Abstract
Whereas ferromagnets have been known and used for millennia, antiferromagnets were only discovered in the 1930s1. At large scale, because of the absence of global magnetization, antiferromagnets may seem to behave like any non-magnetic material. At the microscopic level, however, the opposite alignment of spins forms a rich internal structure. In topological antiferromagnets, this internal structure leads to the possibility that the property known as the Berry phase can acquire distinct spatial textures2,3. Here we study this possibility in an antiferromagnetic axion insulator—even-layered, two-dimensional MnBi2Te4—in which spatial degrees of freedom correspond to different layers. We observe a type of Hall effect—the layer Hall effect—in which electrons from the top and bottom layers spontaneously deflect in opposite directions. Specifically, under zero electric field, even-layered MnBi2Te4 shows no anomalous Hall effect. However, applying an electric field leads to the emergence of a large, layer-polarized anomalous Hall effect of about 0.5e2/h (where e is the electron charge and h is Planck’s constant). This layer Hall effect uncovers an unusual layer-locked Berry curvature, which serves to characterize the axion insulator state. Moreover, we find that the layer-locked Berry curvature can be manipulated by the axion field formed from the dot product of the electric and magnetic field vectors. Our results offer new pathways to detect and manipulate the internal spatial structure of fully compensated topological antiferromagnets4,5,6,7,8,9. The layer-locked Berry curvature represents a first step towards spatial engineering of the Berry phase through effects such as layer-specific moiré potential.
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Acknowledgements
We thank F. Zhao and P. Kim for allowing us to use their glovebox and sample preparation facilities. We thank T. I. Andersen, G. Scuri, H. Park and M. D. Lukin for their help with magnetic measurements. We also thank F. Zhao, P. Kim, Y. Gao and C. Liu for discussions. Work in the Xu group was supported partly by the Center for the Advancement of Topological Semimetals (CATS), an Energy Frontier Research Center (EFRC) funded by the US Department of Energy (DOE) Office of Science, through the Ames Laboratory under contract DE-AC0207CH11358 (fabrication and measurements) and partly through the STC Center for Integrated Quantum Materials (CIQM), National Science Foundation (NSF) award no. ECCS-2025158 (data analysis). S.-Y.X. acknowledges the Corning Fund for Faculty Development. Q.M. acknowledges support from the CATS, an EFRC funded by the US DOE Office of Science, through the Ames Laboratory under contract DE-AC0207CH11358. C.T. acknowledges support from the Swiss National Science Foundation under project P2EZP2_191801. Y.-F.L., A. Akey, J.G., D.C.B. and L.F. were supported by the CIQM, NSF award no. ECCS-2025158. This work was performed in part at the Center for Nanoscale Systems at Harvard University, a member of the National Nanotechnology Coordinated Infrastructure Network, which is supported by the NSF under NSF award no.1541959. Work at UCLA was supported by the US DOE, Office of Science, Office of Basic Energy Sciences (BES) under award no. DE-SC0021117 for bulk sample growth, transport and magnetic property measurements. The work at Northeastern University was supported by the Air Force Office of Scientific Research under award number FA955-20-1-0322, and it benefited from the computational resources of Northeastern University’s Advanced Scientific Computation Center (ASCC) and the Discovery Cluster. B.G. and A. Agarwal thank the Science Education and Research Board and the Department of Science and Technology of the government of India for financial support, and the computer centre IIT Kanpur for providing the High Performance Computing facility. T.-R.C. was supported by the Young Scholar Fellowship Program from the Ministry of Science and Technology (MOST) in Taiwan, under a MOST grant for the Columbus Program MOST110-2636-M-006-016, the National Cheng Kung University, Taiwan, and National Center for Theoretical Sciences, Taiwan. Work at NCKU was supported by MOST, Taiwan, under grant MOST107-2627-E-006-001 and Higher Education Sprout Project, Ministry of Education to the Headquarters of University Advancement at NCKU. H.L. acknowledges support by MOST in Taiwan under grant number MOST 109-2112-M-001-014-MY3. H.-Z.L. was supported by the National Natural Science Foundation of China (11925402), Guangdong province (2016ZT06D348, 2020KCXTD001), the National Key R&D Program (2016YFA0301700), Shenzhen High-level Special Fund (G02206304, G02206404), and the Science, Technology and Innovation Commission of Shenzhen Municipality (ZDSYS20170303165926217, JCYJ20170412152620376, KYTDPT20181011104202253), and Center for Computational Science and Engineering of SUSTech. R.C. was supported by the China Postdoctoral Science Foundation (grant no. 2019M661678) and the SUSTech Presidential Postdoctoral Fellowship. C.F. was supported by the ERC Advanced Grant no. 742068 ‘TOPMAT’ and by the Deutsche Forschungsgemeinschaft (German Research Foundation) under Germany’s Excellence Strategy through Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter—ct.qmat (EXC 2147, project-id 390858490). K.S.B. is grateful for the support of the Office of Naval Research under award no. N00014-20-1-2308. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by MEXT, Japan, grant no. JPMXP0112101001 and JSPS KAKENHI grant no. JP20H00354. Z.Z., N.W., Z.H. and W.G. thank the Singapore National Research Foundation through its Competitive Research Program (CRP award no. NRF-CRP21-2018-0007, NRF-CRP22-2019-0004). X.-Y.Z., Y.-X.W. and B.B.Z. acknowledge support from NSF award no. ECCS-2041779.
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S.-Y.X. conceived the experiment and supervised the project. A.G. fabricated the devices with help from Y.-F.L., J.-X.Q., D.B., C.F., K.S.B. and Q.M. A.G. performed the transport measurements and analysed data with help from Y.-F.L., C.T., J.-X.Q., S.-C.H., D.B., T.D. and Q.M. C.H. and N.N. grew the bulk MnBi2Te4 single crystals. Z.Z., N.W., Z.H., W.G., J.-X.Q., C.T. and A.G. performed optical magnetic circular dichroism measurements. X.-Y.Z., Y.-X.W. and B.B.Z. performed nitrogen-vacancy centre magnetometry experiments. B.G., R.C., H.S., A. Agarwal, C.T., S.-Y.X., H.-Z.L, H.-J.T., B.S., A.B., H.L., L.F. and T.-R.C. made theoretical studies including first-principles calculations and tight-binding modelling. A. Akey, J.G. and D.C.B. performed transmission electron microscopy measurements. J.-X.Q. performed atomic force microscopy measurements. K.W. and T.T. grew the bulk hBN single crystals. S.-Y.X., A.G. and Q.M. wrote the manuscript with input from all authors. S.-Y.X. was responsible for the overall direction, planning and integration among different research units.
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Extended data figures and tables
Extended Data Fig. 1 Spatial engineering of Berry curvature.
a, Topological axion domain wall constructed by the axion field E ⋅ B. b, Spatially modulated Berry curvature moiré superlattice enabled by a MnBi2Te4-twisted hBN heterostructure59.
Extended Data Fig. 2 Topological Chern insulator state in MnBi2Te4.
a, Microscope image of the 6SL MnBi2Te4 device presented in the main text. The circuit for our transport measurements is noted. b, c, Longitudinal Rxx (c) and transverse (Hall) resistance Ryx (b) as a function of VBG and B. d, Rxx and Ryx versus VBG at −9 T.
Extended Data Fig. 3 Electric field dependence of the layer Hall effect in 6SL MnBi2Te4.
a, The AHE conductivity \({\sigma }_{xy}^{{\rm{AHE}}}\) as a function of electric field. The charge density n is set in the hole-doped regime (n = −1.4 × 1012 cm−2). b, Same as a but n is set in the electron-doped regime (n = +1.5 × 1012 cm−2). c, d, First-principles calculated AHE conductivity \({\sigma }_{xy}^{{\rm{AHE}}}\) as a function of electric field. c, Fermi level is set in the valence band (−10 meV). d, Fermi level is set in the conduction band (+30 meV).
Extended Data Fig. 4 Temperature-dependent measurements of 6SL MnBi2Te4.
a, Temperature-dependent Rxx data showing the Néel temperature TN. b, Ryx versus B measurements at different temperatures. Data at different temperatures are offset by 4 kΩ for visibility at electric field 0.6 V nm−1. c, AHE resistance as a function of temperature.
Extended Data Fig. 5 Schematic electronic structure and Berry curvature of even-layered MnBi2Te4.
a, b, Same antiferromagnetic state under opposite electric fields. c, d, Opposite antiferromagnetic states under the same electric field.
Extended Data Fig. 6 First-principles calculated band structures.
a–e, Calculated band structures of 6SL antiferromagnetic MnBi2Te4 for different theoretical electric fields ETHY.
Extended Data Fig. 7 Optical contrast of the MnBi2Te4 flakes.
a, Lower panel, optical image of few-layer flakes of MnBi2Te4 exfoliated on SiO2 substrate. Upper panel, lattice of one SL MnBi2Te4. b, Optical contrast C = (Iflake − Isubstrate)/(Iflake + Isubstrate) as a function of number of layers, which was independently determined by atomic force microscope. This process was repeated on many samples (each symbol in the figure represents an independent sample) to ensure a reproducible and reliable correspondence between C and layer number (see Methods and Supplementary Information section V.1 for details).
Extended Data Fig. 8 Experimental data and microscopic picture for odd-layered MnBi2Te4.
a, b, The AHE for 5SL MnBi2Te4. In contrast to 6SL, the AHE in 5SL does not change sign as one tunes the charge density from the hole-doped regime to the electron-doped regime. Data at different n are offset by 200 μS for visibility. c–f, In an odd-layered antiferromagnetic system, the top and bottom Dirac fermions experience the same magnetizations and hence open up gaps in the same fashion. As such, conduction and valence bands have the opposite Berry curvature. Therefore, the AHE remains the same sign in the hole-doped and electron-doped regimes. This conclusion is independent of E.
Extended Data Fig. 9 Unconventional Hall effects in a wide range of quantum materials.
a, The AHE in ferromagnets induced by the total Berry curvature. b, The valley Hall effect in gapped graphene and transition metal dichalcogenides induced by the valley-locked Berry curvature. c, The spin Hall effect in heavy metals induced by spin-locked Berry curvature. d, The layer Hall effect in the AFM axion state in even-layered MnBi2Te4 induced by layer-locked Berry curvature.
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Gao, A., Liu, YF., Hu, C. et al. Layer Hall effect in a 2D topological axion antiferromagnet. Nature 595, 521–525 (2021). https://doi.org/10.1038/s41586-021-03679-w
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DOI: https://doi.org/10.1038/s41586-021-03679-w
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