- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Finite temperature fluctuation-induced order and responses in magnetic topological insulators

Marius Scholten1, Jorge I. Facio1, Rajyavardhan Ray1,2, Ilya M. Eremin3, Jeroen van den Brink1,4, and Flavio S. Nogueira1

  • 1Institute for Theoretical Solid State Physics, IFW Dresden, Helmholtzstrasse 20, D-01069 Dresden, Germany
  • 2Dresden Center for Computational Materials Science (DCMS), TU Dresden, D-01062 Dresden, Germany
  • 3Institut für Theoretische Physik III, Ruhr-Universität Bochum, D-44780 Bochum, Germany
  • 4Institute for Theoretical Physics and Würzburg-Dresden Cluster of Excellence ct.qmat, TU Dresden, D-01069 Dresden, Germany

PDF

Phys. Rev. Research 3, L032014 – Published 9 July, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L032014

Abstract

We derive an effective field theory model for magnetic topological insulators and predict that a magnetic electronic gap persists on the surface for temperatures above the ordering temperature of the bulk. Our analysis also applies to interfaces of heterostructures consisting of a ferromagnetic and a topological insulator. In order to make quantitative predictions for MnBi2Te4 and for EuS-Bi2Se3 heterostructures, we combine the effective field theory method with density functional theory and Monte Carlo simulations. For MnBi2Te4 we predict an upwards Néel temperature shift at the surface up to 15%, while the EuS-Bi2Se3 interface exhibits a smaller relative shift. The effective theory also predicts induced Dzyaloshinskii-Moriya interactions and a topological magnetoelectric effect, both of which feature a finite temperature and chemical potential dependence.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (55)

  1. C.-X. Liu, S.-C. Zhang, and X.-L. Qi, The quantum anomalous Hall effect: Theory and experiment, Annu. Rev. Condens. Matter Phys. 7, 301 (2016).
  2. T. Yokoyama, J. Zang, and N. Nagaosa, Theoretical study of the dynamics of magnetization on the topological surface, Phys. Rev. B 81, 241410(R) (2010).
  3. I. Garate and M. Franz, Inverse Spin-Galvanic Effect in the Interface between a Topological Insulator and a Ferromagnet, Phys. Rev. Lett. 104, 146802 (2010).
  4. Y. Tserkovnyak and D. Loss, Thin-Film Magnetization Dynamics on the Surface of a Topological Insulator, Phys. Rev. Lett. 108, 187201 (2012).
  5. F. S. Nogueira and I. Eremin, Fluctuation-Induced Magnetization Dynamics and Criticality at the Interface of a Topological Insulator with a Magnetically Ordered Layer, Phys. Rev. Lett. 109, 237203 (2012).
  6. F. S. Nogueira and I. Eremin, Thermal screening at finite chemical potential on a topological surface and its interplay with proximity-induced ferromagnetism, Phys. Rev. B 90, 014431 (2014).
  7. F. S. Nogueira and I. Eremin, Semimetal-insulator transition on the surface of a topological insulator with in-plane magnetization, Phys. Rev. B 88, 085126 (2013).
  8. Y. Tserkovnyak, D. A. Pesin, and D. Loss, Spin and orbital magnetic response on the surface of a topological insulator, Phys. Rev. B 91, 041121(R) (2015).
  9. S. Rex, F. S. Nogueira, and A. Sudbø, Nonlocal topological magnetoelectric effect by Coulomb interaction at a topological insulator-ferromagnet interface, Phys. Rev. B 93, 014404 (2016).
  10. M. Li, W. Cui, J. Yu, Z. Dai, Z. Wang, F. Katmis, W. Guo, and J. Moodera, Magnetic proximity effect and interlayer exchange coupling of ferromagnetic/topological insulator/ferromagnetic trilayer, Phys. Rev. B 91, 014427 (2015).
  11. S. Rex, F. S. Nogueira, and A. Sudbø, Topological magnetic dipolar interaction and nonlocal electric magnetization control in topological insulator heterostructures, Phys. Rev. B 94, 020404(R) (2016).
  12. F. Katmis, V. Lauter, F. S. Nogueira, B. A. Assaf, M. E. Jamer, P. Wei, B. Satpati, J. W. Freeland, I. Eremin, D. Heiman, P. Jarillo-Herrero, and J. S. Moodera, A high-temperature ferromagnetic topological insulating phase by proximity coupling, Nature (London) 533, 513 (2016).
  13. P. Wei, F. Katmis, B. A. Assaf, H. Steinberg, P. Jarillo-Herrero, D. Heiman, and J. S. Moodera, Exchange-Coupling-Induced Symmetry Breaking in Topological Insulators, Phys. Rev. Lett. 110, 186807 (2013).
  14. Q. I. Yang, M. Dolev, L. Zhang, J. Zhao, A. D. Fried, E. Schemm, M. Liu, A. Palevski, A. F. Marshall, S. H. Risbud, and A. Kapitulnik, Emerging weak localization effects on a topological insulator–insulating ferromagnet (Bi2Se3-EuS) interface, Phys. Rev. B 88, 081407(R) (2013).
  15. C. Lee, F. Katmis, P. Jarillo-Herrero, J. S. Moodera, and N. Gedik, Direct measurement of proximity-induced magnetism at the interface between a topological insulator and a ferromagnet, Nat. Commun. 7, 12014 (2016).
  16. Q. L. He, X. Kou, A. J. Grutter, G. Yin, L. Pan, X. Che, Y. Liu, T. Nie, B. Zhang, S. M. Disseler, B. J. Kirby, W. Ratcliff, II, Q. Shao, K. Murata, X. Zhu, G. Yu, Y. Fan, M. Montazeri, X. Han, J. A. Borchers, and K. L. Wang, Tailoring exchange couplings in magnetic topological-insulator/antiferromagnet heterostructures, Nat. Mater. 16, 94 (2017).
  17. 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. Yu. Vyazovskaya, S. V. Eremeev, Yu. 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).
  18. 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).
  19. A. Zeugner, F. Nietschke, A. U. B. Wolter, S. Gaß, R. C. Vidal, T. R. F. Peixoto, D. Pohl, C. Damm, A. Lubk, R. Hentrich, S. K. Moser, C. Fornari, C. H. Min, S. Schatz, K. Kißner, M. Ünzelmann, M. Kaiser, F. Scaravaggi, B. Rellinghaus, K. Nielsch et al., Chemical aspects of the candidate antiferromagnetic topological insulator MnBi2Te4, Chem. Mater. 31, 2795 (2019).
  20. R. C. Vidal, H. Bentmann, T. R. F. Peixoto, A. Zeugner, S. Moser, C.-H. Min, S. Schatz, K. Kißner, M. Ünzelmann, C. I. Fornari, H. B. Vasili, M. Valvidares, K. Sakamoto, D. Mondal, J. Fujii, I. Vobornik, S. Jung, C. Cacho, T. K. Kim, R. J. Koch, C. Jozwiak, A. Bostwick, J. D. Denlinger, E. Rotenberg, J. Buck, M. Hoesch, F. Diekmann, S. Rohlf, M. Kalläne, K. Rossnagel, M. M. Otrokov, E. V. Chulkov, M. Ruck, A. Isaeva, and F. Reinert, Surface states and Rashba-type spin polarization in antiferromagnetic MnBi2Te4(0001), Phys. Rev. B 100, 121104(R) (2019).
  21. M. M. Otrokov, I. P. Rusinov, M. Blanco-Rey, M. Hoffmann, A. Yu. 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).
  22. R. C. Vidal, A. Zeugner, J. I. Facio, R. Ray, M. H. Haghighi, A. U. B. Wolter, L. T. Corredor Bohorquez, F. Caglieris, S. Moser, T. Figgemeier, T. R. F. Peixoto, H. B. Vasili, M. Valvidares, S. Jung, C. Cacho, A. Alfonsov, K. Mehlawat, V. Kataev, C. Hess, M. Richter, B. Büchner, J. van den Brink, M. Ruck, F. Reinert, H. Bentmann, and A. Isaeva, Topological Electronic Structure and Intrinsic Magnetization in MnBi4Te7: A Bi2Te3 Derivative with a Periodic Mn Sublattice, Phys. Rev. X 9, 041065 (2019).
  23. B. Chen, F. Fei, D. Zhang, B. Zhang, W. Liu, S. Zhang, P. Wang, B. Wei, Y. Zhang, Z. Zuo et al., Intrinsic magnetic topological insulator phases in the Sb doped MnBi2Te4 bulks and thin flakes, Nat. Commun. 10, 4469 (2019).
  24. S. Wimmer, J. Sánchez-Barriga, P. Küppers, A. Ney, E. Schierle, F. Freyse, O. Caha, J. Michalicka, M. Liebmann, D. Primetzhofer, M. Hoffmann, A. Ernst, M. M. Otrokov, G. Bihlmayer, E. Weschke, B. Lake, E. V. Chulkov, M. Morgenstern, G. Bauer, G. Springholz, and O. Rader, Ferromagnetic MnSb2Te4: A topological insulator with magnetic gap closing at high Curie temperatures of 45–50 K, arXiv:2011.07052.
  25. T. Hirahara, S. V. Eremeev, T. Shirasawa, Y. Okuyama, T. Kubo, R. Nakanishi, R. Akiyama, A. Takayama, T. Hajiri, S.-i. Ideta, M. Matsunami, K. Sumida, K. Miyamoto, Y. Takagi, K. Tanaka, T. Okuda, T. Yokoyama, S.-i. Kimura, S. Hasegawa, and E. V. Chulkov, Large-gap magnetic topological heterostructure formed by subsurface incorporation of a ferromagnetic layer, Nano Lett. 17, 3493 (2017).
  26. T. Hirahara, M. M. Otrokov, T. T. Sasaki, K. Sumida, Y. Tomohiro, S. Kusaka, Y. Okuyama, S. Ichinokura, M. Kobayashi, Y. Takeda, K. Amemiya, T. Shirasawa, S. Ideta, K. Miyamoto, K. Tanaka, S. Kuroda, T. Okuda, K. Hono, S. V. Eremeev, and E. V. Chulkov, Fabrication of a novel magnetic topological heterostructure and temperature evolution of its massive Dirac cone, Nat. Commun. 11, 4821 (2020).
  27. X.-L. Qi, T. L. Hughes, and S.-C. Zhang, Topological field theory of time-reversal invariant insulators, Phys. Rev. B 78, 195424 (2008).
  28. S. Ryu, J. E. Moore, and A. W. W. Ludwig, Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors, Phys. Rev. B 85, 045104 (2012).
  29. C. Tutschku, F. S. Nogueira, C. Northe, J. van den Brink, and E. M. Hankiewicz, Temperature and chemical potential dependence of the parity anomaly in quantum anomalous Hall insulators, Phys. Rev. B 102, 205407 (2020).
  30. F. S. Nogueira, I. Eremin, F. Katmis, J. S. Moodera, J. van den Brink, and V. P. Kravchuk, Fluctuation-induced Néel and Bloch skyrmions at topological insulator surfaces, Phys. Rev. B 98, 060401(R) (2018).
  31. K. L. Tiwari, J. Lavoie, T. Pereg-Barnea, and W. A. Coish, Tunable skyrmion-skyrmion binding on the surface of a topological insulator, Phys. Rev. B 100, 125414 (2019).
  32. S. Zhang, F. Kronast, G. van der Laan, and T. Hesjedal, Real-space observation of skyrmionium in a ferromagnet-magnetic topological insulator heterostructure, Nano Lett. 18, 1057 (2018).
  33. J. Kim, K.-W. Kim, H. Wang, J. Sinova, and R. Wu, Understanding the Giant Enhancement of Exchange Interaction in Bi2Se3-EuS Heterostructures, Phys. Rev. Lett. 119, 027201 (2017).
  34. H. Wang, Y. Liu, P. Wu, W. Hou, Y. Jiang, X. Li, C. Pandey, D. Chen, Q. Yang, H. Wang, D. Wei, N. Lei, W. Kang, L. Wen, T. Nie, W. Zhao, and K. L. Wang, Above room-temperature ferromagnetism in wafer-scale two-dimensional van der Waals Fe3GeTe2 tailored by a topological insulator, ACS Nano 14, 10045 (2020).
  35. J. A. Krieger, Y. Ou, M. Caputo, A. Chikina, M. Döbeli, M.-A. Husanu, I. Keren, T. Prokscha, A. Suter, C.-Z. Chang, J. S. Moodera, V. N. Strocov, and Z. Salman, Do topology and ferromagnetism cooperate at the EuS/Bi2Se3 interface? Phys. Rev. B 99, 064423 (2019).
  36. A. I. Figueroa, F. Bonell, M. G. Cuxart, M. Valvidares, P. Gargiani, G. van der Laan, A. Mugarza, and S. O. Valenzuela, Absence of Magnetic Proximity Effect at the Interface of Bi2Se3 and (Bi,Sb)2Te3 with EuS, Phys. Rev. Lett. 125, 226801 (2020).
  37. J. Wu, F. Liu, M. Sasase, K. Ienaga, Y. Obata, R. Yukawa, K. Horiba, H. Kumigashira, S. Okuma, T. Inoshita et al., Natural van der Waals heterostructural single crystals with both magnetic and topological properties, Sci. Adv. 5, eaax9989 (2019).
  38. J. W. Negele and H. Orland, Quantum Many-Particle Systems (Addison-Wesley, Reading, MA, 1988).
  39. S. Sachdev, Quantum Phase Transitions, 2nd ed. (Cambridge University Press, Cambridge, UK, 2011).
  40. S. V. Eremeev, V. N. Men'shov, V. V. Tugushev, and E. V. Chulkov, Interface induced states at the boundary between a 3D topological insulator Bi2Se3 and a ferromagnetic insulator EuS, J. Magn. Magn. Mater. 383, 30 (2015).
  41. H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface, Nat. Phys. 5, 438 (2009).
  42. A. Tan, V. Labracherie, N. Kunchur, A. U. B. Wolter, J. Cornejo, J. Dufouleur, B. Büchner, A. Isaeva, and R. Giraud, Metamagnetism of Weakly Coupled Antiferromagnetic Topological Insulators, Phys. Rev. Lett. 124, 197201 (2020).
  43. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L032014 for details on the analytic calculations, density functional theory results, and Monte Carlo simulations, which includes Refs. [47, 48, 49, 50, 51, 52, 53, 54, 55].
  44. B. Li, J.-Q. Yan, D. M. Pajerowski, E. Gordon, A.-M. Nedić, Y. Sizyuk, L. Ke, P. P. Orth, D. Vaknin, and R. J. McQueeney, Competing Magnetic Interactions in the Antiferromagnetic Topological Insulator MnBi2Te4, Phys. Rev. Lett. 124, 167204 (2020).
  45. A. Mauger and C. Godart, The magnetic, optical, and transport properties of representatives of a class of magnetic semiconductors: The europium chalcogenides, Phys. Rep. 141, 51 (1986).
  46. S. Deser, R. Jackiw, and S. Templeton, Three-Dimensional Massive Gauge Theories, Phys. Rev. Lett. 48, 975 (1982).
  47. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77, 3865 (1996).
  48. K. Koepernik and H. Eschrig, Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme, Phys. Rev. B 59, 1743 (1999).
  49. https://www.fplo.de.
  50. R. C. Vidal, H. Bentmann, J. I. Facio, T. Heider, P. Kagerer, C. I. Fornari, T. R. F. Peixoto, T. Figgemeier, S. Jung, C. Cacho, B. Büchner, J. van den Brink, C. M. Schneider, L. Plucinski, E. F. Schwier, K. Shimada, M. Richter, A. Isaeva, and F. Reinert, Orbital Complexity in Intrinsic Magnetic Topological Insulators MnBi4Te7 and MnBi6Te10, Phys. Rev. Lett. 126, 176403 (2021).
  51. Y. J. Chen, L. X. Xu, J. H. Li, Y. W. Li, H. Y. Wang, C. F. Zhang, H. Li, Y. Wu, A. J. Liang, C. Chen, S. W. Jung, C. Cacho, Y. H. Mao, S. Liu, M. X. Wang, Y. F. Guo, Y. Xu, Z. K. Liu, L. X. Yang, and Y. L. Chen, Topological Electronic Structure and its Temperature Evolution in Antiferromagnetic Topological Insulator MnBi2Te4, Phys. Rev. X 9, 041040 (2019).
  52. C. Pérez Vicente, J. L. Tirado, K. Adouby, J. C. Jumas, A. Abba Touré, and G. Kra, X-ray diffraction and Sn119 Mössbauer spectroscopy study of a new phase in the Bi2Se3-SnSe system: SnBi4Se7, Inorg. Chem. 38, 2131 (1999).
  53. P. Wachter, The optical electrical and magnetic properties of the europium chalcogenides and the rare earth pnictides, CRC Crit. Rev. Solid State Sci. 3, 189 (1972).
  54. T. Story, C. H. W. Swüste, H. J. M. Swagten, W. J. M. de Jonge, A. Stachow-Wójcik, A. Twardowski, M. Arciszewska, W. Dobrowolski, R. R. Gałazka, and A. Yu. Sipatov, Magnetic anisotropy in Eus-PbS multilayers, Acta Phys. Pol., A 97, 435 (2000).
  55. M. Ghaemi, G. A. Parsafar, and M. Ashrafizaadeh, Calculation of the critical temperature for 2- and 3-dimensional Ising models and for 2-dimensional Potts models using the transfer matrix method, J. Phys. Chem. B 105, 10355 (2001).

Outline

Information

Phys. Rev. Research 3, L032014– Published 9 July, 2021
  • Received 21 January 2021
  • Accepted 22 June 2021
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation