Skip to main content
SpringerLink
Log in

Topological Skyrmion Dynamics in Chiral Magnets

  • Chapter
  • First Online:
Topological Structures in Ferroic Materials

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 228))

Abstract

The cubic chiral magnets form topological skyrmion textures due to the presence of the Dzyaloshinskii-Moriya interaction. We briefly review in this chapter the dynamics of these magnetic textures and their interaction with magnon and electron currents, which is fundamentally influenced by their topological origin. In particular, the effective Thiele equation of motion of the skyrmion is governed by a gyrotropic force that is proportional to its topological charge. Moreover, the continuity equation associated with the conservation of topological charge can be interpreted as the Maxwell-Faraday equation of an emergent electrodynamics. As a consequence, magnons as well as electron excitations experience, for example, a topological Hall effect as well as a skyrmion-flow Hall effect.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. See section §52 Helicoidal magnetic structures in L.D. Landau, E.M. Lifshitz, L.P. Pitaevskii, Electrodynamics of Continuous Media, 2nd edn. vol. 8 (Butterworth-Heinemann, 1984)

    Google Scholar 

  2. P. Bak, M.H. Jensen, J. Phys. C: Solid State Phys. 13, L881 (1980)

    Article  ADS  Google Scholar 

  3. M. Date, K. Okuda, K. Kadowaki, J. Phys. Soc. Jpn. 42, 1555 (1977)

    Article  ADS  Google Scholar 

  4. A. Hansen, Ph.D. thesis, Technical University of Denmark (1977). Risø Report Nr. 360. http://www.risoe.dk/rispubl/reports_INIS/RISO360.pdf

  5. S.M. Stishov, A.E. Petrova, S. Khasanov, G.K. Panova, A.A. Shikov, J.C. Lashley, D. Wu, T.A. Lograsso, Phys. Rev. B 76, 52405 (2007)

    Google Scholar 

  6. M. Janoschek, M. Garst, A. Bauer, P. Krautscheid, R. Georgii, P. Böni, C. Pfleiderer, Phys. Rev. B 87, 134407 (2013)

    Article  ADS  Google Scholar 

  7. A. Bauer, M. Garst, C. Pfleiderer, Phys. Rev. Lett. 110, 177207 (2013)

    Article  ADS  Google Scholar 

  8. S. Buhrandt and L. Fritz, Phys. Rev. B 88 (2013)

    Google Scholar 

  9. S.A. Brazovskii, I.E. Dzialoshinskii, A.R. Muratov, Sov. Phys. JETP 66, 625 (1987)

    Google Scholar 

  10. S.A. Brazovskii, Sov. Phys. JETP 41, 85 (1975)

    ADS  Google Scholar 

  11. S. Mühlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, P. Böni, Science 323, 915 (2009)

    Article  ADS  Google Scholar 

  12. X.Z. Yu, Y. Onose, N. Kanazawa, J.H. Park, J.H. Han, Y. Matsui, N. Nagaosa, Y. Tokura, Nature 465, 901 (2010)

    Article  ADS  Google Scholar 

  13. T. Adams, S. Mühlbauer, C. Pfleiderer, F. Jonietz, A. Bauer, A. Neubauer, R. Georgii, P. Böni, U. Keiderling, K. Everschor, M. Garst, A. Rosch, Phys. Rev. Lett. 107, 217206 (2011)

    Article  ADS  Google Scholar 

  14. A.N. Bogdanov, D.A. Yablonskii, Sov. Phys. JETP 68, 1 (1989)

    Google Scholar 

  15. A.N. Bogdanov, A. Hubert, J. Magn. Magn. Mater. 138, 255 (1994)

    Article  ADS  Google Scholar 

  16. U.K. Rößler, A.N. Bogdanov, C. Pfleiderer, Nature 442, 797 (2006)

    Article  ADS  Google Scholar 

  17. N. Nagaosa, Y. Tokura, Nat. Nanotechnol. 8, 899 (2013)

    Article  ADS  Google Scholar 

  18. K. Everschor, Ph.D. thesis, University of Cologne (2012). http://kups.ub.uni-koeln.de/4811/1/Thesis_zum_Veroeffentlichen.pdf

  19. T. Schwarze, J. Waizner, M. Garst, A. Bauer, I. Stasinopoulos, H. Berger, C. Pfleiderer, D. Grundler, Nat. Mater. 14, 478 (2015)

    Google Scholar 

  20. F.N. Rybakov, A.B. Borisov, A.N. Bogdanov, Phys. Rev. B 87, 094424 (2013)

    Article  ADS  Google Scholar 

  21. X.Z. Yu, N. Kanazawa, Y. Onose, K. Kimoto, W.Z. Zhang, S. Ishiwata, Y. Matsui, Y. Tokura, Nat. Mater. 10, 106 (2011)

    Article  ADS  Google Scholar 

  22. N.A. Spaldin, M. Fiebig, M. Mostovoy, J. Phys.: Condens. Matter 20, 434203 (2008)

    ADS  Google Scholar 

  23. S. Heinze, K. von Bergmann, M. Menzel, J. Brede, A. Kubetzka, R. Wiesendanger, G. Bihlmayer, S. Blügel, Nat. Phys. 7, 713 (2011)

    Google Scholar 

  24. N. Romming, C. Hanneken, M. Menzel, J.E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka, R. Wiesendanger, Science 341, 636 (2013)

    Article  ADS  Google Scholar 

  25. K.V. Bergmann, A. Kubetzka, O. Pietzsch, R. Wiesendanger, J. Phys.: Condens. Matter 26, 394002 (2014)

    Google Scholar 

  26. S.-Z. Lin, C.D. Batista, A. Saxena, Phys. Rev. B 89, 024415 (2014)

    Article  ADS  Google Scholar 

  27. J. Iwasaki, A.J. Beekman, N. Nagaosa, Phys. Rev. B 89, 064412 (2014)

    Article  ADS  Google Scholar 

  28. C. Schütte, M. Garst, Phys. Rev. B 90, 094423 (2014)

    Article  ADS  Google Scholar 

  29. S. Schroeter, M. Garst, arXiv:1504.02108

  30. A.M. Kosevich, B.A. Ivanov, A.S. Kovalev, Phys. Rep. 194, 117 (1990); B.A. Ivanov, JETP Lett. 61, 917 (1995); B.A. Ivanov, H.J. Schnitzer, F.G. Mertens, G.M. Wysin, Phys. Rev. B 58, 8464 (1998); D.D. Sheka, B.A. Ivanov, F.G. Mertens. Phys. Rev. B 64, 024432 (2001)

    Google Scholar 

  31. M. Ezawa, Phys. Rev. B 83, 100408 (2011)

    Article  ADS  Google Scholar 

  32. A.A. Thiele, Phys. Rev. Lett. 30, 230 (1973)

    Article  ADS  Google Scholar 

  33. L. Kong, J. Zang, Phys. Rev. Lett. 111, 067203 (2013)

    Article  ADS  Google Scholar 

  34. S.-Z. Lin, C.D. Batista, C. Reichhardt, A. Saxena, Phys. Rev. Lett. 112, 187203 (2014)

    Article  ADS  Google Scholar 

  35. A.A. Kovalev, Phys. Rev. B 89, 241101(R) (2014)

    Article  ADS  Google Scholar 

  36. M. Mochizuki, X.Z. Yu, S. Seki, N. Kanazawa, W. Koshibae, J. Zang, M. Mostovoy, Y. Tokura, N. Nagaosa, Nat. Mater. 13, 241 (2014)

    Article  ADS  Google Scholar 

  37. B. Binz, A. Vishwanath, Phys. Rev. B 74, 214408 (2006)

    Article  ADS  Google Scholar 

  38. I. Fischer, N. Shah, A. Rosch, Phys. Rev. B 77, 024415 (2008)

    Article  ADS  Google Scholar 

  39. T. Tanigaki, K. Shibata, N. Kanazawa, X. Yu, S. Aizawa, Y. Onose, H.S. Park, D. Shindo, Y. Tokura, arXiv:1503.03945

  40. O. Petrova, O. Tchernyshyov, Phys. Rev. B 84, 214433 (2011)

    Article  ADS  Google Scholar 

  41. J. Zang, M. Mostovoy, J.H. Han, N. Nagaosa, Phys. Rev. Lett. 107, 136804 (2011)

    Article  ADS  Google Scholar 

  42. M. Mochizuki, Phys. Rev. Lett. 108, 017601 (2012)

    Article  ADS  Google Scholar 

  43. Y. Onose, Y. Okamura, S. Seki, S. Ishiwata, Y. Tokura, Phys. Rev. Lett. 109, 37603 (2012)

    Article  ADS  Google Scholar 

  44. J. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996)

    Article  ADS  Google Scholar 

  45. L. Berger, Phys. Rev. B 54, 9353 (1996)

    Article  ADS  Google Scholar 

  46. S. Zhang, Z. Li, Phys. Rev. Lett. 93, 127204 (2004)

    Article  ADS  Google Scholar 

  47. K. Everschor, M. Garst, R.A. Duine, A. Rosch, Phys. Rev. B 84, 64401 (2011)

    Article  ADS  Google Scholar 

  48. K. Everschor, M. Garst, B. Binz, F. Jonietz, S. Mühlbauer, C. Pfleiderer, A. Rosch, Phys. Rev. B 86, 054432 (2012)

    Article  ADS  Google Scholar 

  49. S.-Z. Lin, C. Reichhardt, C.D. Batista, A. Saxena, Phys. Rev. B 87, 214419 (2013)

    Article  ADS  Google Scholar 

  50. J. Iwasaki, M. Mochizuki, N. Nagaosa, Nat. Comm. 4, 1463 (2013)

    Article  ADS  Google Scholar 

  51. J. He, Z. Li, S. Zhang, Phys. Rev. B 73, 184408 (2006)

    Article  ADS  Google Scholar 

  52. F. Jonietz, S. Mühlbauer, C. Pfleiderer, A. Neubauer, W. Münzer, A. Bauer, T. Adams, R. Georgii, P. Böni, R.A. Duine, K. Everschor, M. Garst, A. Rosch, Science 330, 1648 (2010)

    Google Scholar 

  53. C. Pfleiderer, A. Rosch, Nature 465, 880 (2010)

    Article  ADS  Google Scholar 

  54. R. Ritz, M. Halder, C. Franz, A. Bauer, M. Wagner, R. Bamler, A. Rosch, C. Pfleiderer, Phys. Rev. B 87, 134424 (2013)

    Article  ADS  Google Scholar 

  55. A. Neubauer, C. Pfleiderer, B. Binz, A. Rosch, R. Ritz, P.G. Niklowitz, P. Böni, Phys. Rev. Lett. 102, 186602 (2009)

    Article  ADS  Google Scholar 

  56. M. Lee, W. Kang, Y. Onose, Y. Tokura, N.P. Ong, Phys. Rev. Lett. 102, 186601 (2009)

    Article  ADS  Google Scholar 

  57. P. Bruno, V.K. Dugaev, M. Taillefumier, Phys. Rev. Lett. 93, 96806 (2004)

    Article  ADS  Google Scholar 

  58. R. Ritz, M. Halder, M. Wagner, C. Franz, A. Bauer, C. Pfleiderer, Nature 497, 231 (2013)

    Article  ADS  Google Scholar 

  59. C. Pfleiderer, S.R. Julian, G.G. Lonzarich, Nature 414, 427 (2001)

    Article  ADS  Google Scholar 

  60. C. Pfleiderer, D. Reznik, L. Pintschovius, H.V. Lohneysen, M. Garst, A. Rosch, Nature 427, 227 (2004)

    Article  ADS  Google Scholar 

  61. M. Onoda, G. Tatara, N. Nagaosa, J. Phys. Soc. Jpn. 73, 2624 (2004)

    Article  ADS  MATH  Google Scholar 

  62. F. Freimuth, R. Bamler, Y. Mokrousov, A. Rosch, Phys. Rev. B 88, 214409 (2013)

    Article  ADS  Google Scholar 

  63. T. Schulz, R. Ritz, A. Bauer, M. Halder, M. Wagner, C. Franz, C. Pfleiderer, K. Everschor, M. Garst, A. Rosch, Nat. Phys. 8, 301 (2012)

    Google Scholar 

  64. G. Blatter, M.V. Feigel’man, V.B. Geshkenbein, A.I. Larkin, V.M. Vinokur, Rev. Mod. Phys. 66, 1125 (1994)

    Article  ADS  Google Scholar 

  65. P. Milde, D. Kohler, J. Seidel, L.M. Eng, A. Bauer, A. Chacon, J. Kindervater, S. Mühlbauer, C. Pfleiderer, S. Buhrandt, C. Schütte, A. Rosch, Science 340, 1076 (2013)

    Article  ADS  Google Scholar 

  66. C. Schütte, J. Iwasaki, A. Rosch, N. Nagaosa, Phys. Rev. B 90, 174434 (2014)

    Article  ADS  Google Scholar 

  67. F. Büttner, C. Moutafis, M. Schneider, B. Krüger, C.M. Günther, J. Geilhufe, C.V. Korff Schmising, J. Mohanty, B. Pfau, S. Schaffert, A. Bisig, M. Foerster, T. Schulz, C.A.F. Vaz, J.H. Franken, H.J.M. Swagten, M. Kläui, S. Eisebitt, Nat. Phys. 11, 225 (2015)

    Google Scholar 

  68. J.S. White, K. Prsa, P. Huang, A.A. Omrani, I. Zivkovic, M. Bartkowiak, H. Berger, A. Magrez, J.L. Gavilano, G. Nagy, J. Zang, H.M. Ronnow, Phys. Rev. Lett. 113, 107203 (2014)

    Article  ADS  Google Scholar 

  69. Y. Okamura, F. Kagawa, M. Mochizuki, M. Kubota, S. Seki, S. Ishiwata, M. Kawasaki, Y. Onose, Y. Tokura, Nat. Commun. 4, 2391 (2013)

    Google Scholar 

  70. J. Sampaio, V. Cros, S. Rohart, A. Thiaville, A. Fert, Nat. Nanotechnol. 8, 839 (2013)

    Article  ADS  Google Scholar 

  71. W. Koshibae, N. Nagaosa, Nat. Commun. 5, 5148 (2014)

    Article  ADS  Google Scholar 

  72. J. Müller, A. Rosch, Phys. Rev. B 91, 054410 (2015)

    Article  ADS  Google Scholar 

  73. X. Zhang, M. Ezawa, Y. Zhou, Sci. Rep. 5, 9400 (2015)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

I would like to thank the many people with whom I collaborated on the topic of this review, in particular, B. Binz, K. Everschor, P. Krautscheid, S. Schroeter, C. Schütte and the experimental groups of P. Böni, D. Grundler, and, especially, C. Pfleiderer. I am particularly grateful to A. Rosch for the collaboration and support over many years.

Author information

Authors and Affiliations

  1. Institut Für Theoretische Physik, Universität Zu Köln, Zülpicher Str. 77a, 50937, Cologne, Germany

    Markus Garst

Authors
  1. Markus Garst
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Markus Garst .

Editor information

Editors and Affiliations

  1. School Mat Sci. Eng., University of New South Wales, Sydney, New South Wales, Australia

    Jan Seidel

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Garst, M. (2016). Topological Skyrmion Dynamics in Chiral Magnets. In: Seidel, J. (eds) Topological Structures in Ferroic Materials. Springer Series in Materials Science, vol 228. Springer, Cham. https://doi.org/10.1007/978-3-319-25301-5_2

Download citation

Publish with us

Policies and ethics

Search

Navigation