Advertisement

Frontiers of Physics

, 14:53602 | Cite as

Skyrmion Hall effect with spatially modulated Dzyaloshinskii–Moriya interaction

  • Liping Zhou
  • Ren Qin
  • Ya-Qing Zheng
  • Yong WangEmail author
Research article
  • 7 Downloads

Abstract

The skyrmion Hall effect is theoretically studied in the chiral ferromagnetic film with spatially modulated Dzyaloshinskii–Moriya interaction. Three cases including linear, sinusoidal, and periodic rectangular modulations have been considered, where the increase, decrease, and the periodic modification of the size and velocity of the skyrmion have been observed in the microscopic simulations. These phenomena are well explained by the Thiele equation, where an effective force on the skyrmion is induced by the inhomogeneous Dzyaloshinskii–Moriya interaction. The results here suggest that the skyrmion Hall effect can be manipulated by artificially tuning the Dzyaloshinskii–Moriya interaction in chiral ferromagnetic film with material engineering methods, which will be useful to design skyrmion-based spintronics devices.

Keywords

magnetic skyrmion skyrmion Hall effect Thiele equation 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 61674083 and 11604162) and the Fundamental Research Funds for the Central Universities, Nankai University (No. 63191522).

References

  1. 1.
    A. N. Bogdanov and A. Hubert, Thermodynamically stable magnetic vortex states in magnetic crystals, J. Magn. Magn. Mater. 138(3), 255 (1994)ADSGoogle Scholar
  2. 2.
    A. N. Bogdanov and A. Hubert, The stability of vortexlike structures in uniaxial ferromagnets, J. Magn. Magn. Mater. 195(1), 182 (1999)ADSGoogle Scholar
  3. 3.
    A. N. Bogdanov and U. K. Rößler, Chiral symmetry breaking in magnetic thin films and multilayers, Phys. Rev. Lett. 87(3), 037203 (2001)ADSGoogle Scholar
  4. 4.
    U. K. Rößler, A. N. Bogdanov, and C. Pfleiderer, Spontaneous skyrmion ground states in magnetic metals, Nature 442(7104), 797 (2006)ADSGoogle Scholar
  5. 5.
    S. Mühlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and P. Böni, Skyrmion lattice in a chiral magnet, Science 323(5916), 915 (2009)ADSGoogle Scholar
  6. 6.
    X. Z. Yu, Y. Onose, N. Kanazawa, J. H. Park, J. H. Han, Y. Matsui, N. Nagaosa, and Y. Tokura, Real-space observation of a two-dimensional skyrmion crystal, Nature 465(7300), 901 (2010)ADSGoogle Scholar
  7. 7.
    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(2), 106 (2011)ADSGoogle Scholar
  8. 8.
    S. Heinze, K. von Bergmann, M. Menzel, J. Brede, A. Kubetzka, R. Wiesendanger, G. Bihlmayer, and S. Blügel, Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions, Nat. Phys. 7(9), 713 (2011)Google Scholar
  9. 9.
    T. Schulz, R. Ritz, A. Bauer, M. Halder, M. Wagner, C. Franz, C. Pfleiderer, K. Everschor, M. Garst, and A. Rosch, Emergent electrodynamics of skyrmions in a chiral magnet, Nat. Phys. 8(4), 301 (2012)Google Scholar
  10. 10.
    A. Neubauer, C. Pfleiderer, B. Binz, A. Rosch, R. Ritz, P. G. Niklowitz, and P. Boni, Topological Hall effect in the A phase of MnSi, Phys. Rev. Lett. 102(18), 186602 (2009)ADSGoogle Scholar
  11. 11.
    N. Kanazawa, Y. Onose, T. Arima, D. Okuyama, K. Ohoyama, S. Wakimoto, K. Kakurai, S. Ishiwata, and Y. Tokura, Large topological Hall effect in a short-period helimagnet MnGe, Phys. Rev. Lett. 106(15), 156603 (2011)ADSGoogle Scholar
  12. 12.
    J. D. Zang, M. Mostovoy, J. H. Han, and N. Nagaosa, Dynamics of skyrmion crystals in metallic thin films, Phys. Rev. Lett. 107(13), 136804 (2011)ADSGoogle Scholar
  13. 13.
    N. Romming, C. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, Writing and deleting single magnetic skyrmions, Science 341(6146), 636 (2013)ADSGoogle Scholar
  14. 14.
    J. Sampaio, V. Cros, S. Rohart, A. Thiaville, and A. Fert, Nucleation, stability and current-induced motion of isolated magnetic skyrmions in nanostructures, Nat. Nanotechnol. 8(11), 839 (2013)ADSGoogle Scholar
  15. 15.
    J. Iwasaki, M. Mochizuki, and N. Nagaosa, Currentinduced skyrmion dynamics in constricted geometries, Nat. Nanotechnol. 8(10), 742 (2013)ADSGoogle Scholar
  16. 16.
    Y. F. Li, N. Kanazawa, X. Z. Yu, A. Tsukazaki, M. Kawasaki, M. Ichikawa, X. F. Jin, F. Kagawa, and Y. Tokura, Robust formation of skyrmions and topological Hall effect anomaly in epitaxial thin films of MnSi, Phys. Rev. Lett. 110(11), 117202 (2013)ADSGoogle Scholar
  17. 17.
    Y. Zhou and M. Ezawa, A reversible conversion between a skyrmion and a domain-wall pair in a junction geometry, Nat. Commun. 5(1), 4652 (2014)ADSGoogle Scholar
  18. 18.
    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(6245), 283 (2015)ADSGoogle Scholar
  19. 19.
    A. O. Leonov, T. L. Monchesky, N. Romming, A. Kubetzka, A. N. Bogdanov, and R. Wiesendanger, The properties of isolated chiral skyrmions in thin magnetic films, New J. Phys. 18(6), 065003 (2016)ADSGoogle Scholar
  20. 20.
    W. J. Jiang, X. C. Zhang, G. Q. Yu, W. Zhang, X. Wang, M. B. Jungfleisch, J. E. Pearson, X. M. Cheng, O. Heinonen, K. L. Wang, Y. Zhou, A. Hoffmann, and S. G. E. te Velthuis, Direct observation of the skyrmion Hall effect, Nat. Phys. 13(2), 162 (2017)Google Scholar
  21. 21.
    K. Litzius, I. Lemesh, B. Kruger, P. Bassirian, L. Caretta, K. Richter, F. Buttner, K. Sato, O. A. Tretiakov, J. Forster, R. M. Reeve, M. Weigand, L. Bykova, H. Stoll, G. Schutz, G. S. D. Beach, and M. Klaui, Skyrmion Hall effect revealed by direct time-resolved X-ray microscopy, Nat. Phys. 13(2), 170 (2017)Google Scholar
  22. 22.
    P. J. Hsu, A. Kubetzka, A. Finco, N. Romming, K. von Bergmann, and R. Wiesendanger, Electric-field-driven switching of individual magnetic skyrmions, Nat. Nanotechnol. 12(2), 123 (2016)ADSGoogle Scholar
  23. 23.
    N. Nagaosa and Y. Tokura, Topological properties and dynamics of magnetic skyrmions, Nat. Nanotechnol. 8(12), 899 (2013)ADSGoogle Scholar
  24. 24.
    R. Wiesendanger, Nanoscale magnetic skyrmions in metallic films and multilayers: A new twist for spintronics, Nat. Rev. Mater. 1(7), 16044 (2016)ADSGoogle Scholar
  25. 25.
    A. Fert, N. Reyren, and V. Cros, Magnetic skyrmions: Advances in physics and potential applications, Nat. Rev. Mater. 2(7), 17031 (2017)ADSGoogle Scholar
  26. 26.
    W. Kang, Y. Huang, X. C. Zhang, Y. Zhou, and W. Zhao, Skyrmion-electronics: An overview and outlook, Proc. IEEE 104(10), 2040 (2016)Google Scholar
  27. 27.
    S. Woo, K. M. Song, X. Zhang, M. Ezawa, Y. Zhou, X. Liu, M. Weigand, S. Finizio, J. Raabe, M. C. Park, K. Y. Lee, J. W. Choi, B. C. Min, H. C. Koo, and J. Chang, Deterministic creation and deletion of a single magnetic skyrmion observed by direct time-resolved Xray microscopy, Nat. Electron. 1(5), 288 (2018)Google Scholar
  28. 28.
    I. Dzyaloshinsky, A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics, J. Phys. Chem. Solids 4(4), 241 (1958)ADSGoogle Scholar
  29. 29.
    T. Moriya, Anisotropic superexchange interaction and weak ferromagnetism, Phys. Rev. 120(1), 91 (1960)ADSGoogle Scholar
  30. 30.
    S. A. Siegfried, E. V. Altynbaev, N. M. Chubova, V. Dyadkin, D. Chernyshov, E. V. Moskvin, D. Menzel, A. Heinemann, A. Schreyer, and S. V. Grigoriev, Controlling the Dzyaloshinskii–Moriya interaction to alter the chiral link between structure and magnetism for Fe1-xCoxSi, Phys. Rev. B 91(18), 184406 (2015)ADSGoogle Scholar
  31. 31.
    T. Koretsune, N. Nagaosa, and R. Arita, Control of Dzyaloshinskii–Moriya interaction in Mn1-xFexGe: A first-principles study, Sci. Rep. 5(1), 13302 (2015)ADSGoogle Scholar
  32. 32.
    X. Ma, G. Yu, X. Li, T. Wang, D. Wu, K. S. Olsson, Z. Chu, K. An, J. Q. Xiao, K. L. Wang, and X. Li, Interfacial control of Dzyaloshinskii–Moriya interaction in heavy metal/ferromagnetic metal thin film heterostructures, Phys. Rev. B 94, 180408(R) (2016)ADSGoogle Scholar
  33. 33.
    A. Belabbes, G. Bihlmayer, S. Blügel, and A. Manchon, Oxygen-enabled control of Dzyaloshinskii–Moriya Interaction in ultra-thin magnetic films, Sci. Rep. 6(1), 24634 (2016)ADSGoogle Scholar
  34. 34.
    A. L. Balk, K.-W. Kim, D. T. Pierce, M. D. Stiles, J. Unguris, and S. M. Stavis, Simultaneous control of the Dzyaloshinskii–Moriya interaction and magnetic anisotropy in nanomagnetic trilayers, Phys. Rev. Lett. 119, 077205 (2017)Google Scholar
  35. 35.
    G. Beutier, S. P. Collins, O. V. Dimitrova, V. E. Dmitrienko, M. I. Katsnelson, Y. O. Kvashnin, A. I. Lichtenstein, V. V. Mazurenko, A. G. A. Nisbet, E. N. Ovchinnikova, and D. Pincini, Band filling control of the Dzyaloshinskii–Moriya interaction in weakly ferromagnetic insulators, Phys. Rev. Lett. 119(16), 167201 (2017)ADSGoogle Scholar
  36. 36.
    T. Srivastava, M. Schott, R. Juge, V. Križaková, M. Belmeguenai, Y. Roussigné, A. Bernand-Mantel, L. Ranno, S. Pizzini, S. M. Cheríf, A. Stashkevich, S. Auffret, O. Boulle, G. Gaudin, M. Chshiev, C. Baraduc, and H. Béa, Large-voltage tuning of Dzyaloshinskii–Moriya interactions: A route toward dynamic control of skyrmion chirality, Nano Lett. 18(8), 4871 (2018)ADSGoogle Scholar
  37. 37.
    I. A. Ado, A. Qaiumzadeh, R. A. Duine, A. Brataas, and M. Titov, Asymmetric and symmetric exchange in a generalized 2D Rashba ferromagnet, Phys. Rev. Lett. 121(8), 086802 (2018)ADSGoogle Scholar
  38. 38.
    J. Suwardy, K. Nawaoka, J. Cho, M. Goto, Y. Suzuki, and S. Miwa, Voltage-controlled magnetic anisotropy and voltage-induced Dzyaloshinskii–Moriya interaction change at the epitaxial Fe(001)/MgO(001) interface engineered by Co and Pd atomic-layer insertion, Phys. Rev. B 98(14), 144432 (2018)ADSGoogle Scholar
  39. 39.
    A. Cao, X. Zhang, B. Koopmans, S. Peng, Y. Zhang, Z. Wang, S. Yan, H. Yang, and W. Zhao, Tuning the Dzyaloshinskii–Moriya interaction in Pt/Co/MgO heterostructures through the MgO thickness, Nanoscale 10(25), 12062 (2018)Google Scholar
  40. 40.
    H. Yang, O. Boulle, V. Cros, A. Fert, and M. Chshiev, Controlling Dzyaloshinskii–Moriya interaction via chirality dependent atomic-layer stacking, insulator capping and electric field, Sci. Rep. 8(1), 12356 (2018)ADSGoogle Scholar
  41. 41.
    S. A. Díaz and R. E. Troncoso, Controlling skyrmion helicity via engineered Dzyaloshinskii–Moriya interactions, J. Phys.: Condens. Matter 28, 426005 (2016)Google Scholar
  42. 42.
    R. Menezes, J. Mulkers, C. C. de Souza Silva, and M. V. Miloevic, Deflection of ferromagnetic and antiferromagnetic skyrmions at heterochiral interfaces, Phys. Rev. B 99, 104409 (2019)ADSGoogle Scholar
  43. 43.
    A. O. Leonov and I. Kézsmárki, Skyrmion robustness in noncentrosymmetric magnets with axial symmetry: The role of anisotropy and tilted magnetic fields, Phys. Rev. B 96(21), 214413 (2017)ADSGoogle Scholar
  44. 44.
    S. Seki and M. Mochizuki, Skyrmions in Magnetic Materials, Springer, Switzerland, 2016Google Scholar
  45. 45.
    X. S. Wang, H. Y. Yuan, and X. R. Wang, A theory on skyrmion size, Commun. Phys. 1(1), 31 (2018)Google Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Liping Zhou
    • 1
  • Ren Qin
    • 1
  • Ya-Qing Zheng
    • 1
  • Yong Wang
    • 1
    Email author
  1. 1.School of PhysicsNankai UniversityTianjinChina

Personalised recommendations