Abstract
The Berry curvature and quantum metric are the imaginary part and real part, respectively, of the quantum geometric tensor, which characterizes the topology of quantum states1. The Berry curvature is known to generate a number of important transport phenomena, such as the quantum Hall effect and the anomalous Hall effect2,3; however, the consequences of the quantum metric have rarely been probed by transport measurements. Here we report the observation of quantum-metric-induced nonlinear transport, including both a nonlinear anomalous Hall effect and a diode-like non-reciprocal longitudinal response, in thin films of a topological antiferromagnet, MnBi2Te4. Our observations reveal that the transverse and longitudinal nonlinear conductivities reverse signs when reversing the antiferromagnetic order, diminish above the Néel temperature and are insensitive to disorder scattering, thus verifying their origin in the band-structure topology. They also flip signs between electron- and hole-doped regions, in agreement with theoretical calculations. Our work provides a means to probe the quantum metric through nonlinear transport and to design magnetic nonlinear devices.
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Acknowledgements
We thank S. A. Yang, H. Liu, S. Xu and J. Song for discussions. W.G. acknowledges the financial support from the Singapore National Research Foundation through its Competitive Research Program (CRP Award No. NRF-CRP22-2019-0004). B.Y. acknowledges the financial support by the European Research Council (ERC Consolidator Grant No. 815869, ‘NonlinearTopo’) and Israel Science Foundation (ISF No. 2932/21). A.W. acknowledges the financial support from the National Natural Science Foundation of China (grant no. 12004056), Chongqing Research Program of Basic Research and Frontier Technology, China (grant no. cstc2021jcyj-msxmX0661) and Fundamental Research Funds for the Central Universities, China (grant no. 2022CDJXY-002). X.Z. acknowledges the financial support from the National Key Research and Development Program of the Ministry of Science and Technology of China (2019YFA0704901) and the National Natural Science Foundation of China (grant nos. 52125103 and 52071041).
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Contributions
W.G. and B.Y. conceived and supervised the project. N.W. fabricated the devices and performed the transport and RMCD measurements with help from Z.Z. and C.Z. D.K., T.H. and B.Y. performed the theoretical calculations. N.W. and F.Z. performed the NV measurement with help from Z.J., S.R. and H.C. N.W., W.G., D.K., T.H. and B.Y. analysed the data. N.C., A.W. and X.Z. grew the MnBi2Te4 single crystals. K.W. and T.T. grew the hBN single crystals. N.W., B.Y. and W.G. wrote the paper with input from all authors.
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Extended data figures and tables
Extended Data Fig. 1 The linear conductivity of 4SL-MnBi2Te4 with opposite AFM states.
a,b, The AFM-I and AFM-II states are prepared by sweeping the magnetic field from −7 T to 0T or +7 T to 0 T, respectively. c,d, The linear longitudinal \({{V}}_{x}^{\omega }\) and transverse \({{V}}_{x}^{\omega }\) voltage as a function of current \({{I}}_{x}^{\omega }\) for AFM I and AFM II states, respectively. The solid line is a linear fit to the experimental data.
Extended Data Fig. 2 The fully compensated AFM order in 4SL-MnBi2Te4 device.
a, The magnetic field dependent longitudinal resistance Rxx of the 4SL-MnBi2Te4 device. b, The magnetic field dependent Hall resistance Ryx of the 4SL-MnBi2Te4 device. In zero magnetic field, the AFM order is fully compensated and the Hall resistance Ryx = 0.
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Wang, N., Kaplan, D., Zhang, Z. et al. Quantum-metric-induced nonlinear transport in a topological antiferromagnet. Nature 621, 487–492 (2023). https://doi.org/10.1038/s41586-023-06363-3
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DOI: https://doi.org/10.1038/s41586-023-06363-3
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