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Topological properties of domain walls in antiferromagnetic topological insulators

Gabriele Naselli1,2 and Ion Cosma Fulga1

  • 1Institute for Theoretical Solid State Physics, IFW Dresden and Würzburg-Dresden Cluster of Excellence ct.qmat, Helmholtzstr. 20, 01069 Dresden, Germany
  • 2Dipartimento di Fisica “E. R. Caianiello”, Universitá di Salerno, IT-84084 Fisciano, Italy

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Phys. Rev. B 112, 125411 – Published 9 September, 2025

DOI: https://doi.org/10.1103/n55h-yntb

Abstract

Motivated by the study of stacking faults in weak topological insulators and the observation of magnetic domain walls in MnBi2nTe3n+1, we explore the topological properties of magnetic domain walls in antiferromagnetic topological insulators. We develop two tight-binding models for two different types of antiferromagnetic topological insulators: the first type obtained by adding antiferromagnetic order to a strong topological insulator and another built from stacked Chern insulating layers with alternating Chern numbers. Both systems are dual topological insulators, i.e., they are at the same time antiferromagnetic and crystalline topological insulators, but differ by the type of mirror symmetry protecting the crystalline phase: spinful versus spinless. We show that in the spinful case the mirror Chern number is invariant under time reversal and that it changes sign in the spinless case. This influences the properties of the two systems in the presence of a magnetic domain wall, which we model as an interface between two regions of opposite magnetization. In the first type, the bulk of the magnetic domain wall is gapped but the defect will host chiral edge states when it ends on an external ferromagnetic surface. In the second, due to the change in the sign of the mirror Chern number, the magnetic domain wall is a two-dimensional (2D) embedded semimetal with 2D gapless states protected by mirror symmetry. Our results show that magnetic domain walls can be a source of nontrivial topology, allowing one to generate and manipulate gapless states within the bulk and the ferromagnetic surfaces of antiferromagnetic topological insulators.

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References (62)

  1. B. A. Bernevig, C. Felser, and H. Beidenkopf, Progress and prospects in magnetic topological materials, Nature (London) 603, 41 (2022).
  2. Y. Wang, F. Zhang, M. Zeng, H. Sun, Z. Hao, Y. Cai, H. Rong, C. Zhang, C. Liu, X. Ma, L. Wang, S. Guo, J. Lin, Q. Liu, C. Liu, and C. Chen, Intrinsic magnetic topological materials, Front. Phys. 18, 21304 (2023).
  3. C.-Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y. Ou, P. Wei, L.-L. Wang, Z.-Q. Ji, Y. Feng, S. Ji, X. Chen, J. Jia, X. Dai, Z. Fang, S.-C. Zhang, K. He, Y. Wang et al., Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator, Science 340, 167 (2013).
  4. J. G. Checkelsky, R. Yoshimi, A. Tsukazaki, K. S. Takahashi, Y. Kozuka, J. Falson, M. Kawasaki, and Y. Tokura, Trajectory of the anomalous Hall effect towards the quantized state in a ferromagnetic topological insulator, Nat. Phys. 10, 731 (2014).
  5. M. M. Otrokov, I. I. Klimovskikh, H. Bentmann, D. Estyunin, A. Zeugner, Z. S. Aliev, S. Gaß, A. U. B. Wolter, A. V. Koroleva, A. M. Shikin, M. Blanco-Rey, M. Hoffmann, I. P. Rusinov, A. Y. Vyazovskaya, S. V. Eremeev, Y. M. Koroteev, V. M. Kuznetsov, F. Freyse, J. Sánchez-Barriga, I. R. Amiraslanov et al., Prediction and observation of an antiferromagnetic topological insulator, Nature (London) 576, 416 (2019).
  6. Y. Gong, J. Guo, J. Li, K. Zhu, M. Liao, X. Liu, Q. Zhang, L. Gu, L. Tang, X. Feng, D. Zhang, W. Li, C. Song, L. Wang, P. Yu, X. Chen, Y. Wang, H. Yao, W. Duan, Y. Xu et al., Experimental realization of an intrinsic magnetic topological insulator, Chin. Phys. Lett. 36, 076801 (2019).
  7. H. Li, S.-Y. Gao, S.-F. Duan, Y.-F. Xu, K.-J. Zhu, S.-J. Tian, J.-C. Gao, W.-H. Fan, Z.-C. Rao, J.-R. Huang, J.-J. Li, D.-Y. Yan, Z.-T. Liu, W.-L. Liu, Y.-B. Huang, Y.-L. Li, Y. Liu, G.-B. Zhang, P. Zhang, T. Kondo et al., Dirac surface states in intrinsic magnetic topological insulators EuSn2As2 and MnBi2nTe3n+1, Phys. Rev. X 9, 041039 (2019).
  8. S. V. Eremeev, I. P. Rusinov, Y. M. Koroteev, A. Y. Vyazovskaya, M. Hoffmann, P. M. Echenique, A. Ernst, M. M. Otrokov, and E. V. Chulkov, Topological magnetic materials of the (MnSb2Te4)·(Sb2Te3)n van der Waals compounds family, J. Phys. Chem. Lett. 12, 4268 (2021).
  9. N. Varnava, T. Berry, T. M. McQueen, and D. Vanderbilt, Engineering magnetic topological insulators in Eu5M2X6 Zintl compounds, Phys. Rev. B 105, 235128 (2022).
  10. S. Roychowdhury, K. Samanta, P. Yanda, B. Malaman, M. Yao, W. Schnelle, E. Guilmeau, P. Constantinou, S. Chandra, H. Borrmann, M. G. Vergniory, V. Strocov, C. Shekhar, and C. Felser, Interplay between magnetism and topology: Large topological Hall effect in an antiferromagnetic topological insulator, EuCuAs, J. Am. Chem. Soc. 145, 12920 (2023).
  11. Y. Jiang, H. Wang, and J. Wang, Large-gap quantum anomalous Hall insulators in the ATiX (A=K, Rb, Sr; X=Sb, Bi, Sn) class of compounds, Phys. Rev. B 108, 165122 (2023).
  12. H. Liu, Q.-Y. Wu, C. Zhang, J. Pang, B. Chen, J.-J. Song, Y.-X. Duan, Y.-H. Yuan, H.-Y. Liu, C.-C. Shu, Y.-F. Xu, Y.-G. Shi, and J.-Q. Meng, Exploring intrinsic magnetic topological insulators: The case of EuIn2As2, Phys. Rev. B 110, 195104 (2024).
  13. C. Fang, M. J. Gilbert, X. Dai, and B. A. Bernevig, Multi-weyl topological semimetals stabilized by point group symmetry, Phys. Rev. Lett. 108, 266802 (2012).
  14. P. Tang, Q. Zhou, G. Xu, and S.-C. Zhang, Dirac fermions in an antiferromagnetic semimetal, Nat. Phys. 12, 1100 (2016).
  15. H. Yang, Y. Sun, Y. Zhang, W.-J. Shi, S. S. P. Parkin, and B. Yan, Topological Weyl semimetals in the chiral antiferromagnetic materials Mn3Ge and Mn3Sn, New J. Phys. 19, 015008 (2017).
  16. I. Belopolski, K. Manna, D. S. Sanchez, G. Chang, B. Ernst, J. Yin, S. S. Zhang, T. Cochran, N. Shumiya, H. Zheng, B. Singh, G. Bian, D. Multer, M. Litskevich, X. Zhou, S.-M. Huang, B. Wang, T.-R. Chang, S.-Y. Xu, A. Bansil et al., Discovery of topological Weyl fermion lines and drumhead surface states in a room temperature magnet, Science 365, 1278 (2019).
  17. S. Nie, H. Weng, and F. B. Prinz, Topological nodal-line semimetals in ferromagnetic rare-earth-metal monohalides, Phys. Rev. B 99, 035125 (2019).
  18. J. Cano, B. Bradlyn, and M. G. Vergniory, Multifold nodal points in magnetic materials, APL Mater. 7, 101125 (2019).
  19. C. Li, M. Hu, Z. Li, Y. Wang, W. Chen, B. Thiagarajan, M. Leandersson, C. Polley, T. Kim, H. Liu, C. Fulga, M. G. Vergniory, O. Janson, O. Tjernberg, and J. v. d. Brink, Topological Weyl altermagnetism in CrSb, Commun. Phys. 8, 311 (2025).
  20. H.-Y. Ma and J.-F. Jia, Altermagnetic topological insulator and the selection rules, Phys. Rev. B 110, 064426 (2024).
  21. R. S. K. Mong, A. M. Essin, and J. E. Moore, Antiferromagnetic topological insulators, Phys. Rev. B 81, 245209 (2010).
  22. L. Fu, C. L. Kane, and E. J. Mele, Topological insulators in three dimensions, Phys. Rev. Lett. 98, 106803 (2007).
  23. L. Fu and C. L. Kane, Time reversal polarization and a Z2 adiabatic spin pump, Phys. Rev. B 74, 195312 (2006).
  24. J. E. Moore and L. Balents, Topological invariants of time-reversal-invariant band structures, Phys. Rev. B 75, 121306(R) (2007).
  25. C. Fang, M. J. Gilbert, and B. A. Bernevig, Topological insulators with commensurate antiferromagnetism, Phys. Rev. B 88, 085406 (2013).
  26. I. C. Fulga, B. van Heck, J. M. Edge, and A. R. Akhmerov, Statistical topological insulators, Phys. Rev. B 89, 155424 (2014).
  27. L. Fu, Topological crystalline insulators, Phys. Rev. Lett. 106, 106802 (2011).
  28. T. H. Hsieh, H. Lin, J. Liu, W. Duan, A. Bansil, and L. Fu, Topological crystalline insulators in the SnTe material class, Nat. Commun. 3, 982 (2012).
  29. Y. Ando and L. Fu, Topological crystalline insulators and topological superconductors: From concepts to materials, Annu. Rev. Condens. Matter Phys. 6, 361 (2015).
  30. Z. Zhang, R.-W. Zhang, X. Li, K. Koepernik, Y. Yao, and H. Zhang, High-throughput screening and automated processing toward novel topological insulators, J. Phys. Chem. Lett. 9, 6224 (2018).
  31. J. C. Y. Teo and C. L. Kane, Topological defects and gapless modes in insulators and superconductors, Phys. Rev. B 82, 115120 (2010).
  32. Y. Ran, Y. Zhang, and A. Vishwanath, One-dimensional topologically protected modes in topological insulators with lattice dislocations, Nat. Phys. 5, 298 (2009).
  33. J. C. Teo and T. L. Hughes, Topological defects in symmetry-protected topological phases, Annu. Rev. Condens. Matter Phys. 8, 211 (2017).
  34. V. Juričić, A. Mesaros, R.-J. Slager, and J. Zaanen, Universal probes of two-dimensional topological insulators: Dislocation and π flux, Phys. Rev. Lett. 108, 106403 (2012).
  35. T. L. Hughes, H. Yao, and X.-L. Qi, Majorana zero modes in dislocations of Sr2RuO4, Phys. Rev. B 90, 235123 (2014).
  36. J. C. Y. Teo and T. L. Hughes, Existence of majorana-fermion bound states on disclinations and the classification of topological crystalline superconductors in two dimensions, Phys. Rev. Lett. 111, 047006 (2013).
  37. W. A. Benalcazar, J. C. Y. Teo, and T. L. Hughes, Classification of two-dimensional topological crystalline superconductors and Majorana bound states at disclinations, Phys. Rev. B 89, 224503 (2014).
  38. G. Naselli, V. Könye, S. K. Das, G. G. N. Angilella, A. Isaeva, J. van den Brink, and C. Fulga, Nontrivial gapless electronic states at the stacking faults of weak topological insulators, Phys. Rev. B 106, 094105 (2022).
  39. M. M. Otrokov, T. V. Menshchikova, M. G. Vergniory, I. P. Rusinov, A. Yu Vyazovskaya, Y. M. Koroteev, G. Bihlmayer, A. Ernst, P. M. Echenique, A. Arnau, and E. V. Chulkov, Highly-ordered wide bandgap materials for quantized anomalous Hall and magnetoelectric effects, 2D Mater. 4, 025082 (2017).
  40. M. M. Otrokov, I. P. Rusinov, M. Blanco-Rey, M. Hoffmann, A. Y. Vyazovskaya, S. V. Eremeev, A. Ernst, P. M. Echenique, A. Arnau, and E. V. Chulkov, Unique thickness-dependent properties of the van der Waals interlayer antiferromagnet MnBi2Te4 films, Phys. Rev. Lett. 122, 107202 (2019).
  41. J. Li, Y. Li, S. Du, Z. Wang, B.-L. Gu, S.-C. Zhang, K. He, W. Duan, and Y. Xu, Intrinsic magnetic topological insulators in van der Waals layered MnBi2Te4-family materials, Sci. Adv. 5, eaaw5685 (2019).
  42. Y. Deng, Y. Yu, M. Z. Shi, Z. Guo, Z. Xu, J. Wang, X. H. Chen, and Y. Zhang, Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4, Science 367, 895 (2020).
  43. A. Gao, Y.-F. Liu, C. Hu, J.-X. Qiu, C. Tzschaschel, B. Ghosh, S.-C. Ho, D. Bérubé, R. Chen, H. Sun, Z. Zhang, X.-Y. Zhang, Y.-X. Wang, N. Wang, Z. Huang, C. Felser, A. Agarwal, T. Ding, H.-J. Tien, A. Akey et al., Layer Hall effect in a 2D topological axion antiferromagnet, Nature (London) 595, 521 (2021).
  44. W.-B. Dai, H. Li, D.-H. Xu, C.-Z. Chen, and X. C. Xie, Quantum anomalous layer Hall effect in the topological magnet MnBi2Te4, Phys. Rev. B 106, 245425 (2022).
  45. Y. Lin and J. Feng, Topological surfaces of domain wall-decorated antiferromagnetic topological insulator MnBi2nTe3n+1, arXiv:2201.11938.
  46. H.-K. Xu, M. Gu, F. Fei, Y.-S. Gu, D. Liu, Q.-Y. Yu, S.-S. Xue, X.-H. Ning, B. Chen, H. Xie, Z. Zhu, D. Guan, S. Wang, Y. Li, C. Liu, Q. Liu, F. Song, H. Zheng, and J. Jia, Observation of magnetism-induced topological edge state in antiferromagnetic topological insulator MnBi4Te7, ACS Nano 16, 9810 (2022).
  47. P. M. Sass, J. Kim, D. Vanderbilt, J. Yan, and W. Wu, Robust A-type order and spin-flop transition on the surface of the antiferromagnetic topological insulator MnBi2Te4, Phys. Rev. Lett. 125, 037201 (2020).
  48. W. Ge, J. Kim, Y.-T. Chan, D. Vanderbilt, J. Yan, and W. Wu, Direct visualization of surface spin-flip transition in MnBi4Te7, Phys. Rev. Lett. 129, 107204 (2022).
  49. W. Liang, T. Hou, J. Zeng, Z. Liu, Y. Han, and Z. Qiao, Layer-dependent zero-line modes in antiferromagnetic topological insulators, Phys. Rev. B 107, 075303 (2023).
  50. N. Varnava, J. H. Wilson, J. H. Pixley, and D. Vanderbilt, Controllable quantum point junction on the surface of an antiferromagnetic topological insulator, Nat. Commun. 12, 3998 (2021).
  51. I. P. Rusinov, V. N. Men'shov, and E. V. Chulkov, Spectral features of magnetic domain walls on the surface of three-dimensional topological insulators, Phys. Rev. B 104, 035411 (2021).
  52. S. K. Das, B. Yan, J. van den Brink, and I. C. Fulga, Topological crystalline insulators from stacked graphene layers, Phys. Rev. B 99, 165418 (2019).
  53. J. I. Facio, S. K. Das, Y. Zhang, K. Koepernik, J. van den Brink, and I. C. Fulga, Dual topology in jacutingaite Pt2HgSe3, Phys. Rev. Mater. 3, 074202 (2019).
  54. G. Naselli, A. G. Moghaddam, S. Di Napoli, V. Vildosola, I. C. Fulga, J. van den Brink, and J. I. Facio, Magnetic warping in topological insulators, Phys. Rev. Res. 4, 033198 (2022).
  55. P. Hosur, S. Ryu, and A. Vishwanath, Chiral topological insulators, superconductors, and other competing orders in three dimensions, Phys. Rev. B 81, 045120 (2010).
  56. C. L. Kane and E. J. Mele, Quantum spin Hall effect in graphene, Phys. Rev. Lett. 95, 226801 (2005).
  57. C. L. Kane and E. J. Mele, Z2 topological order and the quantum spin Hall effect, Phys. Rev. Lett. 95, 146802 (2005).
  58. X.-L. Qi, Y.-S. Wu, and S.-C. Zhang, Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors, Phys. Rev. B 74, 085308 (2006).
  59. J. K. Asbóth, L. Oroszlány, and A. Pályi, A Short Course on Topological Insulators (Springer International Publishing, Cham, 2016).
  60. S. Velury and T. L. Hughes, Embedded topological semimetals, Phys. Rev. B 105, 184105 (2022).
  61. C. W. Groth, M. Wimmer, A. R. Akhmerov, and X. Waintal, Kwant: a software package for quantum transport, New J. Phys. 16, 063065 (2014).
  62. G. Naselli and I. C. Fulga, Topological properties of domain walls in antiferromagnetic topological insulators, Zenodo (2025), doi: https://zenodo.org/doi/10.5281/zenodo.15441667.

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Phys. Rev. B 112, 125411– Published 9 September, 2025
  • Received 16 May 2025
  • Revised 13 August 2025
  • Accepted 26 August 2025
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