Quantum anomalous Hall effect driven by magnetic proximity coupling in all-telluride based heterostructure

A three-dimensional topological insulator (TI) is a nontrivial state of matter, hosting insulating bulk and conducting surface states, as protected by time-reversal symmetry.^1,2 The breaking of time reversal symmetry at the surface states of a TI leads to the formation of an exchange gap and the emergence of chiral edge states, which gives the quantum anomalous Hall effect (QAHE) with the quantized Hall resistance to h/e² (h is Planck's constant and e is the elementary charge) when the Fermi level (E_F) is tuned within the exchange gap [Fig. 1(a)].^3–5 Regarding the emergence of chiral edge channels, the QAHE is phenomenologically equivalent to the integer quantum Hall effect (IQHE) which occurs under a magnetic field,⁶ but is different in the microscopic mechanism of gap formation: the Landau level splitting by cyclotron motion of carriers for the QHE vs the magnetic exchange interaction for the QAHE. The distinct nature of the QAHE that does not require an external magnetic field has unveiled unique quantum transport phenomena based on chiral edge states, such as the manipulation of edge conduction at magnetic domain walls and the detection of chiral Majorana edge modes realized by the interplay with superconductivity.^7,8

The QAHE has been studied so far in TIs doped with magnetic elements such as Cr- and V-doped (Bi,Sb)₂Te₃ (Refs. 4, 9, and 10), in which the gap formation and the E_F tuning into the gap are to be simultaneously fulfilled. The magnetic proximity effect has been proposed as one other promising mechanism to induce the QAHE [Fig. 1(b)].¹ When a nonmagnetic TI contacts with a ferromagnetic insulator (FMI) whose magnetic moment is perpendicular to the interface, the magnetic exchange interaction via the interface can open an exchange gap at the surface state of the TI. To date, the proximity coupling has been exemplified in several FMI [e.g., EuS, GaN, Y₃Fe₅O₁₂ (YIG), and Tm₃Fe₅O₁₂ (TIG)]/TI heterostructures with the observation of the anomalous Hall effect (AHE).^11–15 Although these heterostructures indicate an advantage in terms of a wide variety of material choice for FMI and TI, it remains still elusive to design a preferable FMI/TI/FMI sandwich heterostructure [Fig. 1(b)] that maximizes the exchange gap at the top and bottom surface states. In particular, the tangent of Hall angle (tan θ_H = σ_xy/σ_xx, the ratio of the transverse to the longitudinal conductivity), which is a measure of the closeness of the Fermi level to the exchange gap, has been far below 0.01 for the so-far reported FMI/TI magnetic proximity systems, while tan θ_H tends to diverge to infinity or at least exceeds unity to reach the QAHE at a moderately low temperature, e.g., 1 K.

To achieve a sizable exchange gap, one of the most essential parameters is the strength of exchange coupling between electrons on the surface state of TI and the localized spins in the FMI, which should be highly material-dependent. We consider that the combination of Te-based TI and Te-based FMI comprising a 3d-electron transition-metal element may give a strong exchange coupling for the following reason. Since Te is incorporated in both materials in common, the topological surface states originating from the 5p-orbital of Te may deeply extend into the FMI. As revealed by spectroscopy measurements and first-principle calculations for magnetically doped TIs such as Cr- and V-doped (Bi,Sb)₂Te₃ (Refs. 16–18), the energy levels of the spin polarized density of states for the 3d magnetic elements are close to the 5p-orbitals of Te, leading to a large exchange gap formation at the surface states.^19,20 Thus, a strong hybridization can similarly be expected in such proximity coupled systems between the p-orbital of Te in a TI/FMI and the d-orbital in an FMI.

We have chosen (Bi_1-ySb_y)₂Te₃ (BST) as a TI and Zn_1-xCr_xTe (ZCT) as an FMI. In addition to the reasons mentioned above, the combination of BST and ZCT has the following advantages. First, it is known that the Fermi energy E_F of (Bi_1-ySb_y)₂Te₃ can be tuned by the Sb composition y (Ref. 21) and that the surface dominant electrical transport such as integer QHE has been demonstrated.²² Second, ZnTe, a parent compound of ZCT, is an insulator with a relatively large band gap of 2.28 eV (Ref. 23) and shows a much higher resistivity than BST. Doped with Cr, ZCT works as an FMI (with the magnetization perpendicular to the film plane²⁴). Third, the in-plane lattice constant of ZnTe(111) (0.432 nm) is close to those of Sb₂Te₃ (0.426 nm) and Bi₂Te₃ (0.439 nm), which helps to form a heterostructure with smooth interfaces that facilitate the extension of the surface-state wave function into the FMI layer.

We fabricated a ZCT (10 nm)/BST(8 nm)/ZCT(10 nm) sandwich heterostructure by the molecular-beam epitaxy (see Secs. S1 and S2 in the supplementary material). A 2-nm-thick ZnTe buffer layer was adopted to improve the crystallinity of the ZCT layer. Atomic-scale structure and chemical composition of the heterostructure are analyzed by a cross sectional high-angle annular dark-field scanning transmission electron microscopy [Fig. 1(c)] and energy-dispersive X-ray spectroscopy (see Fig. S2 in the supplementary material). The abrupt structural change between the BST and ZCT layers with sharp interfaces can be seen. The topological surface states are expected to locate at around the interfaces. The diffusion of Cr into the BST layer is fairly small or at most not large enough to cause the Cr-doping induced QAHE, as observed in an optimally Cr-doped BST film (see discussions in Sec. S3 in the supplementary material). We defined the Hall-bar devices using a UV photolithography and subsequent wet etching processes for transport measurements (see Sec. S4 in the supplementary material). Figure 1(d) shows the temperature dependence of sheet resistance R_xx for the sandwich heterostructure and the ZCT film. Here, the Cr composition x for ZCT and Sb composition y for BST are set at 0.17 and 0.6, respectively. R_xx of the sandwich heterostructure film shows a weak temperature dependence with a value of around 10⁴ Ω, whereas R_xx of the ZCT film exceeds 10⁸ Ω even at room temperature and further increases as the temperature is decreased. The large difference in R_xx evidences that the electric current mainly flows in the BST layer with topological surface states. As shown in Fig. 1(e), the magnetization curve for the ZCT (shown in gray) at T = 2 K shows a clear hysteresis, representing the ferromagnetism in the ZCT film. The magnetic field dependence of anomalous Hall resistance R_yx^AHE well agrees with that of M in the ZCT film, showing similar coercive fields (the magnetization curve for the other temperature is shown in Fig. S6). Here, R_yx^AHE is defined by subtracting the ordinary Hall component R_yx^AHE = R_yx − R₀B, where R₀ and B are the ordinary Hall coefficient and magnetic field, respectively. Furthermore, the ferromagnetic transition temperatures evaluated from M and R_yx are 60 K and 40 K, respectively, which are close to each other (see Sec. S5 in the supplementary material). This agreement indicates that the AHE is induced by the magnetic proximity coupling with M in the ZCT layers.

Figure 2(a) displays the temperature dependence of R_xx and R_yx for the same sandwich heterostructure under B = 2 T, where the ZCT magnetization is saturated. R_yx shows a monotonic increase with decreasing T from the onset temperature of 50 K. As T is lowered below 0.1 K, R_yx reaches the quantum resistance h/e² (∼25.8 kΩ), while R_xx approaches zero, showing the QAHE (the same data in the conductance form is shown in Fig. S9 in the supplementary material). A similar temperature dependence is found in the Cr-doped BST (Ref. 25) that also shows the QAHE at below 0.1 K (Fig. S10 in the supplementary material), suggesting that the spatial inhomogeneity of the exchange gap also occurs more or less in the present sandwich heterostructure due to the random Cr distribution in the FMI layer and may similarly hinder the system from localization at higher temperatures. In the magnetic field dependence at the lowest temperature T = 0.03 K [Fig. 2(b)], R_yx is nearly constant against B at R_yx = ±h/e² in the magnetic field range |B| > 0.8 T, where the magnetization of ZCT is saturated. The observed R_yx originates from the AHE induced by the interaction between itinerant electrons and localized magnetic moments, excluding the possible contributions of the ordinary Hall effect induced by the electron cyclotron motion. In addition, the R_xx peaks in the magnetic field dependence [Fig. 2(b)] reflect the magnetic multidomain structure of the ZCT layer during the magnetization reversal process. This means that the edge current can be controlled by M in the adjacent FMI layers, which is different from the magnetically doped TI systems. These observations constitute an evidence for the QAHE induced by the magnetic proximity effect in the ZCT/BST/ZCT heterostructure system.

Next, we examine the E_F position dependence of the AHE by changing Sb composition y in the BST channel layer. The Cr compositions for the top and bottom ZCT layers are set to be the same, fixed at x = 0.17 in this series. Figures 3(a)–3(c) display the B dependence of R_yx for the samples with y = 0.50, 0.60, and 0.65, respectively. A schematic band structure with the anticipated E_F position is shown on the top of each panel. The spontaneous Hall resistance is the largest at y = 0.60, as shown in Figs. 3(a)–3(c), indicating that the E_F of y = 0.60 is closely tuned to the exchange gap where the Berry curvature is maximized. This trend is further supported by the sign change of the ordinary Hall coefficient: the negative slope of R_yx for y = 0.50 [Fig. 3(a)] and 0.60 [Fig. 3(b)] and positive for y = 0.65 [Fig. 3(c)]. The dominant carrier-type is converted from electron to hole across the charge neutral point (CNP) between y = 0.60 and 0.65. Figures 3(d) and 3(e), respectively, summarize the y dependence of the carrier density/type and the anomalous Hall resistance R_yx^AHE [the R_yx-B data for all the samples are presented in Fig. S11(a) in the supplementary material]. A systematic variation of the carrier density/type ensures that the E_F position is well regulated by the Sb composition. Although the optimum y is slightly shifted to around 0.6 from y = 0.85 to 0.95 in a single-layer BST,^21,22 the sharp and sizable peak in R_yx^AHE [Fig. 3(e)] shows up around the CNP, which is in accord with the fact that the QAHE is observed at low temperatures below 0.1 K.

Finally, the relationship between the ferromagnetic T_C of the FMI layer and the AHE is discussed with a measure of the tangent of Hall angle, tan θ_H = σ_xy/σ_xx, defined under a saturated magnetization at B = 2 T. Figure 4(a) shows the temperature dependence of tan θ_H for ZCT/BST/ZCT sandwich heterostructures with different Cr compositions x (the temperature dependence of R_xx and R_yx for samples with different y are shown in Fig. S10 in the supplementary material). The Sb composition for the BST layer is tuned at the optimal value y = 0.60 in this series. For the samples with x ≤ 0.17, tan θ_H monotonically increases with decreasing T below the critical temperature. The maximum of the tan θ_H for x = 0.17 exceeds 2.5 at T = 0.5 K, manifesting that the system is approaching the QAH state. In contrast, the samples with x > 0.17 have very small tan θ_H over a wide temperature range. Figure 4(b) displays a color contour plot of tan θ_H as functions of x and T together with the x-dependence of the ferromagnetic transition temperature (black symbols), the latter of which was estimated from the Arrott plot analysis of the anomalous Hall resistance (Fig. S7 in the supplementary material) and referred to as T_C^*. Despite the continuous increase in T_C^* up to x = 0.35, tan θ_H turns to decrease above x = 0.17. This is probably due to the segregation of CrTe in the ZCT layers (see Sec. S6 and Fig. S12 in the supplementary material), resulting in the reduction of the resistivity of the ZCT layer^26,27 or the degradation of the crystal quality of the BST layer. As far as the crystal structure of the FMI layer is maintained in x ≤ 0.17, the observable temperature of the QAHE increases with the composition of the magnetic element, which means that a suitable FMI with higher T_C could increase the observable temperature of the QAHE, e.g., by donor doping to ZCT (Ref. 28).

To summarize, we have observed the QAHE driven by the magnetic proximity coupling in Zn_1-xCr_xTe (ZCT)/(Bi_1-ySb_y)₂Te₃(BST)/ZCT sandwich heterostructures. The observed anomalous Hall response faithfully reflects the magnetic properties of the FMI layer, ensuring the magnetic proximity effect. Clear signatures of the QAHE with quantized R_yx and vanishing R_xx are observed, when the precise tuning of E_F and the relatively high T_C in the ferromagnetic ZCT layer are attained. The key strategy to design a heterostructure is the strong exchange coupling realized through the interface between the all-telluride based TI and FMI. It is noteworthy that the complex telluride materials involve families of not only these TIs and ferromagnets but also ferroelectrics^29,30 and superconductors.^31,32 The present work would pave a way for the exploration of all-telluride based heterostructures that would realize the even more exotic topological quantum phenomena.

See the supplementary material for experimental methods of thin film growth, device fabrication and transport measurement, the calibration of Cr composition in ZCT, STEM-EDX observation, the transport data of sandwich heterostructures, magnetization, and X-ray diffraction data of ZCT thin films.

This research was supported by the Japan Society for the Promotion of Science through JSPS/MEXT Grant-in-Aid for Scientific Research (Nos. 15H05853, 15H05867, 17H04846, 18H04229, and 18H01155) and JST CREST (No. JPMJCR16F1).