Otrokov, M. M. et al. Prediction and observation of an antiferromagnetic topological insulator. Nature 576, 416–422 (2019).
Gong, Y. et al. Experimental realization of an intrinsic magnetic topological insulator. Chin. Phys. Lett. 36, 076801 (2019).
Li, J. et al. Intrinsic magnetic topological insulators in van der Waals layered MnBi2Te4-family materials. Sci. Adv. 5, eaaw5685 (2019).
Zhang, D. et al. Topological axion states in the magnetic insulator MnBi2Te4 with the quantized magnetoelectric effect. Phys. Rev. Lett. 122, 206401 (2019).
Deng, Y. et al. Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4. Science 367, 895–900 (2020).
Liu, C. et al. Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator. Nat. Mater. 19, 522–527 (2020).
Wang, N. et al. Quantum-metric-induced nonlinear transport in a topological antiferromagnet. Nature 621, 487–492 (2023).
Gao, A. et al. Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure. Science 381, 181–186 (2023).
Šmejkal, L., Mokrousov, Y., Yan, B. & MacDonald, A. H. Topological antiferromagnetic spintronics. Nat. Phys. 14, 242–251 (2018).
He, Q. L., Hughes, T. L., Armitage, N. P., Tokura, Y. & Wang, K. L. Topological spintronics and magnetoelectronics. Nat. Mater. 21, 15–23 (2022).
Chang, C.-Z. et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator. Science 340, 167–170 (2013).
Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).
Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).
Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020).
Li, T. et al. Quantum anomalous Hall effect from intertwined moiré bands. Nature 600, 641–646 (2021).
Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74–79 (2023).
Xu, F. et al. Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2. Phys. Rev. 13, 031037 (2023).
Lu, Z. et al. Fractional quantum anomalous Hall effect in multilayer graphene. Nature 626, 759–764 (2024).
Han, T. et al. Large quantum anomalous Hall effect in spin-orbit proximitized rhombohedral graphene. Science 384, 647–651 (2024).
Ge, J. et al. High-Chern-number and high-temperature quantum Hall effect without Landau levels. Natl Sci. Rev. 7, 1280–1287 (2020).
Ying, Z. et al. Experimental evidence for dissipationless transport of the chiral edge state of the high-field Chern insulator in MnBi2Te4 nanodevices. Phys. Rev. B 105, 085412 (2022).
Cai, J. et al. Electric control of a canted-antiferromagnetic Chern insulator. Nat. Commun. 13, 1668 (2022).
Bai, Y. et al. Quantized anomalous Hall resistivity achieved in molecular beam epitaxy-grown MnBi2Te4 thin films. Natl Sci. Rev. 11, nwad189 (2024).
Gao, A. et al. Layer Hall effect in a 2D topological axion antiferromagnet. Nature 595, 521–525 (2021).
Zhang, R.-X., Wu, F. & Das Sarma, S. Möbius Insulator and Higher-Order Topology in MnBi2nTe3n+1. Phys. Rev. Lett. 124, 136407 (2020).
Lei, C., Heinonen, O., MacDonald, A. H. & McQueeney, R. J. Metamagnetism of few-layer topological antiferromagnets. Phys. Rev. Mater. 5, 064201 (2021).
Li, Z. et al. Tunable interlayer magnetism and band topology in van der Waals heterostructures of MnBi2Te4-family materials. Phys. Rev. B 102, 081107 (2020).
Sun, H.-P. et al. Analytical solution for the surface states of the antiferromagnetic topological insulator MnBi2Te4. Phys. Rev. B 102, 241406 (2020).
Yang, S. et al. Odd-even layer-number effect and layer-dependent magnetic phase diagrams in MnBi2Te4. Phys. Rev. 11, 011003 (2021).
Sass, P. M., Kim, J., Vanderbilt, D., Yan, J. & Wu, W. Robust A-type order and spin-flop transition on the surface of the antiferromagnetic topological insulator MnBi2Te4. Phys. Rev. Lett. 125, 037201 (2020).
Ovchinnikov, D. et al. Intertwined topological and magnetic orders in atomically thin Chern insulator MnBi2Te4. Nano Lett. 21, 2544–2550 (2021).
Garnica, M. et al. Native point defects and their implications for the Dirac point gap at MnBi2Te4(0001). npj Quantum Mater. 7, 7 (2022).
Tan, H. & Yan, B. Distinct magnetic gaps between antiferromagnetic and ferromagnetic orders driven by surface defects in the topological magnet MnBi2Te4. Phys. Rev. Lett. 130, 126702 (2023).
Lai, Y., Ke, L., Yan, J., McDonald, R. D. & McQueeney, R. J. Defect-driven ferrimagnetism and hidden magnetization in MnBi2Te4. Phys. Rev. B 103, 184429 (2021).
Du, M.-H., Yan, J., Cooper, V. R. & Eisenbach, M. Tuning Fermi levels in intrinsic antiferromagnetic topological insulators MnBi2Te4 and MnBi4Te7 by defect engineering and chemical doping. Adv. Funct. Mater. 31, 2006516 (2021).
Hou, F. et al. Te-vacancy-induced surface collapse and reconstruction in antiferromagnetic topological insulator MnBi2Te4. ACS Nano 14, 11262–11272 (2020).
Huang, Z., Du, M.-H., Yan, J. & Wu, W. Native defects in antiferromagnetic topological insulator MnBi2Te4. Phys. Rev. Mater. 4, 121202 (2020).
Zeugner, A. et al. Chemical aspects of the candidate antiferromagnetic topological insulator MnBi2Te4. Chem. Mater. 31, 2795–2806 (2019).
Li, H. et al. Antiferromagnetic topological insulator MnBi2Te4: synthesis and magnetic properties. Phys. Chem. Chem. Phys. 22, 556–563 (2020).
Li, Y. et al. Fabrication-induced even-odd discrepancy of magnetotransport in few-layer MnBi2Te4. Nat. Commun. 15, 3399 (2024).
Zhang, Z. et al. Controlled large non-reciprocal charge transport in an intrinsic magnetic topological insulator MnBi2Te4. Nat. Commun. 13, 6191 (2022).
Liu, S. et al. Gate-tunable intrinsic anomalous Hall effect in epitaxial MnBi2Te4 films. Nano Lett. 24, 16–25 (2024).
Li, Y. et al. Reentrant quantum anomalous Hall effect in molecular beam epitaxy-grown MnBi2Te4 thin films. Preprint at arxiv.org/abs/2401.11450 (2024).
Wang, Y. et al. Towards the quantized anomalous Hall effect in AlOx-capped MnBi2Te4. Nat. Commun. 16, 1727 (2025).
Dieny, B. & Chshiev, M. Perpendicular magnetic anisotropy at transition metal/oxide interfaces and applications. Rev. Mod. Phys. 89, 025008 (2017).
Monso, S. et al. Crossover from in-plane to perpendicular anisotropy in Pt/CoFe/AlOx sandwiches as a function of Al oxidation: a very accurate control of the oxidation of tunnel barriers. Appl. Phys. Lett. 80, 4157–4159 (2002).
Rodmacq, B., Auffret, S., Dieny, B., Monso, S. & Boyer, P. Crossovers from in-plane to perpendicular anisotropy in magnetic tunnel junctions as a function of the barrier degree of oxidation. J. Appl. Phys. 93, 7513–7515 (2003).
Chang, C.-Z. et al. High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator. Nat. Mater. 14, 473–477 (2015).
Checkelsky, J. G. et al. Trajectory of the anomalous Hall effect towards the quantized state in a ferromagnetic topological insulator. Nat. Phys. 10, 731–736 (2014).
Kou, X. et al. Scale-invariant quantum anomalous Hall effect in magnetic topological insulators beyond the two-dimensional limit. Phys. Rev. Lett. 113, 137201 (2014).
Mills, D. L. Surface spin-flop state in a simple antiferromagnet. Phys. Rev. Lett. 20, 18–21 (1968).
Bac, S.-K. et al. Topological response of the anomalous Hall effect in MnBi2Te4 due to magnetic canting. npj Quantum Mater. 7, 46 (2022).
Chong, S. K. et al. Intrinsic exchange biased anomalous Hall effect in an uncompensated antiferromagnet MnBi2Te4. Nat. Commun. 15, 2881 (2024).
Bartram, F. M. et al. Real-time observation of magnetization and magnon dynamics in a two-dimensional topological antiferromagnet MnBi2Te4. Sci. Bull. 68, 2734–2742 (2023).
Liu, C. et al. Magnetic-field-induced robust zero Hall plateau state in MnBi2Te4 Chern insulator. Nat. Commun. 12, 4647 (2021).
Luan, J. et al. Controlling the zero Hall plateau in a quantum anomalous Hall insulator by in-plane magnetic field. Phys. Rev. Lett. 130, 186201 (2023).
Coey, J. M. D. Magnetism and Magnetic Materials (Cambridge Univ. Press, 2010).
Chikazumi, S. & Graham, C. D. Physics of Ferromagnetism (Oxford Univ. Press, 1997).
Silevitch, D. M., Aeppli, G. & Rosenbaum, T. F. Switchable hardening of a ferromagnet at fixed temperature. Proc. Natl Acad. Sci. USA 107, 2797–2800 (2010).
Brooke, J., Rosenbaum, T. F. & Aeppli, G. Tunable quantum tunnelling of magnetic domain walls. Nature 413, 610–613 (2001).
Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104 (2010).