Skyrmion Hall effect with spatially modulated Dzyaloshinskii–Moriya interaction


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.

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  1. 1.

    A. N. Bogdanov and A. Hubert, Thermodynamically stable magnetic vortex states in magnetic crystals, J. Magn. Magn. Mater. 138(3), 255 (1994)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google Scholar 

  4. 4.

    U. K. Rößler, A. N. Bogdanov, and C. Pfleiderer, Spontaneous skyrmion ground states in magnetic metals, Nature 442(7104), 797 (2006)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    Article  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)

    Article  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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google Scholar 

  15. 15.

    J. Iwasaki, M. Mochizuki, and N. Nagaosa, Currentinduced skyrmion dynamics in constricted geometries, Nat. Nanotechnol. 8(10), 742 (2013)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    Article  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)

    Article  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)

    ADS  Article  Google Scholar 

  23. 23.

    N. Nagaosa and Y. Tokura, Topological properties and dynamics of magnetic skyrmions, Nat. Nanotechnol. 8(12), 899 (2013)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    Article  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)

    Article  Google Scholar 

  28. 28.

    I. Dzyaloshinsky, A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics, J. Phys. Chem. Solids 4(4), 241 (1958)

    ADS  Article  Google Scholar 

  29. 29.

    T. Moriya, Anisotropic superexchange interaction and weak ferromagnetism, Phys. Rev. 120(1), 91 (1960)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    Article  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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    Article  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)

    ADS  Article  Google 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)

    ADS  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)

    ADS  Article  Google 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)

    ADS  Article  Google Scholar 

  44. 44.

    S. Seki and M. Mochizuki, Skyrmions in Magnetic Materials, Springer, Switzerland, 2016

    Google Scholar 

  45. 45.

    X. S. Wang, H. Y. Yuan, and X. R. Wang, A theory on skyrmion size, Commun. Phys. 1(1), 31 (2018)

    Article  Google Scholar 

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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).

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Correspondence to Yong Wang.

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Zhou, L., Qin, R., Zheng, Y. et al. Skyrmion Hall effect with spatially modulated Dzyaloshinskii–Moriya interaction. Front. Phys. 14, 53602 (2019).

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  • magnetic skyrmion
  • skyrmion Hall effect
  • Thiele equation