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.

  • Article
  • Published:

Domain wall trajectory determined by its fractional topological edge defects

Nature Physics volume 9, pages 505–511 (2013)Cite this article

Subjects

Abstract

A domain wall (DW) in a ferromagnetic nanowire is composed of elementary topological bulk and edge defects with integer and fractional winding numbers, respectively, whose relative spatial arrangement determines the chirality of the DW. Here we show how we can understand and control the trajectory of DWs in magnetic branched networks, composed of connected nanowires, by considering their fractional elementary topological defects and how they interact with those innate to the network. We first develop a highly reliable mechanism for the injection of a DW of a given chirality into a nanowire and show that its chirality determines which branch the DW follows at a symmetric Y-shaped magnetic junction—the fundamental building block of the network. Using these concepts, we unravel the origin of the one-dimensional nature of magnetization reversal of connected artificial spin ice systems that have been observed in the form of Dirac strings.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Characterization of topological defects.
Figure 2: Creation of a vortex DW of a given chirality.
Figure 3: Ascertaining the DW trajectory due to interplay of fractional topological defects.
Figure 4: Experimental verification of the DW-chirality-based trajectory.
Figure 5: Unraveling the origin of 1D Dirac strings in artificial spin ice.

Similar content being viewed by others

References

  1. Mermin, N. D. The topological theory of defects in ordered media. Rev. Mod. Phys. 51, 591–648 (1979).

    ADS  MathSciNet  Google Scholar 

  2. Chaikin, P. M. & Lubensky, T. C. Principles of Condensed Matter Physics (Cambridge Univ. Press, 2000).

    Google Scholar 

  3. Hubert, A. & Schäfer, R. Magnetic Domains (Springer, 2000).

    Google Scholar 

  4. Tchernyshyov, O. & Chern, G-W. Fractional vortices and composite domain walls in flat nanomagnets. Phys. Rev. Lett. 95, 197204 (2005).

    Article  ADS  Google Scholar 

  5. Tanaka, M., Saitoh, E., Miyajima, H., Yamaoka, T. & Iye, Y. Magnetic interactions in a ferromagnetic honeycomb nanoscale network. Phys. Rev. B 73, 052411 (2006).

    Article  ADS  Google Scholar 

  6. Wang, R. F. et al. Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands. Nature 439, 303–306 (2006).

    Article  ADS  Google Scholar 

  7. Ladak, S., Read, D. E., Perkins, G. K., Cohen, L. F. & Branford, W. R. Direct observation of magnetic monopole defects in an artificial spin-ice system. Nature Phys. 6, 359–363 (2010).

    Article  ADS  Google Scholar 

  8. Branford, W. R., Ladak, S., Read, D. E., Zeissler, K. & Cohen, L. F. Emerging chirality in artificial spin ice. Science 335, 1597–1600 (2012).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. Allwood, D. A. et al. Magnetic domain-wall logic. Science 309, 1688–1692 (2005).

    Article  ADS  Google Scholar 

  11. Mengotti, E. et al. Real-space observation of emergent magnetic monopoles and associated Dirac strings in artificial kagome spin ice. Nature Phys. 7, 68–74 (2011).

    Article  ADS  Google Scholar 

  12. McMichael, R. D. & Donahue, M. J. Head to head domain wall structures in thin magnetic strips. IEEE Trans. Magn. 33, 4167–4169 (1997).

    Article  ADS  Google Scholar 

  13. Thiaville, A. & Nakatani, Y. Spin dynamics in confined magnetic structures III. Top. Appl. Phys. 101, 161–205 (2006).

    Article  Google Scholar 

  14. Wachowiak, A. et al. Direct observation of internal spin structure of magnetic vortex cores. Science 298, 577–580 (2002).

    Article  ADS  Google Scholar 

  15. Braun, H-B. Topological effects in nanomagnetism: From superparamagnetism to chiral quantum solitons. Adv. Phys. 61, 1–116 (2012).

    Article  ADS  Google Scholar 

  16. Kunz, A. Field induced domain wall collisions in thin magnetic nanowires. Appl. Phys. Lett. 94, 132502 (2009).

    Article  ADS  Google Scholar 

  17. Clarke, D. J., Tretiakov, O. A., Chern, G. W., Bazaliy, Y. B. & Tchernyshyov, O. Dynamics of a vortex domain wall in a magnetic nanostrip: Application of the collective-coordinate approach. Phys. Rev. B 78, 134412 (2008).

    Article  ADS  Google Scholar 

  18. Tretiakov, O. A., Clarke, D., Chern, G-W., Bazaliy, Y. B. & Tchernyshyov, O. Dynamics of domain walls in magnetic nanostrips. Phys. Rev. Lett. 100, 127204 (2008).

    Article  ADS  Google Scholar 

  19. Schryer, N. L. & Walker, L. R. The motion of 180° domain walls in uniform dc magnetic fields. J. Appl. Phys. 45, 5406–5421 (1974).

    Article  ADS  Google Scholar 

  20. Hayashi, M., Thomas, L., Rettner, C., Moriya, R. & Parkin, S. S. P. Direct observation of the coherent precession of magnetic domain walls propagating along permalloy nanowires. Nature Phys. 3, 21–25 (2007).

    Article  ADS  Google Scholar 

  21. Beach, G. S. D., Nistor, C., Knutson, C., Tsoi, M. & Erskine, J. L. Dynamics of field-driven domain-wall propagation in ferromagnetic nanowires. Nature Mater. 4, 741–744 (2005).

    Article  ADS  Google Scholar 

  22. Tanigawa, H. et al. Dynamical pinning of a domain wall in a magnetic nanowire induced by Walker Breakdown. Phys. Rev. Lett. 101, 207203 (2008).

    Article  ADS  Google Scholar 

  23. Thomas, L., Hayashi, M., Moriya, R., Rettner, C. & Parkin, S. Topological repulsion between domain walls in magnetic nanowires leading to the formation of bound states. Nature Commun. 3, 810 (2012).

    Article  ADS  Google Scholar 

  24. LLG Micromagnetics Simulator; available at http://llgmicro.home.mindspring.com.

  25. Zeisberger, M. & Mattheis, R. Magnetization reversal in magnetic nanostripes via Bloch wall formation. J. Phys. Condens. Matter 24, 024202 (2012).

    Article  ADS  Google Scholar 

  26. Hayashi, M. et al. Dependence of current and field driven depinning of domain walls on their structure and chirality in permalloy nanowires. Phys. Rev. Lett. 97, 207205 (2006).

    Article  ADS  Google Scholar 

  27. Thiele, A. A. Steady-state motion of magnetic domains. Phys. Rev. Lett. 30, 230–233 (1973).

    Article  ADS  Google Scholar 

  28. Tamara, D. Network + Guide to Networks 82–85 (Delmar, 2010).

    Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge discussions with O. Tchernyshyov, S. A. Parameswaran, K. P. Roche, R. Roy, S. Raghu, S. Kivelson and N. P. Aetukuri.

Author information

Author notes

  1. Aakash Pushp and Timothy Phung: These authors contributed equally to this work

Authors and Affiliations

  1. IBM Almaden Research Center, San Jose, California 95120, USA

    Aakash Pushp, Timothy Phung, Charles Rettner, Brian P. Hughes, See-Hun Yang, Luc Thomas & Stuart S. P. Parkin

  2. Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA

    Timothy Phung

Authors
  1. Aakash Pushp
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Timothy Phung
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Charles Rettner
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Brian P. Hughes
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. See-Hun Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Luc Thomas
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Stuart S. P. Parkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

A.P. and T.P. conceived and performed the experiments, and analysed the data. T.P. did the micromagnetic simulations. S-H.Y. grew the films. C.R. and B.P.H. did nanofabrication of the devices. A.P., T.P. and S.S.P.P. wrote the manuscript. S.S.P.P. supervised. All authors discussed the results and implications.

Corresponding authors

Correspondence to Aakash Pushp or Stuart S. P. Parkin.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 3544 kb)

Supplementary Information

Supplementary Movie 1 (AVI 2997 kb)

Supplementary Information

Supplementary Movie 2 (AVI 2985 kb)

Supplementary Information

Supplementary Movie 3 (AVI 3368 kb)

Supplementary Information

Supplementary Movie 4 (AVI 4170 kb)

Supplementary Information

Supplementary Movie 5 (AVI 3304 kb)

Supplementary Information

Supplementary Movie 6 (AVI 4130 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pushp, A., Phung, T., Rettner, C. et al. Domain wall trajectory determined by its fractional topological edge defects. Nature Phys 9, 505–511 (2013). https://doi.org/10.1038/nphys2669

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys2669

This article is cited by

Search

Advanced 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