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An antiferromagnetic diode effect in even-layered MnBi2Te4

Nature Electronics volume 7, pages 751–759 (2024)Cite this article

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Abstract

In a p–n junction, the separation of positive and negative charges leads to diode transport, in which charge flows in only one direction. Non-centrosymmetric polar conductors are intrinsic diodes that could be of use in the development of nonlinear applications. Such systems have recently been extended to non-centrosymmetric superconductors, and the superconducting diode effect has been observed. Here, we report an antiferromagnetic diode effect in a centrosymmetric crystal without directional charge separation. We observed large second-harmonic transport in a nonlinear electronic device enabled by the compensated antiferromagnetic state of even-layered MnBi2Te4. We show that this antiferromagnetic diode effect can be used to create in-plane field-effect transistors and microwave-energy-harvesting devices. We also show that electrical sum-frequency generation can be used as a tool to detect nonlinear responses in quantum materials.

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Fig. 1: Introduction to \(\boldsymbol{{{\mathcal{PT}}}}\)-symmetric antiferromagnetism in even-layered MnBi2Te4.
Fig. 2: Observation of the antiferromagnetic diode effect.
Fig. 3: Systematic investigations of the intrinsic antiferromagnetic diode effect.
Fig. 4: SFG measurements and applications of the AFM diode effect.

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Source data are provided with this paper. Further data related to this work are available from the corresponding authors upon request.

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The computer code used in this study is available from the corresponding authors upon reasonable request.

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Acknowledgements

We thank Y. Gao, C. Xiao, A. Agarwal, J. Ahn, S. Yang, F. de Juan and I. Sodemann for helpful discussions. The work in S.Y.X.’s group was partly supported through the Center for the Advancement of Topological Semimetals, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science (fabrication and measurements), through the Ames National Laboratory (Contract No. DE-AC-0207CH11358) and partly through the Air Force Office of Scientific Research (Grant No. FA9550-23-1-0040 for data analysis and manuscript writing). S.Y.X. acknowledges the Corning Fund for Faculty Development and support from the Alfred P. Sloan Foundation. S.Y.X. and D.B. were supported by the National Science Foundation (NSF; Career Grant No. DMR-2143177). C.T. and Z.S. acknowledge support from the Swiss National Science Foundation (Project Nos. P2EZP2 191801 and P500PT 206914, respectively). Y.F.L., S.Y.X., D.C.B., Y.O. and L.F. were supported by the Science and Technology Center for Integrated Quantum Materials (NSF Grant No. DMR-1231319). This work was performed in part at the Center for Nanoscale Systems, Harvard University, a member of the National Nanotechnology Coordinated Infrastructure Network, which is supported by the NSF (Award No. ECCS-2025158). Bulk single-crystal growth and characterization of MnBi2Te4 were performed at the University of California, Los Angeles, and were supported by the DOE, Office of Science (Award No. DE-SC0021117). The work at Northeastern University was supported by the NSF through NSF-ExpandQISE (Award No. 2329067), and it benefited from the resources of Northeastern University’s Advanced Scientific Computation Center and the Discovery Cluster and of the Quantum Materials and Sensing Institute. The work in Q.M.’s group was supported through the Center for the Advancement of Topological Semimetals, an Energy Frontier Research Center funded by the DOE, Office of Science, through the Ames National Laboratory (Contract No. DE-AC02-07CH11358 for sample fabrication) and was partly supported by the Air Force Office of Scientific Research (Grant No. FA9550-22-1-0270 for manuscript writing) and the Alfred P. Sloan Foundation. L.F. and Q.M. also acknowledge support from the NSF Convergence programme (NSF ITE-2345084) and the Canadian Institute for Advanced Research. T.R.C. was supported by the 2030 Cross-Generation Young Scholars Programme from the National Science and Technology Council, Taiwan (Programme No. MOST111-2628-M-006-003-MY3), National Cheng Kung University, Taiwan, and the National Center for Theoretical Sciences, Taiwan. T.R.C. thanks the National Center for High-performance Computing of the National Applied Research Laboratories, Taiwan, for providing computational and storage resources. This research was supported, in part, by the Higher Education Sprout Project, Ministry of Education, to the Headquarters of University Advancement at National Cheng Kung University. H.L. acknowledges the support of the National Science and Technology Council, Taiwan (Grant No. MOST 111-2112-M-001-057-MY3). The work at the Tata Institute of Fundamental Research, Mumbai, was supported by the Department of Atomic Energy of the Government of India (Project No. 12-R&D-TFR-5.10-0100) and benefited from the computational resources of the Tata Institute of Fundamental Research, Mumbai. K.W. and T.T. acknowledge support from the JSPS KAKENHI (Grant Nos. 21H05233 and 23H02052) and World Premier International Research Center Initiative (WPI), MEXT, Japan. S.W.C. acknowledges partial support from the Harvard Quantum Initiative in Science and Engineering.

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Authors and Affiliations

  1. Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA

    Anyuan Gao, Jian-Xiang Qiu, Yu-Fei Liu, Damien Bérubé, Thao Dinh, Houchen Li, Christian Tzschaschel, Tianye Huang, Zhe Sun, Sheng-Chin Ho & Su-Yang Xu

  2. Department of Physics, Harvard University, Cambridge, MA, USA

    Shao-Wen Chen, Yu-Fei Liu, Thao Dinh, Seunghyun Park & Amir Yacoby

  3. Department of Physics, Northeastern University, Boston, MA, USA

    Barun Ghosh & Arun Bansil

  4. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Yugo Onishi & Liang Fu

  5. Department of Physics and Astronomy and California NanoSystems Institute, University of California, Los Angeles, Los Angeles, CA, USA

    Chaowei Hu, Tiema Qian & Ni Ni

  6. Department of Physics, National Cheng Kung University, Tainan, Taiwan

    Shang-Wei Lien & Tay-Rong Chang

  7. Center for Quantum Frontiers of Research and Technology (QFort), Tainan, Taiwan

    Shang-Wei Lien & Tay-Rong Chang

  8. Physics Division, National Center for Theoretical Sciences, Taipei, Taiwan

    Shang-Wei Lien & Tay-Rong Chang

  9. Department of Physics, Boston College, Chestnut Hill, MA, USA

    Zhe Sun & Qiong Ma

  10. Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Mumbai, India

    Bahadur Singh

  11. Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe

  12. Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan

    Takashi Taniguchi

  13. Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

    David C. Bell

  14. Center for Nanoscale Systems, Harvard University, Cambridge, MA, USA

    David C. Bell

  15. Quantum Materials and Sensing Institute, Northeastern University, Burlington, MA, USA

    Arun Bansil

  16. Institute of Physics, Academia Sinica, Taipei, Taiwan

    Hsin Lin

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  1. Anyuan Gao
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  2. Shao-Wen Chen
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  3. Barun Ghosh
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Contributions

S.Y.X. conceived and supervised the project. A.G. fabricated the devices and performed the transport measurements with help from Y.F.L., J.X.Q., D.B., T.D., H.C.L., C.T., Z.S., S.C.H., T.H., D.C.B. and Q.M. A.G., S.W.C. and S.P. performed the microwave rectification and NV experiments with help from A.Y. A.G. and J.X.Q. performed the optical CD measurement. A.G. performed the SHG measurements with help from C.T., H.C.L., J.X.Q. and Y.F.L. C.H., T.Q. and N.N. grew the bulk MnBi2Te4 single crystals. B.G. completed the theoretical studies including first-principles calculations with help from Y.O. and under the guidance of B.S., A.B., H.L., L.F. and T.R.C. K.W. and T.T. grew the bulk h-BN single crystals. S.Y.X., A.G. and Q.M. wrote the manuscript with input from all authors.

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Correspondence to Su-Yang Xu.

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Extended data

Extended Data Fig. 1 The asymmetric band contours induced by AFM spins in 6SL MnBi2Te4 at Fermi energy Ef = 0.2 eV.

a, The band contours of the Dirac surface states without AFM order. The band contour is symmetric for momentum ± k. ± kx and ± ky are the momentum along x and y direction. b, The band contours of the Dirac surface states for opposite AFM states. The AFM spins make the band to be ± ky asymmetric. This AFM spin-induced asymmetry is opposite for opposite AFM states. This explains the observation that the AFM diode effect signal is opposite for opposite AFM states shown in Figs. 2e–f, 4f and Extended Data Fig. 4.

Extended Data Fig. 2 The fully compensated antiferromagnetism for 6SL MnBi2Te4.

a, b, NV center magnetometry measurement for even- and odd-layered MnBi2Te4 (outlined by blue and red dashed lines in the optical image of the sample in (a)). The magnetization is only observed in odd-layered MnBi2Te4 and negligible in even-layered MnBi2Te4. The cyan dotted line denotes the line cut data shown in Fig. 1e.

Extended Data Fig. 3 The linear and nonlinear signals for opposite AFM states in a 6SL MnBi2Te4.

a, c, At a finite external magnetic field μ0Hz field, AFM-I state can be prepared by sweeping μ0Hz from -8 T to 0 T (panel a); AFM-II state can be prepared by sweeping μ0Hz from +8 T to 0 T (panel c). b, The linear longitudinal voltage \({{{{\rm{V}}}}}_{\parallel }^{\omega }\) as a function of injection current for AFM-I. d, Same as (panel b) but for AFM-II. For different AFM states, the linear signal is the same. These data were taken from Device A and the current was along 30∘ in Fig. 2g.

Extended Data Fig. 4 AFM order determined nonlinear signal.

a, Nonlinear voltage V2ω as a function of z-direction external magnetic field μ0Hz. V2ω is opposite for two AFM orders (∣μ0H∣ < 2 T). The red and blue circles denote the two opposite V2ω at μ0H = 0 T. b, The nonlinear voltage difference \(({{{{\rm{diff}}}}}_{{V}^{2\omega }}=\frac{1}{2}({V}_{{{{\rm{AFM}}}}-{{{\rm{I}}}}}^{2\omega }-{V}_{{{{\rm{AFM}}}}-{{{\rm{II}}}}}^{2\omega }))\) between two AFM orders as a function of μ0H.

Extended Data Fig. 5 The temperature dependence of the nonlinear signal.

a, b, Nonlinear conductivity \({V}_{yxx}^{2\omega }\) and square of linear conductivity \({({\sigma }_{xx}^{\;\omega })}^{2}\) as a function of temperature. \({\sigma }_{yxx}^{2\omega }\) and \({({\sigma }_{xx}^{\;\omega })}^{2}\) show a similar temperature dependence.

Extended Data Fig. 6 Nonlinear voltage versus current direction.

a, b, Longitudinal and transverse nonlinear voltage when the current is injected along x (panel a) and along y (panel b). A crystalline axes is along x in Device A (Fig. 2g,h).

Extended Data Fig. 7 DFT calculated band structure of 6SL MnBi2Te4.

a, Band structure of 6SL MnBi2Te4 in ky direction. b, DFT calculated band contours at specific energies (0.05 eV and 0.10 eV), marked with dashed lines in panel (a). The low energy Dirac bands show dramatic asymmetry between + ky and − ky. c, DFT calculated nonlinear conductivity σ2ω as a function of Fermi level Ef. We obtained the relaxation time τ = 2.1 × 10−14 s based on the Drude conductivity. We note that our calculations are based on the DFT band structure of 6SL MnBi2Te4, which predicts a magnetic gap ~ 50 meV. However, experimentally, the gap size is not settled37,40. In particular, spatial inhomogeneity can smear out the magnetic gap44. Moreover, the antisite defects could suppress the band gap and can increase the quantum metric effect, as predicted in Ref. 32.

Extended Data Fig. 8 The exchange property of transverse conductance.

a, b, Schematics of two different types of linear transverse conductance, the Hall effect (panel a) and the anisotropy induced transverse signal (panel b). The Hall effect occurs due to external magnetic field or internal magnetization. The anisotropy induced transverse signal occurs due to crystalline anisotropy (for example orthorhombic or monoclinic). These two different mechanisms can be distinguished by their exchange properties. The Hall effect is antisymmetric (σxy = − σyx), whereas the anisotropy induce transverse signal is symmetric (σxy = σyx). c, d, Schematic of nonlinear Hall signal (panel c) and the transverse component of the AFM diode signal (panel d). The nonlinear Hall signal is antisymmetric (σyxx = − σxyx), while the AFM diode signal is symmetric (σyxx = σxyx).

Extended Data Fig. 9 Electrical sum-frequency generation (SFG) measurement for 6SL MnBi2Te4.

a, b, Schematic for \({V}_{yxx}^{\;{\omega }_{1}+{\omega }_{2}}\) and \({V}_{xyx}^{\;{\omega }_{1}+{\omega }_{2}}\) measurements, respectively. ω1 = 547.1 Hz and ω2 = 1.77 Hz were used in the measurement. The capacitor and inductor were used to define the current trajectory for \({I}^{{\omega }_{1}}\) and \({I}^{{\omega }_{2}}\) (see Methods for more details).

Extended Data Fig. 10 In-plane field effect in another 6SL MnBi2Te4 device.

a, Measured change of resistance \({R}_{xx}(\Delta {R}_{xx}={V}_{x}^{\;{\omega }_{1}}/{I}_{x}^{\;{\omega }_{1}})\) as a function of an electric field bias along \({V}_{y}^{{{\;{\rm{DC}}}}}\). b, Temperature dependence of ΔRxx.

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Gao, A., Chen, SW., Ghosh, B. et al. An antiferromagnetic diode effect in even-layered MnBi2Te4. Nat Electron 7, 751–759 (2024). https://doi.org/10.1038/s41928-024-01219-8

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