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.

## Relevant articles

• ### Collective skyrmion motion under the influence of an additional interfacial spin-transfer torque

Scientific Reports Open Access 24 June 2022

• ### Toggle-like current-induced Bloch point dynamics of 3D skyrmion strings in a room temperature nanowire

Nature Communications Open Access 24 June 2022

• ### Effect of Chiral Damping on the dynamics of chiral domain walls and skyrmions

Nature Communications Open Access 07 March 2022

## Access options

\$32.00

All prices are NET prices.

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

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

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

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

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

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

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

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

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

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

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).

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

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

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

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).

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

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).

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

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

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

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

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

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

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).

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

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).

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

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

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).

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).

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).

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

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).

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).

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

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

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

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

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

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).

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

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

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

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).

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

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

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).

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

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).

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

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

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).

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

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

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

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

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).

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

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

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

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).

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

## 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

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.

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

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

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/s41928-019-0359-2

• ### Collective skyrmion motion under the influence of an additional interfacial spin-transfer torque

• Callum R. MacKinnon
• Katharina Zeissler

Scientific Reports (2022)

• ### Toggle-like current-induced Bloch point dynamics of 3D skyrmion strings in a room temperature nanowire

• M. T. Birch
• D. Cortés-Ortuño
• G. Schütz

Nature Communications (2022)

• ### Effect of Chiral Damping on the dynamics of chiral domain walls and skyrmions

• C. K. Safeer
• Mohamed-Ali Nsibi
• Ioan-Mihai Miron

Nature Communications (2022)

• ### Current-driven dynamics and ratchet effect of skyrmion bubbles in a ferrimagnetic insulator

• Saül Vélez
• Sandra Ruiz-Gómez
• Pietro Gambardella

Nature Nanotechnology (2022)

• ### Elongation of skyrmions by Dzyaloshinskii–Moriya interaction in helimagnetic films

• Ying-Ying Dai
• Han Wang
• Zhi-Dong Zhang

Rare Metals (2022)

## Search

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