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

The quantum anomalous Hall effect (QAHE) is an exotic quantum phenomenon originating from dissipation-less chiral channels at the sample edge. While the QAHE has been observed in magnetically doped topological insulators (TIs), exploiting magnetic proximity effect on the TI surface from adjacent ferromagnet layers may provide an alternative approach to the QAHE by opening an exchange gap with less disorder than that in the doped system. Nevertheless, the engineering of a favorable heterointerface that realizes the QAHE based on the magnetic proximity effect remains to be achieved. Here, we report on the observation of the QAHE in a proximity coupled system of non-magnetic TI and ferromagnetic insulator (FMI). We have designed sandwich heterostructures of (Zn,Cr)Te/(Bi,Sb)2Te3/(Zn,Cr)Te that fulfills two prerequisites for the emergence of the QAHE; the formation of a sizable exchange gap at the TI surface state and the tuning of the Fermi energy into the exchange gap. The efficient proximity coupling in the all-telluride based heterostructure as demonstrated here will enable a realistic design of versatile tailor-made topological materials coupled with ferromagnetism, ferroelectricity, superconductivity, and so on.

Three-dimensional topological insulator (TI) is a novel state of matter hosting insulating bulk and conducting surface states as protected by time-reversal symmetry 1 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 EF tuning into the gap are to be simultaneously fulfilled. Magnetic proximity effect has been proposed as one other promising mechanism to induce the QAHE [ Fig.1(b)] 1 . When a non-magnetic 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 observation of the anomalous Hall effect (AHE) [11][12][13][14][15] .
Although these heterostructures indicate an advantage in terms of a wide variety of materials 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 top and bottom surface states. In particular, the tangent of Hall angle (tanH = xy/xx, the ratio of transverse to longitudinal conductivity), which is a measure of how close the Fermi level to the exchange gap, has been far below 0.01 for so-far reported FMI/TI magnetic proximity systems, while tan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 materials-dependent. We consider that the combination of Te-based TI and Te-based FMI comprising 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][17][18], the energy levels of spin polarized density of states for the 3d magnetic elements are close to 5p-orbitals of Te, leading to the large exchange gap formation at the surface states 19,20 . Thus, a strong hybridization can similarly be expected in such proximity coupled systems between p-orbital of Te in a TI/FMI and d-orbital in a FMI. We have chosen (Bi1-ySby)2Te3 (BST) as a TI and Zn1-xCrxTe (ZCT) as a 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 EF of (Bi1-ySby)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 a FMI (with the magnetization perpendicular to the film plane 24 ). 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 molecularbeam epitaxy (see Sections S1 and S2 in supplementary material (SM)). A 2-nm-thick ZnTe buffer 6 layer was adopted to improve crystallinity of the ZCT layer. Atomic-scale structure and chemical composition of the heterostructure are analyzed by cross sectional high-angle annular dark-field scanning transmission electron microscopy [ Fig. 1(c)] and energy-dispersive x-ray spectroscopy (see Fig. S2 in SM). The abrupt structural change between the BST and ZCT layers with the sharp interfaces can be seen. The topological surface states are expected to locate at around the interfaces. Diffusion of Cr into the BST layer is fairly small or at most not large enough to cause the Cr-doping induced QAHE effect as observed in an optimally Cr-doped BST film (see discussions in Section S3 in SM). We defined the Hall-bar devices with using a UV photolithography and subsequent wet etching processes for transport measurements (see Section S4 in SM).  negative slope of Ryx 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) in between y = 0.60 and 0.65. Figures 3(d) and 3(e) respectively summarizes the y dependence of the 9 carrier density/type and the anomalous Hall resistance Ryx AHE (the Ryx-B data for all the samples are presented in Fig. S11(a) in SM). Systematic variation of carrier density/type ensures that the EF position is well regulated by the Sb composition. Although the optimum y at around 0.6 is slightly shifted from y = 0.85-0.95 in a single-layer BST 21,22 , the sharp and sizable peak in Ryx 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 ferromagnetic TC of the FMI layer and the AHE is discussed with a measure of the tangent of Hall angle, tanH = yx / xx defined under saturated magnetization at B = 2 T. Figure 4(a) shows temperature dependence of tanH for ZCT/BST/ZCT sandwich heterostructures with different Cr compositions x (temperature dependence of Rxx and Ryx for samples with different y are shown in Fig. S10 in SM). 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H monotonically increases with decreasing T below the critical temperature. The maximum of the tan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H over a wide temperature range. Figure 4(b) displays a color contour plot of tanH as functions of x and T together with the x-dependence of ferromagnetic transition temperature (black symbols), the latter of which was estimated from Arrott plot analysis of anomalous Hall resistance (Fig. S7 in SM) 10 and referred as TC * . Despite the continuous increase in TC * up to x = 0.35, tanH turns to decrease above x = 0.17. This is probably due to the segregation of CrTe in the ZCT layers (see Section S6 and Fig.   S12 in SM), resulting in the reduction of resistivity of ZCT layer 26,27 or degradation of 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 TC could increase the observable temperature of the QAHE, e.g.
To summarize, we have observed the QAHE driven by magnetic proximity coupling in Zn1-xCrxTe (ZCT) /(Bi1-ySby)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 Ryx and vanishing Rxx are observed, when the precise tuning of EF and the relatively high TC 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 even more exotic topological quantum phenomena.