# Concurrence of quantum anomalous Hall and topological Hall effects in magnetic topological insulator sandwich heterostructures

## Abstract

The quantum anomalous Hall (QAH) effect is a consequence of non-zero Berry curvature in momentum space. The QAH insulator harbours dissipation-free chiral edge states in the absence of an external magnetic field. However, the topological Hall (TH) effect, a hallmark of chiral spin textures, is a consequence of real-space Berry curvature. Here, by inserting a topological insulator (TI) layer between two magnetic TI layers, we realized the concurrence of the TH effect and the QAH effect through electric-field gating. The TH effect is probed by bulk carriers, whereas the QAH effect is characterized by chiral edge states. The appearance of the TH effect in the QAH insulating regime is a consequence of chiral magnetic domain walls that result from the gate-induced Dzyaloshinskii–Moriya interaction and occurs during the magnetization reversal process in the magnetic TI sandwich samples. The coexistence of chiral edge states and chiral spin textures provides a platform for proof-of-concept dissipationless spin-textured spintronic applications.

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## Data availability

The data that support the findings of this study are available from C.-Z.C. on reasonable request.

## Code availability

The code for theoretical calculations of spin susceptibility and DM interaction and simulations of the quantum transport simulation through a single chiral magnetic domain wall from C.L. and J.Zang on reasonable request.

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## Acknowledgements

The authors thank X. D. Xu, B. H. Yan, H. Z. Lu and W. D. Wu for helpful discussions. D.X. and N.S. acknowledge support from an ONR grant (N-000141512370) and Penn State 2DCC-MIP under NSF grant DMR-1539916. J.-H.S. and M.H.W.C. acknowledge the support from NSF grant DMR-1707340. C.L. acknowledges the support from an ONR grant (N00014-15-1-2675 and renewal No. N00014-18-1-2793). D.A. and J.Zang acknowledge the support from DOE grants (DE-SC0016424 and DE-SC0020221). C.-Z.C. acknowledges the support from the Gordon and Betty Moore Foundation’s EPiQS Initiative (Grant GBMF9063) and an ARO Young Investigator Program Award (W911NF1810198). Support for transport measurements and data analysis was provided by DOE grant (DE-SC0019064).

## Author information

N.S., M.H.W.C. and C.-Z.C. conceived and designed the experiment. D.X. grew the sandwich heterostructure samples with the help of N.S. and C.-Z.C. F.W., K.W. and J.J. performed characterizations of the samples with the help of C.-Z.C. J.J., F.W., J.-H.S., R.X. and M.K. performed the dilution refrigerator measurements with the help of M.H.W.C. and C.-Z.C. J.J., F.W., Y.-F.Z. and L.Z. carried out the PPMS transport measurement with the help M.H.W.C. and C.-Z.C. D.A., J.Zhang, J. Zang and C. L. provided theoretical support and did all the theoretical calculations. J.J., J.Zang, C.L., N.S., M.H.W.C. and C.-Z.C. analysed the data and wrote the manuscript with contributions from all authors.

Correspondence to Nitin Samarth or Moses H. W. Chan or Cui-Zu Chang.

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### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary Information

I. Characterizations of the TI sandwich heterostructure. II. Determining the Curie temperature of the TI sandwich heterostructure. III. Additional transport results of the TI sandwich heterostructure (3-5-3 sample 1). IV. Transport results of the second 3-5-3 TI sandwich heterostructure (3-5-3 sample 2). V. Transport results of TI sandwich heterostructures with different sample configurations. VI. Theoretical calculations for the spin susceptibility in magnetic TI. VII. Simulation of the quantum transport through a single chiral magnetic domain wall in magnetic TI.

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