The European Physical Journal B

, Volume 60, Issue 1, pp 15–27 | Cite as

Transient domain wall displacement under spin-polarized current pulses

  • A. Thiaville
  • Y. Nakatani
  • F. Piéchon
  • J. Miltat
  • T. Ono
Mesoscopic and Nanoscale Systems


This paper investigates the non steady-state displacement of magnetic domain walls in a nanostrip submitted to a time-dependent spin-polarized current flowing along the nanostrip. First, numerical micromagnetic simulations show that a domain wall can move under application of a current pulse, and that the displacement resulting from a conversion of the domain wall structure is quantized. The numerical findings are subsequently explained in the framework of simplified analytic models, namely the 1D model and the point-core vortex model. We then introduce the concept of an angle linked to the magnetization of a general domain wall, and show that it allows understanding the transient phenomena quite generally. Simple analytic formulas are derived and compared to experiments. For this, charts are given for the key parameters of the domain wall mechanics, as obtained from numerical micromagnetic simulations. We finally discuss the limitations of this work, by looking at the influence of temperature elevation under current, presence of a non-adiabatic term, and of disorder.


72.25.-b Spin polarized transport 85.75.-d Magnetoelectronics; spintronics 75.75.+a Magnetic properties of nanostructures 75.60.Ch Domain walls and domain structure 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. L. Berger, J. Appl. Phys. 49, 2156 (1978) CrossRefADSGoogle Scholar
  2. L. Berger, J. Appl. Phys. 55, 1954 (1984) CrossRefADSGoogle Scholar
  3. T. Ono, H. Miyajima, K. Shigeto, K. Mibu, N. Hosoito, T. Shinjo, Science 284, 468 (1999) CrossRefADSGoogle Scholar
  4. D. Atkinson, D. Allwood, G. Xiong, M. Cooke, C. Faulkner, R. Cowburn, Nature Mater. 2, 85 (2003) CrossRefADSGoogle Scholar
  5. M. Hayashi, L. Thomas, C. Rettner, R. Moriya, Y. Bazaliy, S. Parkin, Phys. Rev. Lett. 98, 037204 (2007) CrossRefADSGoogle Scholar
  6. N. Vernier, D. Allwood, D. Atkinson, M. Cooke, R. Cowburn, Europhys. Lett. 65, 526 (2004) CrossRefADSGoogle Scholar
  7. A. Yamaguchi, T. Ono, S. Nasu, K. Miyake, K. Mibu, T. Shinjo, Phys. Rev. Lett. 92, 077205 (2004) CrossRefADSGoogle Scholar
  8. M. Kläui, P. Jubert, R. Allenspach, A. Bischof, J. Bland, G. Faini, U. Rüdiger, C. Vaz, L. Vila, C. Vouille, Phys. Rev. Lett. 95, 026601 (2005) CrossRefADSGoogle Scholar
  9. P.O. Jubert, M. Kläui, A. Bischof, U. Rüdiger, R. Allenspach, J. Appl. Phys. 99, 08G523 (2006) CrossRefGoogle Scholar
  10. C. Lim, T. Devolder, C. Chappert, J. Grollier, V. Cros, A. Vaurès, A. Fert, G. Faini, Appl. Phys. Lett. 84, 2820 (2004) CrossRefADSGoogle Scholar
  11. J. Miltat, G. Albuquerque, A. Thiaville, Spin Dynamics in Confined Magnetic Structures I (Springer, Berlin, 2002), pp. 1–33 Google Scholar
  12. A. Thiaville, Y. Nakatani, J. Miltat, Y. Suzuki, Europhys. Lett. 69, 990 (2005) CrossRefADSGoogle Scholar
  13. S. Zhang, Z. Li, Phys. Rev. Lett. 93, 127204 (2004) CrossRefADSGoogle Scholar
  14. S. Barnes, S. Maekawa, Phys. Rev. Lett. 95, 107204 (2005) CrossRefADSGoogle Scholar
  15. M. Stiles, W. Saslow, M. Donahue, A. Zangwill, Phys. Rev. B 75, 214423 (2007) CrossRefADSGoogle Scholar
  16. Y. Nakatani, A. Thiaville, J. Miltat, Nature Mater. 2, 521 (2003) CrossRefADSGoogle Scholar
  17. R. McMichael, M. Donahue, IEEE Trans. Magn. 33, 4167 (1997) CrossRefGoogle Scholar
  18. Y. Nakatani, A. Thiaville, J. Miltat, J. Magn. Magn. Mater. 290–291, 750 (2005) Google Scholar
  19. A. Thiaville, Y. Nakatani, J. Miltat, N. Vernier, J. Appl. Phys. 95, 7049 (2004) CrossRefADSGoogle Scholar
  20. G. Tatara, H. Kohno, Phys. Rev. Lett. 92, 086601 (2004) CrossRefADSGoogle Scholar
  21. A. Thiaville, J. García, J. Miltat, J. Magn. Magn. Mater. 242–245, 1061 (2002) Google Scholar
  22. L. Thomas, M. Hayashi, X. Jiang, R. Moriya, C. Rettner, S. Parkin, Nature 443, 197 (2006) CrossRefADSGoogle Scholar
  23. A. Thiaville, Y. Nakatani, Spin Dynamics in Confined Magnetic Structures III (Springer, Berlin, 2006), pp. 161–206 Google Scholar
  24. D. Porter, M. Donahue, J. Appl. Phys. 95, 6729 (2004) CrossRefADSGoogle Scholar
  25. J. Shibata (2006), private communication Google Scholar
  26. A. Thiele, Phys. Rev. Lett. 30, 230 (1973) CrossRefADSGoogle Scholar
  27. D. Huber, J. Appl. Phys. 53, 1899 (1982) CrossRefADSGoogle Scholar
  28. J. Shibata, Y. Nakatani, G. Tatara, H. Kohno, Y. Otani, Phys. Rev. B 73, 020403(R) (2006) CrossRefADSGoogle Scholar
  29. K.Y. Guslienko, X. Han, D. Keavney, R. Divan, S. Bader, Phys. Rev. Lett. 96, 067205 (2006) CrossRefADSGoogle Scholar
  30. J. He, Z. Li, S. Zhang, J. Appl. Phys. 99, 08G509 (2006) Google Scholar
  31. W. Döring, Z. Naturforschg. 3a, 373 (1948) Google Scholar
  32. J. Slonczewski, Physics of Magnetic Materials (World Scientific, Singapore, 1985) Google Scholar
  33. G. Wysin, Phys. Rev. B 54, 15156 (1996) CrossRefADSGoogle Scholar
  34. The TW 1D model as well as the VW point core model express the DW Döring mass as mD = (μ0 Ms / γ0) 2 S ατ/ Δ0 T, in terms of the two micromagnetic quantities α τ and Δ0 T that we consider in this paper, thus allowing direct evaluation of this mass. This relation shows also that, for the same nanostrip sizes, the VW can bee 100 times heavier than the TW (see Fig. 7). Google Scholar
  35. Quantitatively, the values of Dxx, Dyy and Dxy, in units of (μ0 Ms / γ0) 2 πh, are 3.80, 2.79 and ± 0.35 for the VW, 1.94, 0.80 and ± 0.51 for the ATW, and 1.73, 0.40 and 0 for the STW in a 240 ×10 nm2 nanostrip, respectively. Thus Dxx is dominant for a TW, and Dxx ≈Dyy dominate for a VW. Google Scholar
  36. A. Thiele, J. Appl. Phys. 47, 2759 (1976) CrossRefADSGoogle Scholar
  37. J. Slonczewski, J. Magn. Magn. Mater. 12, 108 (1979) CrossRefADSGoogle Scholar
  38. A. Malozemoff, J. Slonczewski, Magnetic Domain Walls in Bubble Materials (Academic Press, New York, 1979) Google Scholar
  39. Z. Li, S. Zhang, Phys. Rev. Lett. 92, 207203 (2004) CrossRefADSGoogle Scholar
  40. M. Kläui, C. Vaz, J. Bland, L. Heyderman, F. Nolting, A. Pavlovska, E. Bauer, S. Cherifi, S. Heun, A. Locatelli, Appl. Phys. Lett. 85, 5637 (2004) CrossRefADSGoogle Scholar
  41. M. Laufenberg, D. Backes, W. Bührer, D. Bedau, M. Kläui, U. Rüdiger, C. Vaz, J. Bland, L. Heyderman, F. Nolting et al., Appl. Phys. Lett. 88, 052507 (2006) CrossRefGoogle Scholar
  42. K. Yamada, S. Kasai, Y. Nakatani, K. Kobayashi, H. Kohno, A. Thiaville, T. Ono, Nature Mater. 6, 269 (2007) CrossRefADSGoogle Scholar
  43. A. Yamaguchi, S. Nasu, H. Tanigawa, T. Ono, K. Miyake, K. Mibu, T. Shinjo, Appl. Phys. Lett. 86, 012511 (2005) CrossRefADSGoogle Scholar
  44. A. Yamaguchi, K. Yano, H. Tanigawa, S. Kasai, T. Ono, Jpn. J. Appl. Phys. 45, 3850 (2006) CrossRefADSGoogle Scholar
  45. R. Duine, A. Núñez, A. MacDonald, Phys. Rev. Lett. 98, 056605 (2007) CrossRefADSGoogle Scholar
  46. E. Martinez, L. Lopez-Diaz, L. Torres, C. Tristan, O. Alejos, Phys. Rev. B 75, 174409 (2007) CrossRefADSGoogle Scholar
  47. A. Hubert, R. Schäfer, Magnetic Domains (Springer Verlag, Berlin, 1998) Google Scholar
  48. L. Thomas, M. Hayashi, X. Jiang, R. Moriya, C. Rettner, S. Parkin, Science 315, 1553 (2007) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • A. Thiaville
    • 1
  • Y. Nakatani
    • 2
  • F. Piéchon
    • 1
  • J. Miltat
    • 1
  • T. Ono
    • 3
  1. 1.CNRS, Laboratoire de Physique des Solides, UMR 8502OrsayFrance
  2. 2.Department of Computer ScienceTokyoJapan
  3. 3.Institute for Chemical ResearchKyotoJapan

Personalised recommendations