows predominantly through the TI layer in the measurement range (T ≤ 3 K) for studies of quantum corrections to MC and AHE; we can thus treat the (Ga,Mn)As layer as an FMI. Similar insulating behavior of the (Ga,Mn)As film was seen by selective removal of the TI overlayer using a lowpower dry etch. We note that the InP substrate is semiinsulating and does not contribute to electronic transport at cryogenic temperatures.
The gatevoltage dependence of the longitudinal sheet resistance R_{xx} and Hall resistance R_{xy} of the TI/(Ga,Mn)As bilayer shows the typical ambipolar transport behavior of TI films (Fig. 1e, f). The Hall resistance R_{xy} changes sign at around V_{G} = 0.3 V while the longitudinal resistance R_{xx} reaches a maximum at V_{G} = −1.3 V. The mismatch of the gate voltages between the charge neutrality point, where the R_{xy} sign changes, and the R_{xx} peak reveals that the carrier densities of top and bottom surfaces do not match each other and the two surfaces could even have different types of carriers in a certain range of gate voltage. The chemical potential of the bottom surface state (interfaced with (Ga,Mn)As) may not be determined solely by the singlegatevoltage dependence of the channel resistance and the Hall resistance of the whole TI layer. However, this chemical potential can be determined using careful studies of the quantum corrections to the MC and the AHE. Figure 2 illustrates the band alignment of the topgated heterostructure and the chemical potential of the two surfaces with gatevoltage tuning, based on the ambipolar transport results and the MC and AHE studies that are discussed below. The band bending at the TI/(Ga,Mn)As interface arises from an estimated conduction band offset of about 1 eV. (See Supplementary Information S2 for more details.)
Quantum corrections to MC
We now discuss the results of magnetotransport measurements in a topgated Hallbar device as a function of both gate voltage and temperature (Fig. 3). At fixed temperatures of T = 0.1 K and T = 0.29 K, at a gate voltage V_{G} = −5 V, we observe a positive MC (Fig. 3a, b). As we decrease the magnitude of V_{G} toward zero and then increase it to +1 V, the positive MC gradually changes to a negative MC. One salient feature in the crossover regime is the coexistence of a negative MC peak near zero magnetic field and a positive MC for larger magnetic fields; this is more pronounced at T = 0.29 K. A similar crossover from positive MC to negative MC is also seen when we raise the temperature at a fixed gate voltage (V_{G} = −5 V) (Fig. 3c). The shape of the MC also changes as a function of temperature: as we increase the temperature from T = 0.1 K, the relatively sharp positive MC first transitions to a superposition of positive and negative MC. Then, at temperatures above T ~ 3 K, the MC shows a parabolic negative MC. The similarity for the crossovers in MC as a function of gate voltage and temperature suggest a unified underlying mechanism for both cases.
We interpret our observations using quantum corrections to the MC in a TI, taking into account diffusive transport in two parallel surface channels with different dephasing lengths, one with an intact Dirac point (preserved TR symmetry) and the other with a magnetic gap (broken TR symmetry).^{46} The former refers to the top surface of the device and the latter to the bottom surface that is interfaced with the (Ga,Mn)As layer. For the top surface, the quantum corrections to diffusive transport result in a negative MC arising from WAL. (See Supplementary S3). For the bottom surface, the exchange interaction with the ferromagnetic (Ga,Mn)As layer is expected to lead to a magnetic gap (Δ). In this case, the quantum corrections to the MC can result in either a negative MC due to WAL or a positive MC due to WL, depending on the ratio Δ/E_{F}, where E_{F} is the chemical potential. The crossover between WAL and WL essentially arises from the modification the πBerry phase of the TI surface state φ = π(1 − Δ/2E_{F}).^{46} When the ratio Δ/E_{F} is small, the Berry phase remains close to π, leading to WAL. When we increase the ratio by decreasing E_{F} using a gate voltage or by increasing the gap Δ by lowering temperature, the Berry phase approaches 0, leading to WL. This WAL–WL crossover in the MC has been experimentally demonstrated in temperaturedependent studies of MC in TI films with an energy gap opened by either hybridization or by magnetic doping/proximity.^{18,31,47,48,49,50,51} Our results show that this crossover can also be systematically engineered using a gate voltage and that it agrees qualitatively with the variation with temperature. Notably, in certain regimes of temperature and gate voltage, we observe the coexistence of a WAL peak near zero magnetic field and WL behavior at larger magnetic fields, agreeing with our model of at least two decoupled transport channels with different dephasing lengths. As the gate voltage is tuned from V_{G} = −5 V to V_{G} = 1 V at 0.29 K, the MC becomes positive (WL) for larger magnetic field while the negative WAL peak is still observed for small magnetic field near zero (Fig. 3b). We attribute the WL contribution to the MC to the gapped surface state of the bottom surface due to proximity with (Ga,Mn)As. The WAL peak near zero magnetic field arises from the gapless surface state of the top surface decoupled from the bottom surface.
To quantitatively analyze the WAL and WL, we fit the data by applying the theoretical expressions developed for the quantum corrections to the MC of a TI in the presence of a magnetic gap.^{46} We note that, in our sample, the film is thick enough to prevent a hybridization gap created by tunnel coupling between the top and bottom surfaces. Further, in the range of gate voltage studied (−5 V ≤ V_{G} ≤ 1 V), the chemical potential of the TI always lies in the region where the bulk is depleted. This is indicated by the carrier density (n_{2D} ≅ 4.3 × 10^{12} cm^{−2}) at V_{G} = −5 V, which is low enough to place the chemical potential in the bulk band gap. At V_{G} = 1 V, the chemical potential is still in the ambipolar transport region (Fig. 1f). Thus the top and bottom surfaces are completely decoupled and we describe the quantum corrections to the MC using a twochannel model:
Here l_{ϕ,i} and α_{i} are the dephasing length and prefactors respectively, corresponding to the topmost gapless surface state (i = 0) and the bottom gapped surface state with i = 1. We fitted the MC data using three parameters, l_{ϕ,0}, l_{ϕ,1}, and α_{1}, fixing α_{0} = −1/2. Note that, for the purposes of our analysis, we neglect corrections to the dephasing length l_{ϕ,1} since this would introduce additional fitting parameters. (See Supplementary S4 for examples of fits to the data.) The prefactor α_{1} corresponds to the quantum corrections to the MC of the bottom surface and provides an indirect way to estimate the chemical potential in this surface state as it is varied with gate voltage. Figure 3d, e show that α_{1} increases as the gate voltage decreases from V_{G} = 1 V to V_{G} = −5 V (−7 V) at 0.1 K (0.29 K). We attribute this behavior to E_{F} at the bottom surface being tuned from the conduction band down toward the magnetic gap but not passing through it as illustrated in Fig. 3f. This qualitatively agrees with the WAL–WL crossover when the Berry phase changes from π to a smaller value by tuning E_{F}. Similarly, if we fix V_{G} = −5 V to place E_{F} close to the gap and vary the temperature, α_{1} increases with decreasing temperature (Fig. 3g): this occurs because Δ increases at lower temperatures due to the temperature dependence of the interfacial exchange coupling with the adjacent (Ga,Mn)As layer (illustrated in Fig. 3h). An unexplained feature of our results is the range of values obtained for α_{1}. Based on theory,^{46} we would anticipate that 0 ≤ α_{1} ≤ 1 as the ratio Δ/E_{F} varies from zero (at high temperature or at large positive gate voltage) to large (at low temperature or at negative gate voltage). Instead, fits to the data yield 0.4 ≤ α_{1} ≤ 0.7. This likely points to oversimplification in our twochannel model and suggests that interchannel scattering probably needs to be considered.
Anomalous Hall effect
We now discuss the results from Hall measurements where we observe a systematic emergence of nonlinear magnetic field dependence of the Hall resistance as the chemical potential is lowered at a fixed temperature by varying the gate voltage (Fig. 4a, c) or as the temperature is decreased at a fixed gate voltage (Fig. 4b, d). We note that, over the range of temperature studied (a few K), the chemical potential of the top and bottom surfaces does not change much at a fixed gate voltage, suggesting that the nonlinear Hall effect is unlikely to arise from two channels with different carrier densities and mobilities. A more consistent interpretation attributes this behavior to the AHE and prompts us to study the effect of a finite energy gap on the Hall conductance. The absence of hysteresis of the AHE indicates that longrange magnetic ordering is not induced in the bottom surface of the TI film by the adjacent (Ga,Mn)As layer in the measurement range of temperature (100 mK–10 K) and gate voltage (−7 to 1 V). To understand the anomalous Hall contribution from the interface between TI and FMI, we consider a twodimensional Dirac model with a finite energy gap (Δ). A direct calculation of the Hall conductance leads to
with \(E_{\mathrm{F}}\) = \(\sqrt {\left( {\hbar v_Fk} \right)^2 + ({\mathrm{\Delta /}}2)^2}\). (See Supplementary Information S5 for detailed calculations). Equation (2) shows that the Hall conductivity is halfquantized in the insulating regime of a single Dirac model, and the halfinteger quantum Hall conductivity monotonically decreases as E_{F} moves above the energy gap or as the gap gradually closes with an E_{F} fixed to a position near the gap.
Since our results are not in the regime of the quantized Hall conductivity, the observed Hall conductivity is smaller than e^{2}/2h. However, it follows the qualitative behavior of Eq. (2). Figure 4c, d (insets) clearly show the systematic emergence of the anomalous Hall term \(R_{xy}^{AH}\) with respect to the gate voltage and temperature, where \(R_{xy}^{AH}\) is obtained after subtracting the ordinary Hall term \(R_{xy}^{OH}\) from the Hall resistance as \(R_{xy}^{AH} = R_{xy}  R_{xy}^{OH}\). We show \(R_{xy}^{AH}\) instead of \(\sigma _{xy}^{AH}\) since R_{xx} term contains a large contribution of the top surface and affects the values of \(\sigma _{xy} = R_{xy}{\mathrm{/}}\left( {R_{xx}^2 + R_{xy}^2} \right)\). The expression for R_{xy} from σ_{xy} can be written as:
with σ_{xx} from the Drude model σ_{xx} = e^{2}τn/m where n, m, and τ are, respectively, the carrier density, the effective mass, and the relaxation time between collisions. For \(E_{\mathrm{F}} > \left \Delta \right{\mathrm{/}}2\), n increases as E_{F} increases (moves away from the gap). Similarly to the case of quantum corrections to MC, the change of R_{xy} reveals a systematic modification of the size of the energy gap and the chemical potential. As the chemical potential lowers and approaches the energy gap by tuning the gate voltage from 1 to −5 V, the estimated magnitude of the anomalous Hall resistance \(R_{xy}^0\) increases. \(R_{xy}^0\) is the intercept obtained by extrapolating a linear line of the high field Hall resistance. \(R_{xy}^0\) is zero in the case of a closed gap (Δ = 0). When a gap opens and widens, a nonzero \(R_{xy}^0\) monotonically increases. Figure 4c shows the evolution of the anomalous Hall resistance \(R_{xy}^0\) as the chemical potential lowers toward the energy gap. Similarly, Fig. 4d shows a monotonic increase of \(R_{xy}^0\) with decreasing temperature, interpreted as the widening of the gap with decreasing temperature. The interpretation of both gatevoltage dependence and temperature dependence of the AHE is consistent with that of the quantum corrections to the MC with varying gate voltage and temperature. The onset temperature of both AHE and WL is much lower than the T_{C} of the adjacent (Ga,Mn)As layer, indicating that the exchange coupling between electrons in TI bottom surface and Mn moments in (Ga,Mn)As is much weaker than the exchange coupling between Mn moments in (Ga,Mn)As (Fig. 5).
In summary, we synthesized and characterized a heterostructure of a TI film (Bi,Sb)_{2}(Te,Se)_{3} on a ferromagnetic semiconductor (Ga,Mn)As. The Ga_{0.95}Mn_{0.05}As layer is highly resistive with a perpendicular component of magnetization below 50 K. With an optimal BitoSb ratio, the chemical potential was placed in the surface state and further tuned by electrical top gating. We observed a crossover between WAL and WL, as well as the systematic emergence of the AHE with varying temperature and gate voltage, interpreted as a result of a gap opening in the Dirac surface state due to the TR symmetry breaking by the exchange coupling between the TI surface state and the adjacent (Ga,Mn)As. The results suggest that the systematic changes in MC and AHE can be used as indirect probes to estimate the position of the chemical potential E_{F} and the opening of a magnetic gap in the surface state. Our study also identifies a valuable new model quantum material for systematic explorations of topological phenomena in the presence of broken TR symmetry. A full exploitation of this platform will require optimization of the TI/(Ga,Mn)As interface, a key measure of which would be the observation of a robust hysteresis in the AHE.
Methods
Experimental techniques
Longitudinal resistance of a topgated (Bi,Sb)_{2}(Te,Se)_{3}/(Ga,Mn)As Hallbar device (above 0.29 K) was measured as a function of gate voltage and temperature in an Oxford Heliox Helium3 cryostat inserted into a liquid Helium dewar equipped with a superconducting magnet. Magnetotransport measurements at temperatures <0.29 K were carried out using a dilution refrigerator in a Physical Property Measurement System from Quantum Design. Longitudinal channel resistance and Hall resistance were simultaneously measured using standard lockin technique with an alternating current excitation current of 200 nA and a low frequency of 19 Hz.
Magnetization measurements of the (Bi,Sb)_{2}(Te,Se)_{3}/(Ga,Mn)As heterostructure were performed using a Quantum Design superconducting quantum interference device. A magnetic field perpendicular to the sample surface was applied to investigate the perpendicular component of magnetization, revealing a Curie temperature of 50 K.
For microstructural characterization, a crosssectional lamella of a topgated Hallbar device of the (Bi,Sb)_{2}(Te,Se)_{3}/(Ga,Mn)As heterostructure was prepared by a focused ion beam (FEI Quanta 200 3D). The lamella was cleaned in an oxygen plasma cleaner to minimize contamination and then transferred into an FEI Titan G2 TEM system. Highangle annular dark field scanning TEM was used for structural analysis of the (Bi,Sb)_{2}(Te,Se)_{3}/(Ga,Mn)As heterostructure, and chemical information of elemental composition of each layer as well as elemental mapping of the whole structure was characterized by EDS.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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Acknowledgements
This work was supported in part by DARPA and CSPIN, one of the six centers of STARnet, a Semiconductor Research Corporation program, sponsored by MARCO and DARPA. N.S. and A.R. acknowledge additional support from ONR grant N000141512370 and C.x.L. from ONR grant N000141512675 and ONR renewal No. N000141812793).
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J.S.L., A.R., and N.S. conceived the project. J.S.L. conducted material characterization, device fabrication, and transport measurements. A.R. synthesized the material. A.R. and R.D.F. conducted SQUID measurements. C.x.L. performed the numerical calculation. J.S.L. and C.x.L. analyzed the results. W.Z. helped with transport measurements. J.S.L and N.S. wrote the manuscript. All authors discussed the results and contributed to the final manuscript.
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Correspondence to Nitin Samarth.
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Further reading

Observation of Interfacial Antiferromagnetic Coupling between Magnetic Topological Insulator and Antiferromagnetic Insulator
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