Article | Published:

Trochoidal motion and pair generation in skyrmion and antiskyrmion dynamics under spin–orbit torques

Nature Electronicsvolume 1pages451457 (2018) | Download Citation

Abstract

Magnetic skyrmions are swirling magnetic spin structures that could be used to build next-generation memory and logic devices. They can be characterized by a topological charge that describes how the spin winds around the core. The dynamics of skyrmions and antiskyrmions, which have opposite topological charges, are typically described by assuming a rigid core. However, this reduces the set of variables that describe skyrmion motion. Here we theoretically explore the dynamics of skyrmions and antiskyrmions in ultrathin ferromagnetic films and show that current-induced spin–orbit torques can lead to trochoidal motion and skyrmion–antiskyrmion pair generation, which occurs only for either the skyrmion or antiskyrmion, depending on the symmetry of the underlying Dzyaloshinskii–Moriya interaction. Such dynamics are induced by core deformations, leading to a time-dependent helicity that governs the motion of the skyrmion and antiskyrmion core. We compute the dynamical phase diagram through a combination of atomistic spin simulations, reduced-variable modelling and machine learning algorithms. It predicts how spin–orbit torques can control the type of motion and the possibility to generate skyrmion lattices by antiskyrmion seeding.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

References

  1. 1.

    Bogdanov, A. & Yablonskii, D. Contribution to the theory of inhomogeneous states of magnets in the region of magnetic-field-induced phase transitions. Mixed state of antiferromagnets. Zh. Eksp. Teor. Fiz. 69, 142–146 (1989).

  2. 2.

    Bogdanov, A. & Hubert, A. The stability of vortex-like structures in uniaxial ferromagnets. J. Magn. Magn. Mater. 195, 182–192 (1999).

  3. 3.

    Hagemeister, J., Romming, N., Von Bergmann, K., Vedmedenko, E. Y. & Wiesendanger, R. Stability of single skyrmionic bits. Nat. Commun. 6, 8455 (2015).

  4. 4.

    Rohart, S., Miltat, J. & Thiaville, A. Path to collapse for an isolated Néel skyrmion. Phys. Rev. B 93, 665–666 (2016).

  5. 5.

    Stosic, D., Mulkers, J., Van Waeyenberge, B., Ludermir, T. B. & Milošević, M. V. Paths to collapse for isolated skyrmions in few-monolayer ferromagnetic films. Phys. Rev. B 95, 214418 (2017).

  6. 6.

    Koshibae, W. & Nagaosa, N. Theory of antiskyrmions in magnets. Nat. Commun. 7, 10542 (2016).

  7. 7.

    Everschor-Sitte, K., Sitte, M., Valet, T., Abanov, A. & Sinova, J. Skyrmion production on demand by homogeneous DC currents. New J. Phys. 19, 092001 (2017).

  8. 8.

    Stier, M., Häusler, W., Posske, T., Gurski, G. & Thorwart, M. Skyrmion–anti-skyrmion pair creation by in-plane currents. Phys. Rev. Lett. 118, 267203 (2017).

  9. 9.

    Thiele, A. A. Steady-state motion of magnetic domains. Phys. Rev. Lett. 30, 230 (1973).

  10. 10.

    Guslienko, K. Y. et al. Eigenfrequencies of vortex state excitations in magnetic submicron-size disks. J. Appl. Phys. 91, 8037 (2002).

  11. 11.

    Choe, S. B. et al. Vortex core-driven magnetization dynamics. Science 304, 420–422 (2004).

  12. 12.

    Ivanov, B. & Zaspel, C. Excitation of spin dynamics by spin-polarized current in vortex state magnetic disks. Phys. Rev. Lett. 99, 247208 (2007).

  13. 13.

    Mistral, Q. et al. Current-driven vortex oscillations in metallic nanocontacts. Phys. Rev. Lett. 100, 257201 (2008).

  14. 14.

    Sampaio, J., Cros, V., Rohart, S., Thiaville, A. & Fert, A. Nucleation, stability and current-induced motion of isolated magnetic skyrmions in nanostructures. Nat. Nanotech. 8, 839–844 (2013).

  15. 15.

    Nagaosa, N. & Tokura, Y. Topological properties and dynamics of magnetic skyrmions. Nat. Nanotech. 8, 899–911 (2013).

  16. 16.

    Lin, S.-Z., Reichhardt, C., Batista, C. D. & Saxena, A. Driven skyrmions and dynamical transitions in chiral magnets. Phys. Rev. Lett. 110, 207202 (2013).

  17. 17.

    Lin, S.-Z. & Hayami, S. Ginzburg–Landau theory for skyrmions in inversion-symmetric magnets with competing interactions. Phys. Rev. B 93, 064430 (2016).

  18. 18.

    Leonov, A. O. & Mostovoy, M. Edge states and skyrmion dynamics in nanostripes of frustrated magnets. Nat. Commun. 8, 14394 (2017).

  19. 19.

    Büttner, F. et al. Dynamics and inertia of skyrmionic spin structures. Nat. Phys. 11, 225–228 (2015).

  20. 20.

    Fert, A., Cros, V. & Sampaio, J. Skyrmions on the track. Nat. Nanotech. 8, 152–156 (2013).

  21. 21.

    Fert, A., Reyren, N. & Cros, V. Magnetic skyrmions: advances in physics and potential applications. Nat. Rev. Mater. 2, 17031 (2017).

  22. 22.

    Nayak, A. K. et al. Magnetic antiskyrmions above room temperature in tetragonal Heusler materials. Nature 548, 561–566 (2017).

  23. 23.

    Hoffmann, M. et al. Antiskyrmions stabilized at interfaces by anisotropic Dzyaloshinskii–Moriya interaction. Nat. Commun. 8, 308 (2017).

  24. 24.

    Güngördü, U., Nepal, R., Tretiakov, O. A., Belashchenko, K. & Kovalev, A. A. Stability of skyrmion lattices and symmetries of quasi-two-dimensional chiral magnets. Phys. Rev. B 93, 064428 (2016).

  25. 25.

    Fert, A. & Levy, P. M. Role of anisotropic exchange interactions in determining the properties of spin-glasses. Phys. Rev. Lett. 44, 1538–1541 (1980).

  26. 26.

    Dupé, B., Hoffmann, M., Paillard, C. & Heinze, S. Tailoring magnetic skyrmions in ultra-thin transition metal films. Nat. Commun. 5, 4030 (2014).

  27. 27.

    Romming, N. et al. Writing and deleting single magnetic skyrmions. Science 341, 636–639 (2013).

  28. 28.

    Dupé, B., Kruse, C. N., Dornheim, T. & Heinze, S. How to reveal metastable skyrmionic spin structures by spin-polarized scanning tunneling microscopy. New J. Phys. 18, 055015 (2016).

  29. 29.

    Böttcher, M., Heinze, S., Egorov, S., Sinova, J. & Dupé, B. B-T phase diagram of Pd/Fe/Ir(111) computed with parallel tempering Monte Carlo. Preprint at https://arxiv.org/abs/1707.01708 (2018).

  30. 30.

    von Malottki, S., Dupé, B., Bessarab, P. F., Delin, A. & Heinze, S. Enhanced skyrmion stability due to exchange frustration. Sci. Rep. 7, 12299 (2017).

  31. 31.

    Leonov, A. O. & Mostovoy, M. Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet. Nat. Commun. 6, 8275 (2015).

  32. 32.

    Zhang, X. et al. Skyrmion dynamics in a frustrated ferromagnetic film and current-induced helicity locking-unlocking transition. Nat. Commun. 8, 1717 (2017).

  33. 33.

    Hu, Y., Chi, X., Li, X., Liu, Y. & Du, A. Creation and annihilation of skyrmions in the frustrated magnets with competing exchange interactions. Sci. Rep. 7, 16079 (2017).

  34. 34.

    Rózsa, L. et al. Skyrmions with attractive interactions in an ultrathin magnetic film. Phys. Rev. Lett. 117, 157205 (2016).

  35. 35.

    Sondheimer, E. H. The mean free path of electrons in metals. Adv. Phys. 50, 499–537 (2001).

  36. 36.

    Rózsa, L. et al. Formation and stability of metastable skyrmionic spin structures with various topologies in an ultrathin film. Phys. Rev. B 95, 094423 (2017).

  37. 37.

    Slonczewski, J. C. Theory of domain-wall motion in magnetic films and platelets. J. Appl. Phys. 44, 1759–1770 (1973).

  38. 38.

    Van Waeyenberge, B. et al. Magnetic vortex core reversal by excitation with short bursts of an alternating field. Nature 444, 461–464 (2006).

  39. 39.

    Yamada, K. et al. Electrical switching of the vortex core in a magnetic disk. Nat. Mater. 6, 270–273 (2007).

  40. 40.

    Gaididei, Y., Kravchuk, V. P. & Sheka, D. D. Magnetic vortex dynamics induced by an electrical current. Int. J. Quantum Chem. 110, 83–97 (2010).

  41. 41.

    Kim, J.-V. in Solid State Physics (eds Camley, R. E. & Stamps, R. L.) 217–294 (Academic, San Diego, 2012).

  42. 42.

    Bogdanov, A. N. & Rößler, U. K. Chiral symmetry breaking in magnetic thin films and multilayers. Phys. Rev. Lett. 87, 037203 (2001).

  43. 43.

    Thiaville, A., Rohart, S., Jué, É., Cros, V. & Fert, A. Dynamics of Dzyaloshinskii domain walls in ultrathin magnetic films. Europhys. Lett. 100, 57002 (2012).

Download references

Acknowledgements

This work was partially supported by the Horizon2020 Framework Programme of the European Commission under grant no. 665095 (MAGicSky). J.-V.K. acknowledges support from the Deutscher Akademischer Austauschdienst under award no. 57314019. U.R. acknowledges support from the Deutsche Forschungsgemeinschaft (grant RI2891/1-1). U.R., B.D. and J.S. acknowledge the Alexander von Humboldt Foundation, the Deutsche Forschungsgemeinschaft (grant DU1489/2-1), the Graduate School of Excellence Materials Science in Mainz (MAINZ), the ERC Synergy Grant SC2 (no. 610115), the Transregional Collaborative Research Center (SFB/TRR) 173 SPIN+X and the Grant Agency of the Czech Republic (grant no. 14-37427G).

Author information

Affiliations

  1. Institute of Physics, Johannes Gutenberg University Mainz, Mainz, Germany

    • Ulrike Ritzmann
    • , Jairo Sinova
    •  & Bertrand Dupé
  2. Department for Physics and Astronomy, Uppsala University, Uppsala, Sweden

    • Ulrike Ritzmann
  3. Institute of Theoretical Physics and Astrophysics, Christian-Albrechts-Universität zu Kiel, Kiel, Germany

    • Stephan von Malottki
    •  & Stefan Heinze
  4. Centre de Nanosciences et de Nanotechnologies, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Palaiseau, France

    • Joo-Von Kim
  5. Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic

    • Jairo Sinova

Authors

  1. Search for Ulrike Ritzmann in:

  2. Search for Stephan von Malottki in:

  3. Search for Joo-Von Kim in:

  4. Search for Stefan Heinze in:

  5. Search for Jairo Sinova in:

  6. Search for Bertrand Dupé in:

Contributions

B.D. and S.H. initiated the project. U.R. and S.v.M. developed the atomistic spin dynamics code and U.R. performed the atomistic spin dynamics simulations. U.R. and J.-V.K. interpreted the simulation results and developed the analytical model. S.H., B.D., J.-V.K. and U.R. wrote the manuscript. All of the authors discussed the data.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Ulrike Ritzmann.

Supplementary information

  1. Supplementary Information

    Supplementary Figures 1–11 and Supplementary Notes 1–5

  2. Supplementary Video 1

    Atomistic spin dynamics simulation showing the linear motion of a skyrmion under spin–orbit torques of \(\hbar \beta _{{\mathrm{FL}}} = \hbar \beta _{{\mathrm{DL}}} = 0.04\) meV. The animation shows the time evolution over 1 ns of the z-component of the magnetization in the system with periodic boundary conditions.

  3. Supplementary Video 2

    Atomistic spin dynamics simulation showing the linear motion of an antiskyrmion under spin–orbit torques of \(\hbar \beta _{{\mathrm{FL}}} = \hbar \beta _{{\mathrm{DL}}} = 0.04\) meV. The animation shows the time evolution over 1 ns of the z-component of the magnetization in the system with periodic boundary conditions.

  4. Supplementary Video 3

    Atomistic spin dynamics simulation showing the deflected motion of an antiskyrmion under spin–orbit torques of \(\hbar \beta _{{\mathrm{FL}}} = \hbar \beta _{{\mathrm{DL}}} = 0.06\) meV. The animation shows the time evolution over 1 ns of the z-component of the magnetization in the system with periodic boundary conditions.

  5. Supplementary Video 4

    Atomistic spin dynamics simulation showing the trochoidal motion of an antiskyrmion under spin–orbit torques of \(\hbar \beta _{{\mathrm{FL}}} = \hbar \beta _{{\mathrm{DL}}} = 0.09\) meV. The animation shows the time evolution over 1 ns of the z-component of the magnetization in the system with periodic boundary conditions.

  6. Supplementary Video 5

    Atomistic spin dynamics simulation showing skyrmion–antiskyrmion pair generation from a single antiskyrmion seed under spin–orbit torques of \(\hbar \beta _{{\mathrm{FL}}} = 0.01\) meV and \(\hbar \beta _{{\mathrm{DL}}} = 1.35\) meV. The animation shows the time evolution over 0.1 ns of the topological charge density in a system with periodic boundary conditions.

About this article

Publication history

Received

Accepted

Published

Issue Date

DOI

https://doi.org/10.1038/s41928-018-0114-0

Further reading