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Scientific Reports Volume 6, Article Number: 21334 (2016) Cite this article

Many of the exotic physics expected in topological insulators need to break the time reversal symmetry to open gaps for their topological surface states. The gap opening is achieved by doping with magnetic impurities, however, this will inevitably generate additional carriers and disorder, thereby disrupting electron transport. In contrast, proximity to ferromagnetic/ferrimagnetic insulators can improve device quality, so it is expected to provide a better way to open the gap while minimizing side effects. Here, we use van der Waals epitaxy technology to grow thin single crystal Sb1.9Bi0.1Te3 microflakes on insulating ferrimagnet BaFe12O19. Microflakes show negative magnetoresistance in a weak vertical field below 50 K, which can be quenched by increasing the temperature. The signature implies that the weak localization effect is its origin, which does not exist in inherent topological insulators unless the surface state gap is opened. The surface state gap is estimated to be 10 meV by using gap-induced weak localization effect theory. These results indicate that the magnetic proximity effect may open the gap connected to the topological surface of the BaM insulating ferrimagnet. This heterogeneous structure may pave the way for the realization of new physical effects and the potential applications of spintronic devices.

The gap opened for the surface state by breaking the time reversal symmetry in the topological insulator is expected to carry many new physics1,2,3,4,5,6,7,8. Experimentally, the gap can be achieved by magnetic doping 9,10,11,12,13,14,15 or by magnetic proximity to the ferromagnetic insulator 16,17,18. One of the characteristics of the gap opening is the weak positioning effect 19. This effect can produce positive low-field permeability 19, 20, 21, 22 at low temperatures. In contrast, for the gapless surface state, the π Berry phase always leads to weak reverse positioning and associated negative permeability 23, 24, 25, 26. However, in actual samples, magnetic doping inevitably introduces magnetic scattering centers, defects, and magnetic clusters, resulting in surface phase and bulk phase mixing in magnetic transmission27,28. Therefore, it is difficult to distinguish magnetically doped topological insulators from dilute magnetic semiconductors. In the latter, weak localized permeability can also be expected, not due to gaps in surface states. Compared with magnetic doping, the magnetic proximity effect may also cause gaps in the surface states of topological insulators. If the Curie temperature of the ferromagnetic insulator is high enough, a higher Curie temperature magnetic sequence can be achieved in the heterostructure of topological insulator and ferromagnetic insulator. In addition, topological insulator-ferromagnetic insulator heterostructures are expected to suppress external magnetic impurities and magnetic clusters; therefore, gaps that induce topological surface states may be better experimental candidates. Many heterostructures 29,30,31,32,33,34 and different ferromagnetic insulator substrates have been studied, such as EuS30,31, yttrium iron garnet 29,33, GdN32 and BaFe12O19 (BaM)34. In the experiment, only the weak reverse positioning effect with negative permeability was achieved. The suppressed weak antilocalization cannot be clearly attributed to gap opening, because random magnetic scattering can also induce the suppression of weak antilocalization19,26. In the Bi2Se3-EuS heterostructure, the Bi2Se3 layer is thinner than 4nm31, which proves the negative magnetoresistance in the low field. However, it is not enough to conclude that magnetic proximity does open the gap, because the finite size effect can also open the gap 35 in the film and cause a weak localization effect 22. Recently, low-field positive permeability has been observed in the Bi2Se3-BaM heterostructure in a parallel magnetic field, but the perpendicular permeability is still negative. In a very weak parallel field, the domain wall may be the possible origin of the permeance of the positive parallel field. Most heterostructures are manufactured by molecular beam epitaxy (MBE), and the size of these heterostructures is much larger than the magnetic domains of ferrimagnetic insulators. Therefore, a large number of Dirac electrons are expected in the magnetic domain region, but remain massless at the domain walls. The domain wall can suppress the conductivity 28; then a positive permeability is generated when the magnetic field removes the domain wall.

In this work, we fabricated BaFe12O19-Sb1.9Bi0.1Te3 heterostructures using van der Waals epitaxy technology. The size of the topological insulator flakes can be controlled to be comparable to the magnetic domains of BaM. In a vertical magnetic field, positive permeability, which may be related to weak local effects, is observed, indicating that magnetic proximity opens a gap for the surface state of topological insulators. Parallel field permeability shows negative permeability near zero field, because the in-plane magnetization of BaM cannot open the gap of surface states. Using the permeance formula that competes between weak antilocalization and weak localization effects, we fit the permeance curve in the vertical field and find that the surface gap Δ caused by magnetic proximity is about 10 meV. Our results show that magnetic proximity can break the time reversal symmetry and open a considerable gap for the surface state of topological insulators. Therefore, this topological insulator-BaM heterostructure may pave the way for further experimental research on new physics and potential applications of spintronic devices.

Hexagonal BaFe12O19 is a well-known ferrimagnetic insulator with uniaxial anisotropy along the c crystal axis. The magnetic domain structure of single crystal BaM has been verified by the positive and reverse magnetic domains along the c-axis under different magnetization directions. The size of the magnetic domain is about 5 μm. When the magnetic field is tilted from the c axis to the ab plane, these domains exhibit maze, fringe, and honeycomb patterns36,37. We prepared BaM single crystal by the floating zone method. We chose a large and flat single crystal with a natural cleavage plane (0001) as the ferrimagnetic insulator substrate. Figure 1(a) shows the magnetization of BaM substrate measured by the magnetic measurement system, where M is the magnetic moment and MS is the saturation magnetic moment. The saturation magnetization field HS of BaM along the in-plane (perpendicular to the c-axis) and out-of-plane directions are 1.5 T and 0.5 T, respectively. When the temperature increases from 2 K to 50 K, there is no significant change in HS in both directions. Since the domain walls move freely in response to changes in the external field, no obvious hysteresis is observed under low fields.

(a) Magnetic moment of single crystal ferromagnetic insulator BaFe12O19 (BaM). The out-of-plane and in-plane magnetic moments are represented by "||". c" and "⊥ c", respectively. When the temperature increases from 2 K to 50 K, the magnetic moments in the two directions do not change. Illustration: XRD pattern of single crystal BaM. Only the ( 00l) Peak. (b) RT curve of BaM substrate only and heterostructure of topological insulator and BaM. Illustration: Scanning electron microscope image of Sb1.9Bi0.1Te3-BaFe12O19 heterostructure with current (I and I- ) And voltage (V and V-) probes. White dots are excess tellurium particles generated during cooling. The warped edges show a large lattice mismatch between Sb1.9Bi0.1Te3 and BaFe12O19. The scale bar is 10 μm.

Van der Waals epitaxy is an easy way to grow high-quality nanostructures on clean substrate surfaces without having to consider large lattice mismatches39,40. In this way, we successfully fabricated the Sb1.9Bi0.1Te3-BaM heterostructure in a 1-inch horizontal tube furnace through a catalyst-free gas-solid (vs) growth technology similar to that in the reference. 41. We choose the stoichiometric Sb1.9Bi0.1Te3 because it can effectively raise the position of the Dirac point beyond the body valence band, and at the same time adjust the Fermi level 42 in the body gap through charge compensation. The inset of Figure 1(b) shows a scanning electron microscope (SEM) image of Sb1.9Bi0.1Te3 nanosheets on a BaM substrate. The warped edges of the nanoplates indicate a large lattice mismatch between Sb1.9Bi0.1Te3 and BaM. The white spots on the Sb1.9Bi0.1Te3 nanoplate are the excess tellurium produced during the cooling process. Figure 1(b) shows the RT curve of the heterostructure and BaM substrate. BaM is a ferrimagnetic insulator with high room temperature resistance. After growing a topological insulator on BaM, the resistance of BaM drops to 200 Ω at 300 K, indicating that BaM becomes conductive after being annealed at around 300 °C for 1 hour. When the temperature drops to 125 K, the resistance of BaM increases sharply. On the contrary, the resistance of the heterostructure increases slowly as the temperature decreases. For example, when T = 100 K, the resistance of the BaM substrate reaches more than 2 × 106 Ω, which is 100 times the resistance of the heterostructure. This high resistance indicates that when T <100 K, the current mainly flows through the topological insulating film. Here, the temperature range we are interested in is below 55 K, when the BaM substrate becomes a complete insulator.

We measured the permeability of our samples by standard four-probe transmission measurement. Figure 2(a) shows the permeability of the Sb1.9Bi0.1Te3-BaM heterostructure at different temperatures in a vertical magnetic field. We observe positive permeability (ie, negative magnetoresistance) in vertical fields up to 7 T at low temperatures. The positive permeability decreases with the increase of temperature, and finally when the temperature rises to 50 K, the permeability exhibits a mixed behavior from the positive of the low field to the negative of the high field. In a vertical field, the classical permeance caused by the Lorentz force always gives a negative permeance (positive magnetoresistance). In a strong disorder state, transmission can exhibit negative magnetoresistance 43, but it requires conductivity. At 2 K, the conductivity of our heterostructure is somewhere in between, rather than being in a strong disordered state. The positive permeance here is probably the result of the weak local effect of the gapped surface state, and therefore has the origin of quantum interference. As the temperature rises to T = 55 K, the permeability becomes completely negative. The magnetization of our BaM substrate does not change significantly around 50 K. Therefore, the sign change of permeability observed around 50 K is not due to the closure of the gap and the disappearance of the magnetization, but may be because the temperature quenches the quantum interference. Then the classic permeance becomes unstoppable. For comparative study, we also grow Sb1.9Bi0.1Te3 on SiO2 substrate. As shown in Figure 3(a), the vertical field permeability of Sb1.9Bi0.1Te3 on the SiO2 substrate shows a sharp peak near the zero field. Due to its quality as a massless Dirac fermion, the tip is a typical feature of the weak antilocalization effect of topological surface states.

(a) In a vertical magnetic field. (b) In a parallel magnetic field. The solid line within 1 T in (a) is the curve fitted using the equation. (2). For clarity, the data curves at different temperatures are shifted.

(a) Comparison of the magnetic permeability of the control sample (topological insulator on SiO2) and the topological insulator on BaM in the vertical field at 2 K. The black curve is the experimental data, and the red curve is the fit. Fitted yield = 135 nm. (b) Hall resistance of topological insulators grown on SiO2 and BaM substrates, respectively.

Functionally, the permeability of weak anti-localization and weak localization effects can always be fitted by the Hikami-Larkin-Nagaoka (HLN) formula,

Where is the digamma function. The pre-factor α and the phase coherence length are used as two fitting parameters. However, the HLN formula cannot give information about gap opening. In order to quantitatively study the gap opening of the surface state, we adopted the permeability formula derived from the weak delocalization-localization crossover of a large number of Dirac fermions,

Where the magnetic length,,,,, is an explicit function of Δ/2EF (see method), where Δ is the gap between the surface states and the Fermi level measured from the Dirac point. Under the weak anti-localization limit,,, and under the weak localization limit,,. When the mean free path is much smaller than the length of the magnetic field, equation (2) is valid. We use formula (2) to fit the permeability in the vertical field. The solid line in Figure 2(a) is by using equation (2). Figure 4(a) is the fitting result of Δ/2EF with temperature. When T=2K, Δ/2EF is about 0.329. As the temperature increases, Δ/2EF decreases. When T=50, K, Δ/2EF = 0.304, the change is less than 10%. These Δ/2EF values ​​are in the range between the unitary symmetry class and the orthogonal symmetry class, where the weakly localized effect of suppression can produce positive permeability19. Experiments 45, 46, the higher Fermi energy in the topological insulators Bi2Se3 and Bi2Te3 may greatly reduce the Δ/2EF, and according to the theory, only lead to weak magnetic permeability similar to delocalization19.

(a) Fitted Δ/2EF as a function of temperature, where Δ is the gap between the surface states and is the Fermi level. Illustration: Schematic diagram of the energy band structure of a topological insulator on BaM. Body conduction band, body valence band and surface state are denoted by BCB, BVB and SS, respectively. (b) The fitted phase coherence length is suppressed as the temperature increases. The relative change of Δ/2EF with temperature is much smaller than the change of phase coherence length. The fitting is performed by using equations. (2).

To evaluate the surface gap, we use the 2D carrier density obtained from the Hall measurement to estimate the Fermi level. By measuring the Hall resistance of two similar devices on SiO2 and BaM substrates, as shown in Figure 3(b), we have obtained the Hall resistance on SiO2 and BaM substrates. According to the ARPES data in Reference 42, the carrier density value means that the Fermi energy is located at the bottom of the bulk conduction band, about 0.1-0.2 eV from the Dirac point of the surface state. We estimate that the magnitude of the surface state gap caused by magnetic proximity is

As shown in Figure 4(b), as the temperature increases, the fitted phase coherence length is reduced by half, from 28 nm at 2 K to 14 nm at 50 K. Compared with Δ/2EF, it shows Stronger temperature dependence. Therefore, the fitting results show that the reduction of the phase coherence length is the main reason why the weakly localized positive permeability in Fig. 2 is suppressed.

We also show the permeability data in the parallel field in Figure 2(b). The positive permeability can still be identified in the high field range, but deflection occurs near 1.5 T, and the permeability becomes negative near the zero field, as shown in Figure 2(b). The negative permeability near the zero field indicates that the surface state in the parallel magnetic field has no gap opening. There is no gap because when an external magnetic field is applied in the in-plane direction, the spin of the BaM substrate will rotate to the in-plane direction. Accordingly, the surface state of the topological insulator remains gap-free. As the temperature rises to 30 K, the deflection of the permeability curve weakens and disappears at 50 K. This deflection behavior is also observed in the magnetically doped topological insulator 47 and undoped ultra-thin topological insulator films 22, 48, 49. Theoretically, if the permeability curve is deflected, the permeability is contributed by multiple channels. In addition to the surface state, the body state may contribute to the transmission 50, 51. In the topological insulator ultrathin film, this can be well explained by the 2D modified Dirac model35, while in our heterostructure, the thickness of the topological insulator nanoflake is about 20 nm, which is less than the ultrathin limit (<5 nm) Much thicker. In addition, in a parallel field, the observed permeance deflection occurs at 1.5 T. At this time, the weak field limit of weak anti-localization and weak localization effects (usually within 0.5 T) has been violated. The permeability observed in the parallel field cannot be explained by the competition between weak delocalization and weak localization. The mechanism of the deflection of the parallel field permeance is currently unclear. One possible explanation is similar to that in Reference 28, where the domain wall suppresses the conductivity, and the magnetic field may gradually remove the domain wall, resulting in positive permeability at high fields. The size of our heterostructure is comparable to that of a single magnetic domain in BaM, but the observed deflection cannot be explained by this mechanism. Another possible explanation is related to the magnetization tilt discussed in References 29 and 30. When the parallel field is greater than 1.5 T, the magnetization of BaM is saturated in the in-plane direction. Due to the strong spin-orbit coupling and the large anisotropy of the Lande g-factor of the interface electrons, an out-of-plane magnetization tilt may be formed at the interface of our heterostructure 29,30. The surface state gap may also be opened obliquely by magnetization in the high field range. In addition, we can see in Figure 2 that the Δσ caused by the magnetization tilt is much smaller than the vertical magnetic field direction.

The magnetic proximity effect is usually short-range, especially for materials with weak spin-orbit interactions. If the ferrimagnetic substrate cannot affect the top surface, the resistance should not change significantly. However, in our Figure 1(b), the resistance has increased by an order of magnitude because the SiO2 substrate is replaced by the ferrimagnetic BaFe12O19. Considering that the resistance of BaFe12O19 is several orders of magnitude higher, the increase in resistance is not caused by BaFe12O19 alone, but is likely to come from the topological insulator film under the influence of the long-range magnetic proximity effect. One of the possible reasons for the long-distance proximity effect is strong spin-orbit coupling. It has been shown that the magnetic proximity effect can cause significant negative magnetoresistance in the platinum film attached to the ferrimagnetic insulator YIG, and the film thickness can reach 14 nm52. The topological insulator Sb1.9Bi0.1Te3 also has strong spin-orbit coupling, so the magnetic proximity between Sb1.9Bi0.1Te3 and BaFe12O19 may also be long-range. In the device used for Hall bar measurement in Figure 3(b), the thickness of the topological insulator is 30 nm. In the Hall bar device, we did not observe negative magnetoresistance, which may be due to poor interface contact or thick topological insulating layer.

The mixed powder of Sb2Te3 and Bi2Te3 with a molar ratio of 19:1 is placed in the hot center of the tube furnace. The hexagonal BaM single crystal with clean cleavage surface (0001) is placed about 9-12 cm from the thermal center. Clean the tube 5 times with ultra-pure Ar gas before growth, and then fix the Ar gas flow rate at 50sccm. To avoid tellurium escape, heat the thermal center to 475°C within 5 minutes and keep it at this temperature for one hour, and then naturally cool down. Throughout the process, we kept the pressure inside the tube at 2.8 Torr. Only when the substrate is placed 11.5 cm away from the thermal center can we obtain high-quality van der Waals epitaxial heterostructures of topological insulators and ferromagnetic insulators.

In order to fabricate standard four-probe devices on topological insulator-BaM heterostructures for transmission measurement, we transferred the heterostructures to the FEI SEM/FIB dual-beam system to deposit Pt electrodes. The four Pt strip electrodes have a nominal width of 0.8 μm and a thickness of 200 nm. They are deposited from the precursor gas of (methylcyclopentadienyl)trimethylplatinum (CH3)3CH3C5H4Pt. In order to avoid Pt pollution and Ga ion radiation, we designed the distance between two adjacent electrodes to be greater than 2 μm. Throughout the manufacturing process, we only use electron beams to guide Pt deposition.

We use equation (2) to fit the permeability in the vertical magnetic field. The parameters in equation (2) are defined as

Where is the mean free path,,, and. We assume that the effect of random magnetic scattering is to reduce the phase coherence length and is included in the definition.

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Thanks to Murong Lang for the fruitful discussion. This work was supported by the National Natural Science Foundation of China (approval numbers: 11174294, 11374302, 11574127, U1432251, and U1332209), the Excellent User Program, the Hefei Science Center of the Chinese Academy of Sciences, and the CAS/SAFEA Innovation International Cooperation Program. Chinese research team.

Zheng Guolin and Wang Ning: These authors made the same contribution to this work.

Strong Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031

Zheng Guolin, Wang Ning, Yang Jiyong, Wang Weike, Du Haifeng, Wei Ning, Yang Zhaorong, Zhang Yuheng and Tian Mingliang

University of Science and Technology of China, Hefei 230026

Zheng Guolin, Wang Ning, Yang Jiyong, Wang Weike, Du Haifeng, Wei Ning, Yang Zhaorong, Zhang Yuheng and Tian Mingliang

Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing 210093

Yang Zhaorong, Zhang Yuheng, Tian Mingliang

Department of Physics, Southern University of Science and Technology, Shenzhen, China

Hefei Science Center, Chinese Academy of Sciences, Hefei 230031, Anhui, China

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GZ, NW, HZL and MT conceived and designed the experiment. GZ and NW synthesized samples and manufactured equipment. Transmission measurements were performed for WN, HD, JY, WW, and ZY. HZL, GZ, MT and YZ provide analysis and theoretical explanations. GZ, HZL, and MT wrote this paper with the assistance of all co-authors.

Communication to Haizhou Road or Tian Mingliang.

The author declares that there are no competing economic interests.

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Zheng, G., Wang, N., Yang, J. etc. Weak localization effect of topological insulator microflakes grown on insulating ferrimagnet BaFe12O19. Scientific Report 6, 21334 (2016). https://doi.org/10.1038/srep21334

DOI: https://doi.org/10.1038/srep21334

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