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Regulation of Te atomic vacancy defects in the intrinsic magnetic topological insulator \(\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}\)

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Abstract

Recently, the newly discovered magnetic topological insulator \(\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}\) has become a hot research topic in condensed matter physics because of its effects such as quantum anomalous Hall effect, axion insulation effect, and topological magnetoelectric effect. The magnetic topological insulator \(\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}\) is a potential energy material with superlattice like stacking structure. Based on first-principles calculations, we computed the band structure and density of states of five unequal Te atomic vacancy defects in ferromagnetic \(\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}\) and found that \(\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}\) has defects and, like intrinsic \(\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}\), the band inversion occurs near the \(\varGamma \)-high-symmetry point, where the conduction band is mainly contributed by the \(\textit{p}\) orbitals of Bi, but the valence band is mainly occupied by the \(\textit{p}\) orbitals of Te. But with defective sites, \(\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}\) changes from having a band gap to having no band gap. This implies that the defect of \(\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}\) is transformed from the intrinsic topological phase of \(\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}\) to the metallic phase. By calculating the density of states, we find that the Fermi level crosses the valence band in the \(\hbox {V}_{{Te}}\)1 and \(\hbox {V}_{{Te}}\)4 defect systems, while it crosses the conduction band in the \(\hbox {V}_{{Te}}\)2, \(\hbox {V}_{{Te}}\)3 and \(\hbox {V}_{{Te}}\)5 systems. The charge density difference calculations show that the Te vacancy defects at different equivalence sites mainly affect some atomic layers in their vicinity and exhibit different charge distribution characteristics for the neighboring atomic layers, respectively, essentially because of the different bonding environments in which the defects are located. Our results of different Te defect states in \(\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}\) provides valuable theoretical guidance for the experimental synthesis of single-crystal materials and the regulation of defect states in practical applications, and in addition, it has an important impact on the exploration of new quantum materials.

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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: No specific calculation data has been uploaded in this paper, and the data has not been uploaded to any website.]

References

  1. M.M. Otrokovand, T.V. Menshchikova, M.G. Vergniory, I.P. Rusinov, A.Y. Vyazovskaya, Y.M. Koroteev, G. Bihlmayer, A. Ernst, P.M. Echenique, A. Arnau, Highly-ordered wide bandgap materials for quantized anomalous Hall and magnetoelectric effects. 2D Mater. 4(2), 025082 (2017)

    Article  Google Scholar 

  2. Y. Gong, J.W. Guo, J.H. Li, K.J. Zhu, M.H. Liao, X.Z. Liu, Q.H. Zhang, L. Gu, L. Tang, X. Feng, Experimental realization of an intrinsic magnetic topological insulator. Chin. Phys. Lett. 36(7), 076801 (2019)

    Article  ADS  Google Scholar 

  3. J.H. Li, Y. Li, S.Q. Du, Z. Wang, B.L. Gu, S.C. Zhang, K. He, W.H. Duan, Y. Xu, Intrinsic magnetic topological insulators in van der Waals layered MnBi\(_{2}\)Te\(_{4}\)-family materials. Sci. Adv. 5(6), eaaw5685 (2019)

    Article  ADS  Google Scholar 

  4. D.Q. Zhang, M.J. Shi, T.S. Zhu, D.Y. Xing, H.J. Zhang, J. Wang, Topological axion states in the magnetic insulator MnBi\(_{2}\)Te\(_{4}\) with the quantized magnetoelectric effect. Phys. Rev. Lett. 122(20), 206401 (2019)

    Article  ADS  Google Scholar 

  5. M.M. Otrokov, I.P. Rusinov, M. Blanco-Rey, M. Hoffmann, A.Y. Vyazovskaya, S.V. Eremeev, A. Ernst, P.M. Echenique, A. Arnau, E.V. Chulkov, Unique thickness-dependent properties of the van der Waals interlayer antiferromagnet MnBi\(_{2}\)Te\(_{4}\) films. Phys. Rev. Lett. 122(10), 107202 (2019)

    Article  ADS  Google Scholar 

  6. M.M. Otrokov, I.I. Klimovskikh, H. Bentmann, A. Zeugner, Z.S. Aliev, S. Gass, A.U.B. Wolter, A.V. Koroleva, D. Estyunin, A.M. Shikin, Prediction and observation of the first antiferromagnetic topological insulator. Nature 576, 416–422 (2019)

    Article  ADS  Google Scholar 

  7. Y.J. Deng, Y.J. Yu, M.Z. Shi, Z.X. Guo, Z.H. Xu, J. Wang, X.H. Chen, Y.B. Zhang, Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi\(_{2}\)Te\(_{4}\). Science 367(6480), 895–900 (2020)

    Article  ADS  Google Scholar 

  8. C. Liu, Y.C. Wang, H. Li, Y. Wu, Y.X. Li, J.H. Li, K. He, Y. Xu, J.S. Zhang, Y.Y. Wang, Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator. Nat. Mater. 19, 522–527 (2020)

  9. W.T. Guo, L. Huang, G.G. Xu, K.H. Zhong, J.M. Zhang, Z.G. Huang, Pressure strain control of electronic structure of intrinsic magnetic topological insulator MnBi\(_{2}\)Te\(_{4}\). Acta Phys. Sin. 70(4), 047101 (2021)

    Google Scholar 

  10. C.Z. Chang, W.W. Zhao, D.Y. Kim, H.J. Zhang, B.A. Assaf, D. Heiman, S.C. Zhang, C.X. Liu, M.H.W. Chan, J.S. Moodera, High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator. Nat. Mater. 14(5), 473–477 (2015)

    Article  ADS  Google Scholar 

  11. C.Z. Chang, J. Zhang, X. Feng, J. Shen, Q.K. Xue, Experimental observation of the quantum anomalous hall effect in a magnetic topological insulator. Science 340(6129), 167–170 (2013)

    Article  ADS  Google Scholar 

  12. F.D.M. Haldane, Model for a quantum hall effect without Landau levels: Condensed-matter realization of the Parity Anomaly. Phys. Rev. Lett. 61(18), 2015–2018 (1988)

    Article  ADS  Google Scholar 

  13. M.Z. Shi, B. Lei, C.S. Zhu, D.H. Ma, J.H. Cui, Z.L. Sun, J.J. Ying, X.H. Chen, Magnetic and transport properties in the magnetic topological insulators MnBi\(_{2}\)Te\(_{4}\)(Bi\(_{2}\)Te\(_{3}\) ) \(_{n}\) (n= 1, 2). Phys. Rev. B 100(15), 155144 (2019)

    Article  ADS  Google Scholar 

  14. Z.S. Aliev, I.R. Amiraslanov, D.I. Nasonova, A.V. Shevelkov, N.A. Abdullayev, Z.A. Jahangirli, E.N. Orujlu, M.M. Otrokov, N.T. Mamedov, M.B. Babanly, Novel ternary layered manganese bismuth tellurides of the MnTe-Bi\(_{2}\)Te\(_{3}\) system: Synthesis and crystal structure. J. Alloys Compd. 789(15), 443–450 (2019)

    Article  Google Scholar 

  15. R.C. Vidal, H. Bentmann, J.I. Facio, P.Kagerer, C.I. Fornari, T.R.F. Peixoto, T. Figgemeier, S. Jung, C. Cacho, B. Büchner, Orbital complexity in intrinsic magnetic topological insulators MnBi\(_{4}\)Te\(_{7}\) and MnBi\(_{6}\)Te\(_{10}\). Phys. Rev. Lett. 126, 176403 (2021)

  16. Y. Hu, L.X. Xu, M.Z. Shi, A.Y. Luo, S.T. Peng, Z.Y. Wang, J.J. Ying, T. Wu, Z.K. Liu, C.F. Zhang, Universal gapless Dirac cone and tunable topological states in (MnBi\(_{2}\)Te\(_{4}\))\(_{m}\)(Bi\(_{2}\)Te\(_{3}\))\(_{n}\) heterostructures. Phys. Rev. B 101(16), 161113 (2020)

    Article  ADS  Google Scholar 

  17. J.Q. Yan, Y.H. Liu, D.S. Parker, Y. Wu, A.A. Aczel, M. Matsuda, M.A. McGuire, B.C. Sales, A-type antiferromagnetic order in MnBi\(_{4}\)Te\(_{7}\) and MnBi\(_{6}\)Te\(_{10}\) single crystals. Phys. Rev. Mater. 4(5), 054202 (2020)

    Article  Google Scholar 

  18. I.I. Klimovskikh, M.M. Otrokov, D. Estyunin, S.V. Eremeev, E.V. Chulkov, Tunable 3D/2D magnetism in the (MnBi\(_{2}\)Te\(_{4}\))(Bi\(_{2}\)Te\(_{3}\))\(_{m}\) topological insulators family. npj Quantum Mater. 5(1), 54 (2020)

    Article  ADS  Google Scholar 

  19. S.J. Tian, S.Y. Gao, S.M. Nie, Y.T. Qian, C.S. Gong, Y. Fu, H. Li, W.H. Fan, P. Zhang, T. Kondo, Magnetic topological insulator in MnBi\(_{6}\)Te\(_{10}\) with zero-field ferromagnetic state. Phys. Rev. B 102(3), 035144 (2020)

    Article  ADS  Google Scholar 

  20. N.H. Jo, L.L. Wang, R.J. Slang, J.Q. Yan, Y. Wu, K. Lee, B. Schrunk, A. Vishwanath, A. Kaminski, Intrinsic axion insulating behavior in antiferromagnetic MnBi\(_{6}\)Te\(_{10}\). Phys. Rev. B 102(4), 045130 (2020)

    Article  ADS  Google Scholar 

  21. H.Y. Sun, B. Xia, Z.J. Chen, Y.J. Zhang, P.F. Liu, Q.S. Yao, H. Tang, Y.J. Zhao, H. Xu, Q.H. Liu, Rational design principles of the quantum anomalous Hall effect in superlatticelike magnetic topological insulators. Phys. Rev. Lett. 123(9), 096401 (2019)

    Article  ADS  Google Scholar 

  22. J.Z. Wu, F.C. Liu, M. Sasase, K. Ienaga, Y. Obata, R. Yukawa, K. Horiba, H. Kumigashira, S. Okuma, T. Inoshita, Natural van der Waals heterostructural single crystals with both magnetic and topological properties. Sci. Adv. 5(11), eaax9989 (2019)

    Article  ADS  Google Scholar 

  23. J.F. Shao, Y.T. Liu, M. Zeng, J.Y. Li, X.M. Ma, F. Jin, R.E. Lu, Y.C. Sun, M.Q. Gu, W.B. Wu, Pressure-tuned intralayer exchange in superlattice-like MnBi\(_{2}\)Te\(_{4}\)/(Bi\(_{2}\)Te\(_{3}\))\(_{n}\) topological insulators. Nano Lett. 21(13), 5874–5880 (2021)

  24. M.H. Du, J.Q. Yan, V.R. Cooper, M. Eisenbach, Tuning fermi levels in intrinsic antiferromagnetic topological insulators MnBi\(_{2}\)Te\(_{4}\) and MnBi\(_{4}\)Te\(_{7}\) by defect engineering and chemical doping. Adv. Funct. Mater. 31(3), 2006516 (2021)

    Article  Google Scholar 

  25. Z.L. Huang, M.H. Du, J.Q. Yan, W.D. Wu, Native defects in antiferromagnetic topological insulator MnBi\(_{2}\)Te\(_{4}\). Phys. Rev. Mater. 4(12), 121202 (2020)

    Article  Google Scholar 

  26. A. Bafekry, B. Akgenc, S.F. Shayesteh, B. Mortazavi, Tunable electronic and magnetic properties of graphene/carbon-nitride van der Waals heterostructures. Appl. Surf. Sci. 505, 144450 (2020)

    Article  Google Scholar 

  27. G.J. Xiao, C.Y. Zhu, Y.M. Ma, B.B. Liu, G.T. Zou, B. Zou, Unexpected room-temperature ferromagnetism in nanostructured Bi\(_{2}\)Te\(_{3}\). Angew. Chem. 126(3), 748–752 (2014)

    Article  ADS  Google Scholar 

  28. P.E. Blöchl, Projector augmented-wave method. Phys. Rev. B 50(24), 17953 (1994)

    Article  ADS  Google Scholar 

  29. G. Kresse, J. Hafner, Ab initio molecular dynamics for open-shell transition metals. Phys. Rev. B 48(17), 13115 (1993)

    Article  ADS  Google Scholar 

  30. G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54(16), 11169 (1996)

    Article  ADS  Google Scholar 

  31. J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple. Phys. Rev. Lett. 77(18), 3865 (1996)

    Article  ADS  Google Scholar 

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Acknowledgements

We acknowledge the financial support by the National Natural Science Foundation of China (No. 11874113), the Natural Science Foundation of Fujian Province of China (No. 2020J02018) and Undergraduate Innovation Training Program of Fujian Normal University (No. S202010394017). The work was carried out at National Supercomputer Center in Tianjin,and the calculations were performed on TianHe-1(A).

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J.-M. Zhang conceived and supervised this work. L. Huang, W.-T. Guo and S. Guo performed the calculations. L. Huang and W.-T. Guo wrote the original draft. L.Huang, Q. Ye and J.-M. Zhang review and edit the manuscript. Z. Huang analyzed the data and provided constructive suggestions.

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Correspondence to Jian-Min Zhang.

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Huang, L., Guo, WT., Guo, S. et al. Regulation of Te atomic vacancy defects in the intrinsic magnetic topological insulator \(\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}\). Eur. Phys. J. B 94, 206 (2021). https://doi.org/10.1140/epjb/s10051-021-00196-7

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