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Exchange-biased quantum anomalous Hall effect

The quantum anomalous Hall (QAH) effect is characterized by a dissipationless chiral edge state with a quantized Hall resistance at zero magnetic field. Manipulating the QAH state is of great importance in both the understanding of topological quantum physics and the implementation of dissipationless electronics. Here, we realized the QAH effect in the magnetic topological insulator Cr-doped (Bi,Sb)2Te3 (CBST) grown on an uncompensated antiferromagnetic insulator Al-doped Cr2O3. Through polarized neutron reflectometry (PNR), we find a strong exchange coupling between CBST and Al-Cr2O3 surface spins fixing interfacial magnetic moments perpendicular to the film plane. The interfacial coupling results in an exchange-biased QAH effect. We further demonstrate that the magnitude and sign of the exchange bias can be effectively controlled using a field training process to set the magnetization of the Al-Cr2O3 layer. Our work demonstrates the use of the exchange bias effect to effectively manipulate the QAH state, opening new possibilities in QAH-based spintronics.

Here, we report on exchange coupling between the QAH state of an MTI and an antiferromagnetic (AFM) insulator Al-doped Cr 2 O 3 . Cr 2 O 3 is an antiferromagnetic insulator with a Né el temperature near or above room temperature and is a suitable substrate for the growth of high-quality MTI 24,26 . Cr 2 O 3 has been reported to induce exchange bias in an adjacent MTI layer, but never simultaneously with the existence of the QAH state. On its own, Cr 2 O 3 is of interest as a magnetoelectric material with potential applications in electrical control of either AFM domains or adjacent ferromagnetic (FM) layers through exchange coupling [28][29][30][31] . While this makes Cr 2 O 3 promising for low energy spintronic applications, the single domain state necessary for practical applications is challenging to achieve in AFM devices. This issue may be resolved through the introduction of nonmagnetic Al dopants into the Cr 2 O 3 thin film during the growth, which yields a ferrimagnetic-like moment also known as a parasitic magnetization.
This emergent magnetization has been attributed to the preferential occupation of Al on one of the two Cr sublattices 32,33 . As illustrated in Fig. 1a, the Cr spins in pure Cr 2 O 3 align parallel or antiparallel to [0001] forming a Né el vector along the c-axis, while the introduction of Al dopants breaks the symmetry of the two AFM sublattices. This unique parasitic magnetization enables deterministic control of the AFM domain structure and strengthens exchange-coupling with neighboring layers while preserving exciting properties, such as magnetoelectricity, from the parent compound.
The 50 nm thick 3.7% Al-doped Cr 2 O 3 was deposited on α-Al 2 O 3 (0001) substrates by magnetron sputtering, and its magnetic properties were characterized using a superconducting quantum interference device (SQUID) magnetometer. Fig. 1b shows the out-of -plane magnetization profile of the Al-doped Cr 2 O 3 measured at multiple temperatures. Clear hysteresis loops were observed, consistent with the expected ferrimagnetic-like dopant-induced parasitic magnetization, which combined with the observation of hysteresis loops under the in-plane field with a lower saturation magnetization (supplementary Fig. S1), indicates a perpendicular magnetic anisotropy (PMA). However, a strong perpendicular exchange coupling can still be achieved in this bilayer system. The temperature evolution of the saturated magnetization in Fig. 1c indicates a critical temperature near 300 K, which is consistent with the Né el temperature (T N ) of 307 K 31 in pristine Cr 2 O 3 .
CBST layers were grown with a thickness of 6 quintuple layer (QL) for transport studies, while thicker films (20 QL) were prepared for high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) characterization and polarized neutron reflectometry (PNR) studies. Both the sputtered Al-Cr 2 O 3 and MBE grown CBST showed good single-crystalline quality, as indicated by the streaky reflection high-energy electron diffraction (RHEED) patterns both before and after the epitaxy of CBST (Fig. 1d). An atomically sharp interface between Al 2 O 3 and Al-Cr 2 O 3 , as well as the sharp interface to CBST layer can be seen from the HAADF-STEM in Fig. 1e and Fig. 1f, respectively.
To probe the interfacial coupling between the Al-doped Cr 2 O 3 and CBST, we performed PNR measurements on a 20 QL CBST grown on a 50 nm Al-doped Cr 2 O 3 . PNR gives a measure of the depthdependent magnetization of these bilayers. Specular reflectometry ( ⃗ perpendicular to the surface) is sensitive to in-plane moments only, so measurements were performed with an in -plane applied field, at a base temperature of 6 K. The summed spin-dependent reflectivity (R ++ + R --) and spin-dependent splitting (R ++ -R --) extracted from these measurements are plotted on the Fresnel scale in Fig. 2

(a)-(d)
along with the best-fit nuclear and magnetic profiles shown in Fig. 2(e). Overall, the PNR indicates bulk-like nuclear scattering length densities (SLDs) and extremely high-quality interfaces without the transitional growth regions recently observed in some recent studies of oxide/topological insulator heterostructures 34 .
As has been previously reported in related Cr 2 O 3 /CBST structures, the interface of this system is magnetically complex. Past work 24,26 indicated antiparallel alignment of the CBST and Cr 2 O 3 spins along with strong out-of-plane pinning of the CBST magnetization at the interface. This pinning was attributed to exchange coupling with the unusual surface reconstruction of Cr 2 O 3 which leads to spins fixed along the [0001] direction. In this context, we note that the best-fit model indicates a region of zero in-plane magnetization at the interface between the CBST and Al-Cr 2 O 3 at all measured fields. While the absence of any in-plane magnetization in this region could indicate the presence of a magnetic dead layer, it is also consistent with the previously reported pinning of the CBST magnetization along the film normal direction through antiparallel exchange coupling to reconstructed surface spins with giant magnetic anisotropy. Given that magnetically dead layers are rarely observed in CBST films, and a robust and repeatable exchange biasing effect in these films are latter observed, we conclude that a conventional dead layer at the interface is unlikely. Rather, we propose that a strong exchange coupling between the CBST and Al-Cr 2 O 3 surface spins pins the interfacial magnetization along the film normal where PNR is insensitive.
Further supporting this picture, the best model is one in which the magnetic moments within the CBST layer gradually cant from an out-of -plane orientation at the interface towards the in-plane direction at the top surface of the film. A schematic of the moment orientation is shown in Fig. 2f. The moments in the CBST layer, up to a maximum of 28 emu/cc (1 emu/cc = 1 kA/m) in-plane at 3 T, have a larger in-plane component canting over longer length scales as the field decreases, indicating strong exchange coupling between Cr moments within the CBST; however, this gradual moment canting is not present in the Al-Cr 2 O 3 layer, which exhibits a uniform increase in magnetization with increasing field. This matches the magnetometry observation that Al-Cr 2 O 3 has stronger perpendicular magnetic anisotropy than CBST. Further, the maximum in-plane magnetization at 7 K and 3 T in-plane of 20 emu/cc within the Al-Cr 2 O 3 extracted from the PNR result matches the suppressed saturation magnetization of the in-plane hysteresis behavior measured using SQUID (supplementary Fig. S1). We conclude, therefore, that some fraction of the Al-Cr 2 O 3 spins remain pinned along the film normal at all fields. Comparisons with alternate models, without these features, can be found in supplementary Fig.   S2.
Having measured the vertical magnetization profile in Al-Cr 2 O 3 /CBST bilayers, we carried out transport measurements to show the exchange-biased QAH effect in these heterostructures. The films were patterned into Hall-bar devices with a geometry of 1 mm by 0.5 mm, as previously shown in Fig.   1g, using a hard mask and dry etching method. The samples were cooled from 300 K to 50 mK with a +1 T perpendicular magnetic field applied. Al-Cr 2 O 3 thus has a significant advantage over its undoped counterpart Cr 2 O 3 as the sign of any exchange bias may be changed through the application of an external magnetic field alone, without requiring the system be raised above its Né el temperature T N .
To demonstrate this advantage, we show that the magnetism in Al-Cr 2 O 3 , and consequently the sign of the interfacial exchange bias, may be initialized using both field training and traditional field cooling methods. For field cooling, the sample was subjected to ±3 T fields while cooling down from above T N = 330 K to 2 K. For field training, the sample was cooled down to 2 K without applying field and then was subjected to ±3 T and ±9 T fields. In all Al-Cr 2 O 3 initialization scenarios, small magnetic field sweeps between ±0.2 T were then performed at 2 K. As shown in Fig. 4a, after +3 T field cooling, +3 T field training, or +9 T field training, the device displays the same behavior; most notably, a pronounced exchange bias when compared to the similar field cooling or field training process using a negative field, indicating that field training and field cooling are equally effective methods for establishing exchange bias in this system.
The exchange bias was shown to be directly related to Al-Cr 2 O 3 magnetization from the dependence of exchange bias on the externally applied training field. Before each small field sweep (±0.2 T), a negative exchange bias was set using a +3 T field, and the sample was subsequently subjected to a training field of opposing sign − 0 (Fig. 4b). The magnitude of this training field was varied between 0.2 T and 3 T, resulting in a gradual switching of Al-Cr 2 O 3 magnetization. Shown in

Data availability
The data of the study are available from the corresponding author upon reasonable re quest.

Competing interests
The authors declare no competing financial interests.  nuclear and in-plane magnetic depth-profile models at each field. Magnetic scattering length density (SLD) has been scaled by a factor of 10 for clarity but corresponds to the magnetization as plotted.
Differences in the nuclear SLD profiles at the surface between subsequent measurements are likely due to sample aging, as discussed in Fig. S3. f. Possible orientation and relative magnitude of the net magnetization near the interface, deduced from (e), the in-plane magnetization, and magnetometry results. This schematic assumes that the Al-Cr 2 O 3 sublattices rotate together and does not illustrate the effect of domains. All error bars represent ±1 standard deviation. b. Temperature dependences of σ xx and σ xy converted from ρ xx and ρ yx . c. Evolution of the σ xx versus σ xy when scanning the magnetic field at 50mK. d and e. Magnetic field dependences of ρ xx and ρ yx after training the sample using -3 T and +3 T to polarize the Al-Cr 2 O 3 magnetization. The magnetic field was swept between ±0.2 T and the data was taken at 50 mK. magnetization. d. Summarized temperature dependence of H eb . The same device that has been described in Fig. 3 is studied for this measurement.