Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

The role of temperature and drive current in skyrmion dynamics

Abstract

Magnetic skyrmions are topologically stabilized nanoscale spin structures that could be of use in the development of future spintronic devices. When a skyrmion is driven by an electric current it propagates at an angle relative to the flow of current—known as the skyrmion Hall angle (SkHA)—that is a function of the drive current. This drive dependence, as well as thermal effects due to Joule heating, could be used to tailor skyrmion trajectories, but are not well understood. Here we report a study of skyrmion dynamics as a function of temperature and drive amplitude. We find that the skyrmion velocity depends strongly on temperature, while the SkHA does not and instead evolves differently in the low- and high-drive regimes. In particular, the maximum skyrmion velocity in ferromagnetic devices is limited by a mechanism based on skyrmion surface tension and deformation (where the skyrmion transitions into a stripe). Our mechanism provides a complete description of the SkHA in ferromagnetic multilayers across the full range of drive strengths, illustrating that skyrmion trajectories can be engineered for device applications.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Measurement principle and typical observed skyrmion contrast.
Fig. 2: Skyrmion velocity as a function of current density.
Fig. 3: SkHA as a function of skyrmion velocity.
Fig. 4: Simulations of SkHA versus skyrmion velocity for temperature-dependent material parameters with thermal fluctuations.
Fig. 5: Different types of skyrmion deformation.
Fig. 6: Influence of DL- and FL-SOT on the SkHA.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors on reasonable request.

References

  1. 1.

    Boulle, O., Malinowski, G. & Kläui, M. Current-induced domain wall motion in nanoscale ferromagnetic elements. Mater. Sci. Eng. R 72, 159–187 (2011).

    Google Scholar 

  2. 2.

    Kent, A. D. & Worledge, D. C. A new spin on magnetic memories. Nat. Nanotechnol. 10, 187–191 (2015).

    Google Scholar 

  3. 3.

    Parkin, S. S. P., Hayashi, M. & Thomas, L. Magnetic domain-wall racetrack memory. Science 320, 190–194 (2008).

    Google Scholar 

  4. 4.

    Parkin, S. S. P. & Yang, S.-H. Memory on the racetrack. Nat. Nanotechnol. 10, 195–198 (2015).

    Google Scholar 

  5. 5.

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

    Google Scholar 

  6. 6.

    Tomasello, R. et al. A strategy for the design of skyrmion racetrack memories. Sci. Rep. 4, 6784 (2014).

    Google Scholar 

  7. 7.

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

    Google Scholar 

  8. 8.

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

    Google Scholar 

  9. 9.

    Hellman, F. et al. Interface-induced phenomena in magnetism. Rev. Mod. Phys. 89, 025006 (2017).

    MathSciNet  Google Scholar 

  10. 10.

    Finocchio, G., Büttner, F., Tomasello, R., Carpentieri, M. & Kläui, M. Magnetic skyrmions: from fundamental to applications. J. Phys. D 49, 423001 (2016).

    Google Scholar 

  11. 11.

    Purnama, I., Gan, W. L., Wong, D. W. & Lew, W. S. Guided current-induced skyrmion motion in 1D potential well. Sci. Rep. 5, 10620 (2015).

    Google Scholar 

  12. 12.

    Legrand, W. et al. Room-temperature current-induced generation and motion of sub-100 nm skyrmions. Nano Lett. 17, 2703–2712 (2017).

    Google Scholar 

  13. 13.

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

    Google Scholar 

  14. 14.

    Rohart, S., Miltat, J. & Thiaville, A. Path to collapse for an isolated Néel skyrmion. Phys. Rev. B 93, 214412 (2016).

    Google Scholar 

  15. 15.

    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. 95, 214418 (2017).

    Google Scholar 

  16. 16.

    Bessarab, P. F. et al. Lifetime of racetrack skyrmions. Sci. Rep. 8, 3433 (2018).

    Google Scholar 

  17. 17.

    Müller, G. P. et al. Duplication, collapse, and escape of magnetic skyrmions revealed using a systematic saddle point search method. Phys. Rev. Lett. 121, 197202 (2018).

    Google Scholar 

  18. 18.

    Dzyaloshinskii, I. E. A thermodynamic theory of weak ferromagnetism of antiferromagnets. J. Phys. Chem. Solids 4, 241–255 (1958).

    Google Scholar 

  19. 19.

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

    Google Scholar 

  20. 20.

    Brataas, A. & Hals, K. M. D. Spin–orbit torques in action. Nat. Nanotechnol. 9, 86–88 (2014).

    Google Scholar 

  21. 21.

    Litzius, K. et al. Skyrmion Hall effect revealed by direct time-resolved X-ray microscopy. Nat. Phys. 13, 170–175 (2017).

    Google Scholar 

  22. 22.

    Jiang, W. et al. Direct observation of the skyrmion Hall effect. Nat. Phys. 13, 162–169 (2017).

    Google Scholar 

  23. 23.

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

    Google Scholar 

  24. 24.

    Woo, S. et al. Observation of room-temperature magnetic skyrmions and their current-driven dynamics in ultrathin metallic ferromagnets. Nat. Mater. 15, 501–506 (2016).

    Google Scholar 

  25. 25.

    Boulle, O. et al. Room-temperature chiral magnetic skyrmions in ultrathin magnetic nanostructures. Nat. Nanotechnol. 11, 449–454 (2016).

    Google Scholar 

  26. 26.

    Moreau-Luchaire, C. et al. Additive interfacial chiral interaction in multilayers for stabilization of small individual skyrmions at room temperature. Nat. Nanotechnol. 11, 444–448 (2016).

    Google Scholar 

  27. 27.

    Caretta, L. et al. Fast current-driven domain walls and small skyrmions in a compensated ferrimagnet. Nat. Nanotechnol. 13, 1154–1160 (2018).

    Google Scholar 

  28. 28.

    Jiang, W. et al. Skyrmions in magnetic multilayers. Phys. Rep. 704, 1–49 (2017).

    MathSciNet  MATH  Google Scholar 

  29. 29.

    Desplat, L., Suess, D., Kim, J.-V. & Stamps, R. L. Thermal stability of metastable magnetic skyrmions: entropic narrowing and significance of internal eigenmodes. Phys. Rev. B 98, 134407 (2018).

    Google Scholar 

  30. 30.

    Miltat, J., Rohart, S. & Thiaville, A. Brownian motion of magnetic domain walls and skyrmions, and their diffusion constants. Phys. Rev. B 97, 214426 (2018).

    Google Scholar 

  31. 31.

    Kravchuk, V. P., Sheka, D. D., Rößler, U. K., van den Brink, J. & Gaididei, Y. Spin eigenmodes of magnetic skyrmions and the problem of the effective skyrmion mass. Phys. Rev. B 97, 064403 (2018).

    Google Scholar 

  32. 32.

    Zázvorka, J. et al. Thermal skyrmion diffusion used in a reshuffler device. Nat. Nanotechnol. 14, 658–661 (2019).

    Google Scholar 

  33. 33.

    Everschor, K., Garst, M., Duine, R. A. & Rosch, A. Current-induced rotational torques in the skyrmion lattice phase of chiral magnets. Phys. Rev. B 84, 064401 (2011).

    Google Scholar 

  34. 34.

    Woo, S. et al. Current-driven dynamics and inhibition of the skyrmion Hall effect of ferrimagnetic skyrmions in GdFeCo films. Nat. Commun. 9, 959 (2018).

    Google Scholar 

  35. 35.

    Zhang, X., Zhou, Y. & Ezawa, M. Magnetic bilayer-skyrmions without skyrmion Hall effect. Nat. Commun. 7, 10293 (2016).

    Google Scholar 

  36. 36.

    Zhang, X., Zhou, Y. & Ezawa, M. Antiferromagnetic skyrmion: stability, creation and manipulation. Sci. Rep. 6, 24795 (2016).

    Google Scholar 

  37. 37.

    Kim, S. K., Lee, K.-J. & Tserkovnyak, Y. Self-focusing skyrmion racetracks in ferrimagnets. Phys. Rev. B 95, 140404(R) (2017).

    Google Scholar 

  38. 38.

    Tomasello, R. et al. Performance of synthetic antiferromagnetic racetrack memory: domain wall versus skyrmion. J. Phys. D 50, 325302 (2017).

    Google Scholar 

  39. 39.

    Hirata, Y. et al. Vanishing skyrmion Hall effect at the angular momentum compensation temperature of a ferrimagnet. Nat. Nanotechnol. 14, 232–236 (2019).

    Google Scholar 

  40. 40.

    Reichhardt, C. & Reichhardt, C. J. O. Noise fluctuations and drive dependence of the skyrmion Hall effect in disordered systems. New J. Phys. 18, 095005 (2016).

    Google Scholar 

  41. 41.

    Kim, J.-V. & Yoo, M.-W. Current-driven skyrmion dynamics in disordered films. Appl. Phys. Lett. 110, 132404 (2017).

    Google Scholar 

  42. 42.

    Weigand, M. Realization of a New Magnetic Scanning X-Ray Microscope and Investigation of Landau Structures under Pulsed Field Excitation. PhD thesis, Univ. Stuttgart (2014).

  43. 43.

    Schütz, G. et al. Absorption of circularly polarized X rays in iron. Phys. Rev. Lett. 58, 737–740 (1987).

    Google Scholar 

  44. 44.

    Jiang, W. et al. Blowing magnetic skyrmion bubbles. Science 349, 283–286 (2015).

    Google Scholar 

  45. 45.

    You, C.-Y. & Ha, S.-S. Temperature increment in a current-heated nanowire for current-induced domain wall motion with finite thickness insulator layer. Appl. Phys. Lett. 91, 022507 (2007).

    Google Scholar 

  46. 46.

    Laufenberg, M. et al. Temperature dependence of the spin torque effect in current-induced domain wall motion. Phys. Rev. Lett. 97, 046602 (2006).

    Google Scholar 

  47. 47.

    Yamaguchi, A. & Nasu, S. Effect of Joule heating in current-driven domain wall motion. Appl. Phys. Lett. 86, 012511 (2005).

    Google Scholar 

  48. 48.

    Rózsa, L., Atxitia, U. & Nowak, U. Temperature scaling of the Dzyaloshinsky-Moriya interaction in the spin wave spectrum. Phys. Rev. B 96, 094436 (2017).

    Google Scholar 

  49. 49.

    Wang, J. et al. Temperature dependence of magnetic anisotropy constant in iron chalcogenide Fe3Se4. J. Appl. Phys. 112, 103905 (2012).

    Google Scholar 

  50. 50.

    Lin, S.-Z., Reichhardt, C., Batista, C. D. & Saxena, A. Particle model for skyrmions in metallic chiral magnets: dynamics, pinning, and creep. Phys. Rev. B 87, 214419 (2013).

    Google Scholar 

  51. 51.

    Salimath, A., Abbout, A., Brataas, A. & Manchon, A. Current-driven skyrmion depinning in magnetic granular films. Phys. Rev. B 99, 104416 (2019).

    Google Scholar 

  52. 52.

    Reichhardt, C. & Reichhardt, C. J. O. Thermal creep and the skyrmion Hall angle in driven skyrmion crystals. J. Phys. Condens. Matter 31, 07LT01 (2018).

  53. 53.

    Juge, R. et al. Current-driven skyrmion dynamics and drive-dependent skyrmion Hall effect in an ultrathin film. Phys. Rev. Appl. 12, 044007 (2019).

    Google Scholar 

  54. 54.

    Leliaert, J. et al. Adaptively time stepping the stochastic Landau-Lifshitz-Gilbert equation at nonzero temperature: implementation and validation in MuMax3. AIP Adv. 7, 125010 (2017).

    Google Scholar 

  55. 55.

    Vansteenkiste, A. et al. The design and verification of MuMax3. AIP Adv. 4, 107133 (2014).

    Google Scholar 

  56. 56.

    Rodrigues, D. R., Abanov, A., Sinova, J. & Everschor-Sitte, K. Effective description of domain wall strings. Phys. Rev. B 97, 134414 (2018).

    Google Scholar 

  57. 57.

    Woo, S. et al. Spin-orbit torque-driven skyrmion dynamics revealed by time-resolved X-ray microscopy. Nat. Commun. 8, 15573 (2017).

    Google Scholar 

  58. 58.

    Leliaert, J. et al. Current-driven domain wall mobility in polycrystalline Permalloy nanowires: a numerical study. J. Appl. Phys. 115, 233903 (2014).

    Google Scholar 

  59. 59.

    Hayashi, M., Kim, J., Yamanouchi, M. & Ohno, H. Quantitative characterization of the spin-orbit torque using harmonic Hall voltage measurements. Phys. Rev. B 89, 144425 (2014).

    Google Scholar 

  60. 60.

    Legrand, W. et al. Hybrid chiral domain walls and skyrmions in magnetic multilayers. Sci. Adv. 4, eaat0415 (2018).

    Google Scholar 

  61. 61.

    Dovzhenko, Y. et al. Magnetostatic twists in room-temperature skyrmions explored by nitrogen-vacancy center spin texture reconstruction. Nat. Commun. 9, 2712 (2018).

    Google Scholar 

  62. 62.

    Lemesh, I. & Beach, G. S. D. Twisted domain walls and skyrmions in perpendicularly magnetized multilayers. Phys. Rev. B 98, 104402 (2018).

    Google Scholar 

  63. 63.

    Mizukami, S. et al. Gilbert damping in perpendicularly magnetized Pt/Co/Pt films investigated by all-optical pump–probe technique. Appl. Phys. Lett. 96, 152502 (2010).

    Google Scholar 

  64. 64.

    Moon, K.-W. et al. Domain wall motion driven by an oscillating magnetic field. J. Phys. D 50, 125003 (2017).

    Google Scholar 

Download references

Acknowledgements

We thank C. Reichhardt and C. J. O. Reichhardt for a helpful discussion about the effects proposed in their recent paper52. K.L., D.R., N.Kerber, M.K. and R.M.R. gratefully acknowledge financial support by the Graduate School of Excellence Materials Science in Mainz (MAINZ, GSC266). Work at MIT was supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under award DE-SC0012371 K.E.-S. acknowledges funding from the German Research Foundation (DFG) under project EV 196/2-1. Measurements were carried out at the MAXYMUS end station at Helmholtz-Zentrum Berlin. We thank HZB for the allocation of beamtime. M.K. and the groups in Mainz acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—projects 290319996/TRR173, 403502522/SPP 2137 Skyrmionics and 290396061/TRR173. This work was supported by the Fonds Wetenschappelijk Onderzoek (FWO-Vlaanderen) through project G098917N and a postdoctoral fellowship (J.L). J.L was also supported during part of this research by the Ghent University Special Research Fund with a BOF postdoctoral fellowship. We gratefully acknowledge the support of NVIDIA Corporation with the donation of the graphics processing units (GPUs) used for this research.

Author information

Affiliations

Authors

Contributions

K.L. and M.K. proposed the study. M.K., G.S., B.V.W. and G.S.D.B. supervised the respective members of the study. I.L. and K.L. fabricated devices. K.L., P.B., S.K., N.Kerber, D.H., N.Keil and M.W. were part of the beamtime teams. K.L. performed and supervised the beamtime experiments. K.L., P.B. and S.K. analysed the beamtime data. K.-Y.L., J.Z. and K.L. performed the sample characterization. I.L. performed numerical calculations on the three-dimensional magnetization in the stack. J.L. and J.M. performed MuMax3 simulations. D.R. and K.E.-S. provided the surface tension model. All authors participated in the discussion and interpreted results. K.L. drafted the manuscript with the help of M.K. and R.M.R. and assistance from G.S.D.B. All authors commented on the manuscript.

Corresponding authors

Correspondence to Geoffrey S. D. Beach or Mathias Kläui.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Notes 1–7, including Supplementary Figs. 1–15.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Litzius, K., Leliaert, J., Bassirian, P. et al. The role of temperature and drive current in skyrmion dynamics. Nat Electron 3, 30–36 (2020). https://doi.org/10.1038/s41928-019-0359-2

Download citation

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing