- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Materials

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
  • Open Access

High-throughput magnetic co-doping and design of exchange interactions in topological insulators

Rubel Mozumder1, Johannes Wasmer1,2, David Antognini Silva1,2, Stefan Blügel1, and Philipp Rüßmann1,3,*

  • *Contact author: p.ruessmann@fz-juelich.de
PDF

Phys. Rev. Materials 8, 104201 – Published 17 October, 2024

DOI: https://doi.org/10.1103/PhysRevMaterials.8.104201

Abstract

Using high-throughput automation of ab initio impurity embedding simulations, we create a database of 3d and 4d transition metal defects embedded into the prototypical topological insulators (TIs) Bi2Te3 and Bi2Se3. We simulate both single impurities as well as impurity dimers at different impurity-impurity distances inside the topological insulator matrix. We extract changes to magnetic moments, analyze the polarizability of nonmagnetic impurity atoms via nearby magnetic impurity atoms and calculate the exchange coupling constants for a Heisenberg Hamiltonian. We uncover chemical trends in the exchange coupling constants and discuss the impurities' abilities with respect to magnetic order in the fields of quantum anomalous Hall insulators and topological quantum computing. In particular, we confirm that co-doping of different magnetic dopants is a viable strategy to engineer the magnetic ground state in magnetic TIs.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (50)

  1. M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  2. Y. Tokura, K. Yasuda, and A. Tsukazaki, Magnetic topological insulators, Nat. Rev. Phys. 1, 126 (2019).
  3. B. Bernevig, C. Felser, and H. Beidenkopf, Progress and prospects in magnetic topological materials, Nature (London) 603, 41 (2022).
  4. 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).
  5. C. Z. Chang, W. Zhao, D. Y. Kim, H. Zhang, B. A. Assaf, D. Heiman, S. C. Zhang, C. Liu, M. H. Chan, and J. S. Moodera, High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator, Nat. Mater. 14, 473 (2015).
  6. X. Kou, Y. Fan, M. Lang, P. Upadhyaya, and K. L. Wang, Magnetic topological insulators and quantum anomalous Hall effect, Solid State Commun. 215-216, 34 (2015).
  7. A. J. Bestwick, E. J. Fox, X. Kou, L. Pan, K. L. Wang, and D. Goldhaber-Gordon, Precise quantization of the anomalous Hall effect near zero magnetic field, Phys. Rev. Lett. 114, 187201 (2015).
  8. S. Grauer, S. Schreyeck, M. Winnerlein, K. Brunner, C. Gould, and L. W. Molenkamp, Coincidence of superparamagnetism and perfect quantization in the quantum anomalous Hall state, Phys. Rev. B 92, 201304(R) (2015).
  9. C.-Z. Chang, C.-X. Liu, and A. H. MacDonald, Colloquium: Quantum anomalous Hall effect, Rev. Mod. Phys. 95, 011002 (2023).
  10. 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).
  11. T. Li, S. Jiang, B. Shen, Y. Zhang, L. Li, Z. Tao, T. Devakul, K. Watanabe, T. Taniguchi, L. Fu, J. Shan, and K. Mak, Quantum anomalous Hall effect from intertwined moiré bands, Nature (London) 600, 641 (2021).
  12. M. Mogi, R. Yoshimi, A. Tsukazaki, K. Yasuda, Y. Kozuka, K. S. Takahashi, M. Kawasaki, and Y. Tokura, Magnetic modulation doping in topological insulators toward higher-temperature quantum anomalous Hall effect, Appl. Phys. Lett. 107, 182401 (2015).
  13. Y. Ou, C. Liu, G. Jiang, Y. Feng, D. Zhao, W. Wu, X. X. Wang, W. Li, C. Song, L. L. Wang, W. Wang, W. Wu, Y. Wang, K. He, X. C. Ma, and Q. K. Xue, Enhancing the quantum anomalous Hall effect by magnetic codoping in a topological insulator, Adv. Mater. 30, 1703062 (2018).
  14. Y. Fan, P. Upadhyaya, X. Kou, M. Lang, S. Takei, Z. Wang, J. Tang, L. He, L. T. Chang, M. Montazeri, G. Yu, W. Jiang, T. Nie, R. N. Schwartz, Y. Tserkovnyak, and K. L. Wang, Magnetization switching through giant spin–orbit torque in a magnetically doped topological insulator heterostructure, Nat. Mater. 13, 699 (2014).
  15. J. Wang, B. Lian, X.-L. Qi, and S.-C. Zhang, Quantized topological magnetoelectric effect of the zero-plateau quantum anomalous Hall state, Phys. Rev. B 92, 081107(R) (2015).
  16. D. Zhuo, Z.-J. Yan, Z.-T. Sun, L.-J. Zhou, Y.-F. Zhao, R. Zhang, R. Mei, H. Yi, K. Wang, M. Chan, C.-X. Liu, K. Law, and C.-Z. Chang, Axion insulator state in hundred-nanometer-thick magnetic topological insulator sandwich heterostructures, Nat. Commun. 14, 7596 (2023).
  17. P. Rüßmann, F. Bertoldo, and S. Blügel, The AiiDA-KKR plugin and its application to high-throughput impurity embedding into a topological insulator, npj Comput. Mater. 7, 13 (2021).
  18. https://go.fzj.de/judit
  19. S. H. Vosko, L. Wilk, and M. Nusair, Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis, Can. J. Phys. 58, 1200 (1980).
  20. H. Ebert, D. Ködderitzsch, and J. Minár, Calculating condensed matter properties using the KKR-Green's function method – recent developments and applications, Rep. Prog. Phys. 74, 096501 (2011).
  21. P. Rüßmann, D. Antognini Silva, D. S. G. Bauer, P. Baumeister, M. Bornemann, J. Bouaziz, S. Brinker, J. Chico, P. H. Dederichs, B. H. Drittler, F. Dos Santos, M. dos Santos Dias, N. Essing, G. Géranton, I. Klepetsanis, A. Kosma, N. H. Long, S. Lounis, P. Mavropoulos, E. Mendive Tapia et al., JuDFTteam/JuKKR: v3.6, Zenodo (2022), doi:10.5281/zenodo.7284738.
  22. P. Sessi, P. Rüßmann, T. Bathon, A. Barla, K. A. Kokh, O. E. Tereshchenko, K. Fauth, S. K. Mahatha, M. A. Valbuena, S. Godey, F. Glott, A. Mugarza, P. Gargiani, M. Valvidares, N. H. Long, C. Carbone, P. Mavropoulos, S. Blügel, and M. Bode, Superparamagnetism-induced mesoscopic electron focusing in topological insulators, Phys. Rev. B 94, 075137 (2016).
  23. T. R. Peixoto, H. Bentmann, P. Rüßmann, A. V. Tcakaev, M. Winnerlein, S. Schreyeck, S. Schatz, R. C. Vidal, F. Stier, V. Zabolotnyy, R. J. Green, C. H. Min, C. I. Fornari, H. Maaß, H. B. Vasili, P. Gargiani, M. Valvidares, A. Barla, J. Buck, M. Hoesch et al., Non-local effect of impurity states on the exchange coupling mechanism in magnetic topological insulators, npj Quantum Mater. 5, 87 (2020).
  24. A. Tcakaev, V. B. Zabolotnyy, C. I. Fornari, P. Rüßmann, T. R. F. Peixoto, F. Stier, M. Dettbarn, P. Kagerer, E. Weschke, E. Schierle, P. Bencok, P. H. O. Rappl, E. Abramof, H. Bentmann, E. Goering, F. Reinert, and V. Hinkov, Incipient antiferromagnetism in the Eu-doped topological insulator Bi2Te3, Phys. Rev. B 102, 184401 (2020).
  25. S. Nakajima, The crystal structure of Bi2Te3−xSex, J. Phys. Chem. Solids, 24 479 (1963).
  26. R. W. G. Wyckoff, Crystal Structures, 2 ed. (John Wiley and Sons, New York, USA, 1964).
  27. N. Stefanou, H. Akai, and R. Zeller, An efficient numerical method to calculate shape truncation functions for Wigner-Seitz atomic polyhedra, Comput. Phys. Commun. 60, 231 (1990).
  28. N. Stefanou and R. Zeller, Calculation of shape-truncation functions for Voronoi polyhedra, J. Phys.: Condens. Matter 3, 7599 (1991).
  29. R. Zeller, An elementary derivation of Lloyd's formula valid for full-potential multiple-scattering theory, J. Phys.: Condens. Matter 16, 6453 (2004).
  30. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevMaterials.8.104201 for an illustration of the geometries and Jij maps of the impurity dimers at larger distances, distance-dependent inter-QL vs intra-QL contributions to the Jij's, the resulting mean-field Tc from inter-QL and intra-QL contributions, convergence plots of the Jij calculations, and the corresponding results for Bi2Se3.
  31. D. S. G. Bauer, Development of a relativistic full-potential first-principles multiple scattering Green function method applied to complex magnetic textures of nano structures at surfaces, Ph.D. thesis, RWTH Aachen University, 2013.
  32. A. Liechtenstein, M. Katsnelson, V. Antropov, and V. Gubanov, Local spin density functional approach to the theory of exchange interactions in ferromagnetic metals and alloys, J. Magn. Magn. Mater. 67, 65 (1987).
  33. P. Rüßmann, D. Antognini Silva, R. Aliberti, J. Bröder, H. Janssen, R. Mozumder, M. Struckmann, J. Wasmer, and S. Blügel, JuDFTteam/aiida-kkr: v2.1.0. Zenodo (2023), doi:10.5281/zenodo.3628250.
  34. S. P. Huber, S. Zoupanos, M. Uhrin, L. Talirz, L. Kahle, R. Häuselmann, D. Gresch, T. Müller, A. V. Yakutovich, C. W. Andersen, F. F. Ramirez, C. S. Adorf, F. Gargiulo, S. Kumbhar, E. Passaro, C. Johnston, A. Merkys, A. Cepellotti, N. Mounet, N. Marzari et al., AiiDA 1.0, a scalable computational infrastructure for automated reproducible workflows and data provenance, Sci. Data 7, 300 (2020).
  35. J. Wasmer, R. Kovacic, and P. Rüßmann, JuDFTteam/aiida-jutools: v0.1.2, Zenodo (2023), doi:10.5281/zenodo.10429636.
  36. D. Di Miceli, E. Zsurka, J. Legendre, K. Moors, T. L. Schmidt, and L. Serra, Conductance asymmetry in proximitized magnetic topological insulator junctions with majorana modes, Phys. Rev. B 108, 035424 (2023).
  37. J. Legendre, E. Zsurka, D. Di Miceli, L. Serra, K. Moors, and T. L. Schmidt, Topological properties of finite-size heterostructures of magnetic topological insulators and superconductors, arXiv:2404.16520.
  38. Note that for Ru max|Δm1|>m because for Ru–Nb the Ru moment increases in magnitude but also flips the sign to an antiparallel alignment with respect to the Nb moment.
  39. E. Koch, Correlated Electrons: From Models to Materials Modeling and Simulation (Forschungszentrum Jülich GmbH Zenralbibliothek, Verlag, Jülich, 2012), Chap. Exchange Mechanisms.
  40. M. Pajda, J. Kudrnovský, I. Turek, V. Drchal, and P. Bruno, Ab initio calculations of exchange interactions, spin-wave stiffness constants, and curie temperatures of Fe, Co, and Ni, Phys. Rev. B 64, 174402 (2001).
  41. Note that the prefactor here is 1/3 instead of 2/3 due to the different definition of the Heisenberg Hamiltonian Eq. (2) that contains a factor 1/2 in our work.
  42. X. Kou, S.-T. Guo, Y. Fan, L. Pan, M. Lang, Y. Jiang, Q. Shao, T. Nie, K. Murata, J. Tang, Y. Wang, L. He, T.-K. Lee, W.-L. Lee, and K. L. Wang, Scale-invariant quantum anomalous Hall effect in magnetic topological insulators beyond the two-dimensional limit, Phys. Rev. Lett. 113, 137201 (2014).
  43. J. Checkelsky, R. Yoshimi, A. Tsukazaki, K. 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).
  44. In contrast to Eq. (3), the summation starts at j=2 instead of j=1.
  45. Y. S. Hor, P. Roushan, H. Beidenkopf, J. Seo, D. Qu, J. G. Checkelsky, L. A. Wray, D. Hsieh, Y. Xia, S.-Y. Xu, D. Qian, M. Z. Hasan, N. P. Ong, A. Yazdani, and R. J. Cava, Development of ferromagnetism in the doped topological insulator Bi2−xMnxTe3, Phys. Rev. B 81, 195203 (2010).
  46. K. Sato, P. H. Dederichs, H. Katayama-Yoshida, and J. Kudrnovský, Exchange interactions in diluted magnetic semiconductors, J. Phys.: Condens. Matter 16, S5491 (2004).
  47. E. Zsurka, C. Wang, J. Legendre, D. Di Miceli, L. Serra, D. Grützmacher, T. L. Schmidt, P. Rüßmann, and K. Moors, Low-energy modeling of three-dimensional topological insulator nanostructures, Phys. Rev. Mater. 8, 084204 (2024).
  48. L. B. Duffy, A. I. Figueroa, G. van der Laan, and T. Hesjedal, Codoping of Sb2Te3 thin films with V and Cr, Phys. Rev. Mater. 1, 064409 (2017).
  49. R. Mozumder, J. Wasmer, D. Antognini Silva, S. Blügel, and P. Rüßmann, Dataset to “High-throughput magnetic co-doping and design of exchange interactions in topological insulators”, Mater. Cloud Archive 2024, 141 (2024).
  50. P. Thörnig, JURECA: Data Centric and Booster Modules implementing the Modular Supercomputing Architecture at Jülich Supercomputing Centre, J. Large-Scale Res. Facilities 7, A182 (2021).

Outline

Information

Phys. Rev. Materials 8, 104201– Published 17 October, 2024
  • Received 5 July 2024
  • Accepted 19 September 2024
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