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

Topological magnetic textures in magnetic topological insulators

Nisarga Paul1,2 and Liang Fu2

  • 1Department of Physics, Harvard University, Cambridge, Massachusetts, USA
  • 2Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

Phys. Rev. Research 3, 033173 – Published 20 August, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.033173

Abstract

The surfaces of intrinsic magnetic topological insulators (TIs) host magnetic moments exchange-coupled to Dirac electrons. We study the magnetic phases arising from tuning the electron density using variational and exact diagonalization approaches. In the dilute limit, we find that magnetic skyrmions are formed, which bind to electrons, leading to a skyrmion Wigner crystal phase while at higher densities spin spirals accompanied by chiral one-dimensional channels of electrons are formed. The binding of electrons to textures raises the possibility of manipulating textures with electrostatic gating. We determine the phase diagram capturing the competition of intrinsic spin-spin interactions and carrier density and comment on the possible application to experiments in magnetic TIs and spintronic devices such as skyrmion-based memory.

View figure in article

Physics Subject Headings (PhySH)

See Also

Twisted magnetic topological insulators

Chao-Kai Li, Xu-Ping Yao, and Gang Chen
Phys. Rev. Research 3, 033156 (2021)

Article Text

References (54)

  1. D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall Conductance in a Two-Dimensional Periodic Potential, Phys. Rev. Lett. 49, 405 (1982).
  2. F. D. M. Haldane, Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the Parity Anomaly, Phys. Rev. Lett. 61, 2015 (1988).
  3. C. L. Kane and E. J. Mele, Z2 Topological Order and the Quantum Spin Hall Effect, Phys. Rev. Lett. 95, 146802 (2005).
  4. M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  5. J. M. Kosterlitz and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C: Solid State Phys. 6, 1181 (1973).
  6. C. Castelnovo, R. Moessner, and S. L. Sondhi, Magnetic monopoles in spin ice, Nature (London) 451, 42 (2008).
  7. U. K. Rößler, A. N. Bogdanov, and C. Pfleiderer, Spontaneous skyrmion ground states in magnetic metals, Nature (London) 442, 797 (2006).
  8. S. Mühlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and Böni, Skyrmion lattice in a chiral magnet, Science 323, 915 (2009).
  9. N. Nagaosa and Y. Tokura, Topological properties and dynamics of magnetic skyrmions, Nat. Nanotechnol. 8, 899 (2013).
  10. J. Liu and L. Balents, Anomalous Hall Effect and Topological Defects in Antiferromagnetic Weyl Semimetals: Mn3Sn/Ge, Phys. Rev. Lett. 119, 087202 (2017).
  11. H. Ochoa and Y. Tserkovnyak, Quantum skyrmionics, Int. J. Mod. Phys. B 33, 1930005 (2019).
  12. X. Z. Yu, N. Kanazawa, W. Z. Zhang, T. Nagai, T. Hara, K. Kimoto, Y. Matsui, Y. Onose, and Y. Tokura, Skyrmion flow near room temperature in an ultralow current density, Nat. Commun. 3, 988 (2012).
  13. S. Woo, K. Litzius, B. Krüger, M.-Y. Im, L. Caretta, K. Richter, M. Mann, A. Krone, R. M. Reeve, M. Weigand, P. Agrawal, I. Lemesh, M.-A. Mawass, P. Fischer, M. Kläui, and G. S. D. Beach, Observation of room-temperature magnetic skyrmions and their current-driven dynamics in ultrathin metallic ferromagnets, Nat. Mater. 15, 501 (2016).
  14. T. Lin, H. Liu, S. Poellath, Y. Zhang, B. Ji, N. Lei, J. J. Yun, L. Xi, D. Z. Yang, T. Xing, Z. L. Wang, L. Sun, Y. Z. Wu, L. F. Yin, W. B. Wang, J. Shen, J. Zweck, C. H. Back, Y. G. Zhang, and W. S. Zhao, Observation of room-temperature magnetic skyrmions in Pt/Co/W structures with a large spin-orbit coupling, Phys. Rev. B 98, 174425 (2018).
  15. W. Jiang, P. Upadhyaya, W. Zhang, G. Yu, M. B. Jungfleisch, F. Y. Fradin, J. E. Pearson, Y. Tserkovnyak, K. L. Wang, O. Heinonen, S. G. E. te Velthuis, and A. Hoffmann, Blowing magnetic skyrmion bubbles, Science 349, 283 (2015).
  16. F. Büttner, I. Lemesh, and G. S. D. Beach, Theory of isolated magnetic skyrmions: From fundamentals to room temperature applications, Sci. Rep. 8, 4464 (2018).
  17. A. Bogdanov and A. Hubert, The stability of vortex-like structures in uniaxial ferromagnets, J. Magn. Magn. Mater. 195, 182 (1999).
  18. A. Fert, N. Reyren, and V. Cros, Magnetic skyrmions: advances in physics and potential applications, Nat. Rev. Mater. 2, 17031 (2017).
  19. K. Nomura and N. Nagaosa, Electric charging of magnetic textures on the surface of a topological insulator, Phys. Rev. B 82, 161401(R) (2010).
  20. H. M. Hurst, D. K. Efimkin, J. Zang, and V. Galitski, Charged skyrmions on the surface of a topological insulator, Phys. Rev. B 91, 060401(R) (2015).
  21. K. Yasuda, R. Wakatsuki, T. Morimoto, R. Yoshimi, A. Tsukazaki, K. S. Takahashi, M. Ezawa, M. Kawasaki, N. Nagaosa, and Y. Tokura, Geometric Hall effects in topological insulator heterostructures, Nat. Phys. 12, 555 (2016).
  22. 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).
  23. 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).
  24. L. Fu and C. L. Kane, Topological insulators with inversion symmetry, Phys. Rev. B 76, 045302 (2007).
  25. 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 et al., Ferromagnetic MnSb2Te4: A topological insulator with magnetic gap closing at high Curie temperatures of 45–50 K, arXiv:2011.07052 [cond-mat.mtrl-sci].
  26. C. Lei, S. Chen, and A. H. MacDonald, Magnetized topological insulator multilayers, Proc. Natl. Acad. Sci. USA 117, 27224 (2020).
  27. T. Moriya, Anisotropic superexchange interaction and weak ferromagnetism, Phys. Rev. 120, 91 (1960).
  28. I. Dzyaloshinskii, A thermodynamic theory of weak ferromagnetism of antiferromagnetics, J. Phys. Chem. Solids 4, 241 (1958).
  29. I. Dzyaloshinskii, Theory of helicoidal structures in antiferromagnets. I. Nonmetals, Sov. Phys. JETP 19, 960 (1963).
  30. A. Bogdanov and A. Hubert, Thermodynamically stable magnetic vortex states in magnetic crystals, J. Magn. Magn. Mater. 138, 255 (1994).
  31. X. Z. Yu, N. Kanazawa, Y. Onose, K. Kimoto, W. Z. Zhang, S. Ishiwata, Y. Matsui, and Y. Tokura, Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe, Nat. Mater. 10, 106 (2011).
  32. Y. Onose, Y. Okamura, S. Seki, S. Ishiwata, and Y. Tokura, Observation of Magnetic Excitations of Skyrmion Crystal in a Helimagnetic Insulator Cu2OSeO3, Phys. Rev. Lett. 109, 037603 (2012).
  33. V. M. Kuchkin, B. Barton-Singer, F. N. Rybakov, S. Blügel, B. J. Schroers, and N. S. Kiselev, Magnetic skyrmions, chiral kinks, and holomorphic functions, Phys. Rev. B 102, 144422 (2020).
  34. J. H. Han, J. Zang, Z. Yang, J.-H. Park, and N. Nagaosa, Skyrmion lattice in a two-dimensional chiral magnet, Phys. Rev. B 82, 094429 (2010).
  35. B.-J. Yang and N. Nagaosa, Skyrmion quantum numbers and quantized pumping in two-dimensional topological chiral magnets, Phys. Rev. B 84, 245123 (2011).
  36. F. Freimuth, R. Bamler, Y. Mokrousov, and A. Rosch, Phase-space Berry phases in chiral magnets: Dzyaloshinskii-Moriya interaction and the charge of skyrmions, Phys. Rev. B 88, 214409 (2013).
  37. S. L. Sondhi, A. Karlhede, S. A. Kivelson, and E. H. Rezayi, Skyrmions and the crossover from the integer to fractional quantum Hall effect at small Zeeman energies, Phys. Rev. B 47, 16419 (1993).
  38. D.-H. Lee and C. L. Kane, Boson-Vortex-Skyrmion Duality, Spin-Singlet Fractional Quantum Hall Effect, and Spin-1/2 Anyon Superconductivity, Phys. Rev. Lett. 64, 1313 (1990).
  39. K. Moon, H. Mori, K. Yang, S. M. Girvin, A. H. MacDonald, L. Zheng, D. Yoshioka, and S.-C. Zhang, Spontaneous interlayer coherence in double-layer quantum Hall systems: Charged vortices and Kosterlitz-Thouless phase transitions, Phys. Rev. B 51, 5138 (1995).
  40. L. Brey, Magnetic skyrmionic polarons, Nano Lett. 17, 7358 (2017).
  41. S. E. Barrett, G. Dabbagh, L. N. Pfeiffer, K. W. West, and R. Tycko, Optically Pumped NMR Evidence for Finite-Size Skyrmions in GaAs Quantum Wells Near Landau Level Filling ν=1, Phys. Rev. Lett. 74, 5112 (1995).
  42. H. Zhou, H. Polshyn, T. Taniguchi, K. Watanabe, and A. Young, Solids of quantum Hall skyrmions in graphene, Nat. Phys. 16, 154 (2020).
  43. R. Wakatsuki, M. Ezawa, and N. Nagaosa, Domain wall of a ferromagnet on a three-dimensional topological insulator, Sci. Rep. 5, 13638 (2015).
  44. F. Ye, G. H. Ding, H. Zhai, and Z. B. Su, Spin helix of magnetic impurities in two-dimensional helical metal, Europhys. Lett. 90, 47001 (2010).
  45. 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).
  46. S. Kim, K. Ueda, G. Go, P.-H. Jang, K.-J. Lee, A. Belabbes, and A. Manchon, Correlation of the Dzyaloshinskii-Moriya interaction with Heisenberg exchange and orbital asphericity, Nat. Commun. 9, 1648 (2018).
  47. S. Sorn, S. Divic, and A. Paramekanti, Tunable skyrmion crystals and topological quantum oscillations in magnetic metals, Phys. Rev. B 100, 174411 (2019).
  48. B. Ludbrook, G. Dubuis, A.-H. Puichaud, B. J. Ruck, and S. Granville, Nucleation and annihilation of skyrmions in Mn2CoAl observed through the topological Hall effect, Sci. Rep. 7, 13620 (2017).
  49. C. Liu, Y. Zang, W. Ruan, Y. Gong, K. He, X. Ma, Q.-K. Xue, and Y. Wang, Dimensional Crossover-Induced Topological Hall Effect in a Magnetic Topological Insulator, Phys. Rev. Lett. 119, 176809 (2017).
  50. J. Matsuno, N. Ogawa, K. Yasuda, F. Kagawa, W. Koshibae, N. Nagaosa, Y. Tokura, and M. Kawasaki, Interface-driven topological Hall effect in SrRuO3−SrIrO3 bilayer, Sci. Adv. 2, e1600304 (2016).
  51. L. Vistoli, W. Wang, A. Sander, Q. Zhu, B. Casals, R. Cichelero, A. Barthélémy, S. Fusil, G. Herranz, S. Valencia, R. Abrudan, E. Weschke, K. Nakazawa, H. Kohno, J. Santamaria, W. Wu, V. Garcia, and M. Bibes, Giant topological Hall effect in correlated oxide thin films. Nat. Phys. 15, 67 (2018).
  52. K. M. Fijalkowski, M. Hartl, M. Winnerlein, P. Mandal, S. Schreyeck, K. Brunner, C. Gould, and L. W. Molenkamp, Coexistence of Surface and Bulk Ferromagnetism Mimics Skyrmion Hall Effect in a Topological Insulator, Phys. Rev. X 10, 011012 (2020).
  53. S. Divic, H. Ling, T. Pereg-Barnea, and A. Paramekanti, Magnetic skyrmion crystal at a topological insulator surface, arXiv:2103.15841 [cond-mat.mes-hall].
  54. C.-K. Li, X.-P. Yao, and G. Chen, Twisted magnetic topological insulators, Phys. Rev. Research 3, 033156 (2021).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation