Large anomalous Hall effect in ferromagnetic insulator-topological insulator heterostructures

Introducing a magnetic exchange gap into the Dirac spectrum of a topological insulator (TI) surface generates circumferential, half-integer quantum Hall states.^1–4 Recently, independent experimental groups^5–7 have detected the quantum anomalous Hall effect (QAHE) in thin films of magnetically doped topological insulators, in which the upper and lower surfaces are ferromagnetically gapped. However, the host TI materials are disordered due to the extreme concentration of magnetic dopants, which may contribute to the milli-Kelvin temperature scale at which the QAHE is observed and the reported sensitivity of the effect to fabrication details.⁵ In contrast, introducing ferromagnetism into the TI surface by proximity to a ferromagnetic insulator (FI) leaves the TI ordered and can break time reversal symmetry without directly alloying the TI with magnetic elements. To date, epitaxy of TI-FI systems has been investigated using the FI materials EuS, GdN, and Y₃Fe₅O₁₂.^8–11 As compared to the layered TI crystal structure, these FI compounds possess 3D structures (e.g., the NaCl-type structure in the case of EuS) producing radicals at a TI-FI interface. To create a pristine interface, a FI compound is sought with a stable, lattice-matched surface. The strong anisotropy of the Bi₂Te₃ crystal structure causes films to grow in the [001] direction, further constraining the problem by requiring a match to that lattice plane.

Here, we employ the ferromagnetic insulator Cr₂Ge₂Te₆ (CGT) as a substrate for the growth of Bi₂Te₃, a standard TI material.^12–14 Like Bi₂Te₃, the CGT structure consists of layered units terminated with hexagonal Te planes. While Bi₂Te₃ consists of quintuple layers (QL) made of five alternating layers of Te and Bi, the layered units of CGT are narrower triple layers (TL), in which two hexagonal Te planes surround a layer of Cr ions and Ge pairs. In both crystals, van der Waals bonds join adjacent planes of Te [see Fig. 1(a)]. The hexagonal lattice of Te in CGT has a lattice constant of 3.94 Å (=1/2 the lattice constant of the full cell), which we show below to be a good match to that of the Te surface of Bi₂Te₃ when rotated by 30° (4.39 Å) and similarly to the Se surface of Bi₂Se₃ (4.14 Å).¹⁵ In addition to this fortuitous crystal structure, CGT has a relatively high Curie temperature of 61 K, a resistivity greater than 10³ Ω cm below 77 K, and an easy axis of magnetization that points along the c-axis in bulk crystals.¹³ Taken together, these factors favor the study of the CGT-Bi₂Te₃ (CGT-BT) system for the introduction of ferromagnetic order in TIs. Through Hall measurements, we show that the magnetization of CGT has a large impact on electrical transport through the Bi₂Te₃ layer.

To form CGT-BT heterostructures, we first grow large single crystals of CGT.¹³ We mix high purity Cr (99.99%), Ge (99.999%), and Te (99.999%) in a molar ratio of 2:6:36, where the Ge and Te excess acts as flux. The mixture is heated to 700 °C for 20 days and cooled to 500 °C over 36 h, followed by centrifugation to separate the CGT crystals from the flux. The CGT crystals are then annealed in vacuum to remove any residual Te flux. Flat single crystals with sizes ranging from 0.5 to 3 mm can be manually isolated from the product. X-ray diffraction, transport measurements, and magnetization measurements confirm that the samples are single crystal (with space group $R3¯$⁠), insulating (E_g = 0.2 eV), and ferromagnetic (T_C = 61 K).^12,13

We grow the Bi₂Te₃ layer using metal organic chemical vapor deposition (MOCVD).¹⁶ CGT is prepared for epitaxy using two different methods. We either adhere ∼500 μm CGT squares to a SiO₂ carrier chip using polyimide or exfoliate mesoscopic crystals of CGT onto a SiO₂ chip using the scotch tape method.¹⁷ In both cases, the process prepares a freshly cleaved CGT surface prior to Bi₂Te₃ deposition. To initiate growth of Bi₂Te₃, the CGT substrate is heated to 280 °C in a 600 sccm flow of H₂ (6 N) at 100 Torr. Tellurium and bismuth are introduced into the growth chamber by flowing hydrogen gas through diisopropyl telluride (DiPTe) and trimethyl bismuth (TMBi) bubblers, resulting in partial pressures $pTMBi=7×10−6$ atm and $pDiPTe=2.8×10−5$ atm. The precursors thermally decompose at the sample, producing atomic Bi and Te. After 2700 s, the TMBi flow is stopped, terminating growth, and the sample is cooled to $125 °C$ under continued DiPTe flow.

Cross-sectional transmission electron microscope (TEM) imaging allows for a direct characterization of the heterostructure (see Fig. 1). In cross-section, the layered units of the two crystal structures are directly visible, indicating that the Te layers are stacked along the growth direction. The TEM images displayed in Figs. 1(b)–1(c) show that the interface between the two structures occurs over a distance of less than 1 nm. We attribute the high quality interface to the similarity of the two crystal structures.

Electron diffraction is used to determine the relative orientation of the Bi₂Te₃ and CGT layers. The indexed diffraction pattern is shown in Fig. 2(b). By comparing with simulated diffraction patterns, we confirm precise alignment of the Bi₂Te₃ and CGT (001) axes. Additionally, Bi₂Te₃ (110) is parallel to CGT (100). As illustrated in Fig. 2(a), this orientation corresponds to an alignment of the interfacial Te planes. Although TEM demonstrates the alignment locally, electron backscatter diffraction (EBSD) can be used to compare the Bi₂Te₃ orientation across the entire film surface. An illustration of the method is shown in Fig. 2(c), where EBSD patterns from a micron-sized Bi₂Te₃ island and the surrounding CGT are automatically indexed, showing a 30° relative rotation of the unit cells, consistent with the TEM diffraction results. Similar analysis at many points on the Bi₂Te₃ film surface shows this registry to be a global feature of the CGT-BT films.

Transport measurements are performed on the CGT-BT heterostructures. We electrically contact two types of heterostructures: (a) macroscopic Bi₂Te₃ films grown on squares of CGT ∼ 500 μm wide and ∼10 μm thick (similar to those studied with TEM) and contacted with silver paint following the van der Pauw method, and (b) mesoscopic CGT-BT bilayers formed by exfoliation of CGT on a SiO₂ substrate followed by Bi₂Te₃ deposition, which produces a ∼150 nm thick layer of Bi₂Te₃ on a ∼50 nm thick CGT layer, with lateral dimensions of tens of microns. We use electron beam lithography (EBL) to define six Ti/Au contacts to each mesoscopic sample for measurements of the longitudinal and Hall resistance. Control devices consisting of EBL-contacted exfoliated CGT on SiO₂ and MOCVD Bi₂Te₃ on SiO₂ are studied in parallel with the CGT-BT heterostructures. The Bi₂Te₃ control samples were fabricated from Bi₂Te₃ islands that grew near the CGT-BT platelets (on the same chip) and measured in the same cryostat to exclude any extrinsic origin to the AHE measured in the CGT-BT samples.

Longitudinal resistance R_xx is measured as a function of temperature to distinguish metallic (insulating) contributions from Bi₂Te₃ (CGT). Whereas all Bi₂Te₃ control samples studied show metallic $Rxx(T)$ characteristics, the resistances of the CGT control samples (pre- and post-EBL) show thermally activated behavior with an energy gap of 0.2 eV, as shown in Fig. 3(a). For the CGT-BT bilayer, we construct a parallel resistor model by summing the Bi₂Te₃ and CGT conductivities

From the sample of Fig. 3(b), we extract R_0,BT = 2140 Ω, a = 1.4 Ω/K, R_0,CGT = 65 Ω, and gap energy E_g = 0.14 eV. The corresponding room temperature resistivities of the two layers of this sample (width = 200, length = 500 μm, Bi₂Te₃ thickness = 30 nm, CGT thickness = 10 μm) are ρ_CGT = 40 mΩ cm and ρ_BT = 0.3 mΩ cm, in agreement with the typical values for both materials in the literature.^12,14 The model gives a Bi₂Te₃ conductivity that is more than 1000 times greater than CGT at temperatures below 78 K in this sample. All other samples have thinner CGT and therefore smaller contributions of the CGT to the conductivity. At 4.2 K, the three Bi₂Te₃ control samples show resistivities ranging from 0.40 to 1.1 mΩ cm, while the five CGT-BT samples show resistivities in the range of 0.3–6.2 mΩ cm, with a mean resistivity of 2 mΩ cm. The similarity of the resistivity of the CGT-BT bilayers to Bi₂Te₃ control samples fabricated on SiO₂ indicates that transport in the CGT-BT samples occurs primarily in the Bi₂Te₃ layer.

We study magnetotransport in one CGT-BT film and in four mesoscopic CGT-BT samples, with similar results in all cases. As shown in Fig. 3(c), the Bi₂Te₃ control samples (and Bi₂Te₃ samples generally) show either a linear Hall resistance (R_xy) or a linear Hall resistance with superimposed Shubnikov de Haas (SdH) oscillations in the case of high mobility samples.^14,18 In contrast, the heterostructures all show a nonlinear Hall resistance but without large oscillations. The nonlinearity decreases with increasing temperature, as shown in Fig. 3(d). Whereas the Bi₂Te₃ control samples show sharp antilocalization features, the CGT-BT magnetoresistance R_xx(B) does not.¹⁶ The inset of Fig. 4(a) shows a typical example of R_xx(B). Strong magnetic dephasing may suppress localization effects in the bilayer samples.¹⁹ 

In addition to the high field nonlinearity, the CGT-BT heterostructures exhibit a hysteretic AHE at low fields, as shown in Fig. 4. The hysteresis is absent in all control samples consisting only of CGT or Bi₂Te₃. The hysteresis observed in the CGT-BT samples is suggestive of a ferromagnetic origin. As shown in Fig. 4(b), the magnetoresistance, R_xx, also displays hysteresis, with peaks at the coercive fields. Tilted field measurements show that the coercive field of the hysteresis loop increases and the background Hall contribution falls off linearly as the field is rotated into the plane of the CGT-BT interface. The dependence is consistent with the easy axis of the ferromagnet pointing along the c-axis, as observed in several layered ferromagnets.^13,20,21

The coercive field of the hysteresis observed here, which is ∼0.1 T at low temperatures, is similar to the field required for saturation of bulk CGT (0.26 T). However, bulk measurements found the width of the magnetization loop to be narrower than 0.01 T, while we observe a substantial hysteresis loop in the AHE of CGT-BT heterostructures. The apparent hardening of the magnetization is consistent with recent measurements of EuS-Bi₂Se₃ heterostructures, where the authors attributed the increase in the observed perpendicular anisotropy to exchange coupling between the TI and FI layers.¹¹ The persistence of the hysteresis to ∼110 K, which is considerably above the known Curie temperature of bulk CGT (61 K), is also surprising.

We consider two origins of the observed high field nonlinear Hall effect. The first model considers the AHE, with the nonlinearity due to a magnetic origin. The second picture relies on a two-band model of transport, with multiple conduction channels of differing mobility. Both models result in nearly identical predictions for $Rxy(B)$⁠.

The AHE, as observed in magnetic conductors, correlates strongly with the magnetization, leading to the conventional representation $Rxy=RsMz+R0B/μ0$ where M_z is the out-of-plane component of the magnetization, R_s is the anomalous Hall coefficient, B is the external applied field, and R₀ is the ordinary Hall coefficient.^22–24 In magnetic conductors, nonlinearity originates in M(B) which often exceeds the linear component (⁠$Rs≫R0$⁠) to the extent that R_xy appears to saturate at accessible fields, as in Fig. 3(c).²² Studies of EuS-Bi₂Se₃ ascribe a similar, but smaller (⁠$Rs≪R0$⁠) Hall nonlinearity to a ferromagnetic AHE, since it correlates clearly with the Brillouin dependence of the magnetization of EuS.¹¹ In contrast, the nonlinear Hall effect in CGT-BT does not reflect the typical M(B) of CGT. Magnetization measurements show that CGT saturates at fields below 0.3 T, while here we observe saturation at ∼6 T. However, it is possible that ferromagnetic order within the CGT is strongly modified near the interface, where it would contribute most to the Hall effect.

Alternatively, the presence of parallel conduction channels with differing mobilities but comparable overall conductance will produce a similar nonlinearity, as observed in many heterojunction systems.^14,25,26 The CGT bulk is insulating at low temperatures, so any conduction channels lie in the Bi₂Te₃ bulk or at the CGT-BT interface. In the two-band model, the measured Hall resistance depends on the magnetic field as

where n_i are the two-dimensional carrier densities, μ_i are the mobilities, and e is the carrier charge.²⁶ This model nicely fits the data [see fits plotted in Fig. 3(c)] and implies a high mobility, low density (HMLD) channel and a low mobility, high density (LMHD) channel of the same sign (n-type) in all samples. Due to variations in film thickness and roughness, n_i and μ_i vary within one order of magnitude from sample to sample, and we consider the mean values for discussion. At 4.2 K, the mean 2D carrier densities are n_LMHD = 5 × 10¹⁵cm⁻² and n_HMLD = 6 × 10¹³cm⁻² and the mean mobilities are μ_LMHD = 200 cm²/V s and μ_HMLD = 7000 cm²/V s. The samples with the highest μ_HMLD obtained from the fits (40 000 cm²/V s) far exceed the highest known mobility for Bi₂Te₃. However, large SdH oscillations are not observed in any of the CGT-BT samples.

One of the channels is consistent with bulk transport through the Bi₂Te₃ layer. The fit parameters of the LMHD channel are similar to those extracted from the Bi₂Te₃ control samples. The mean carrier density of the LMHD channel is n_3D = 3 × 10²⁰cm⁻³ a value typical of strongly doped Bi₂Te₃ and close to the control samples n_3D = 4 × 10¹⁹cm⁻³. The mobility of this channel (200 cm²/V s) is also similar to the control samples (400 cm²/V s). While the LMHD channel is consistent with bulk Bi₂Te₃ conduction, the second high-mobility channel suggested by the two-band model could only originate from the interface between the two materials, since it is absent in either type of control sample. In principle, a HMLD channel could be present at the interface, but this does not explain the noted absence of SdH oscillations.

We demonstrate ferromagnetic coupling in a TI-FI heterostructure with a high level of crystalline order. To date, hysteretic AHE has not been observed in TI-FI heterostructures. The large magnitude of both the hysteretic AHE and the high field nonlinearity in this system make this an exciting development for realizing more complex experiments based on TIs. The hysteretic AHE reflects the bulk properties CGT, while the high-field nonlinearity implies that either an additional type of magnetic order impacts transport through the Bi₂Te₃ or a high mobility state arises at the interface. Tuning the Fermi energy of the Bi₂Te₃ by applying a gate potential through the CGT layer would do much to clarify the properties of the AHE and reduce bulk conduction in the Bi₂Te₃. It is likely that heterostructures with more insulating Bi₂Te₃ and therefore greater sensitivity to the interface will display still further enhanced AHE.

We thank Tian Liang and Phuan Ong for valuable discussions. This work was supported by the Packard Foundation, the National Science Foundation through the Princeton Center for Complex Materials (No. DMR-0819860), and the Eric and Wendy Schmidt Transformative Technology Fund.