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.

Real-space observation of emergent magnetic monopoles and associated Dirac strings in artificial kagome spin ice

Abstract

Magnetic monopoles have been predicted to occur as emergent fractional quasiparticles inside pyrochlore spin ice, a frustrated magnetic insulator. Experimental signatures of such emergent monopoles accompanied by Dirac strings have been detected by means of neutron scattering in reciprocal space in pyrochlore spin ice at sub-Kelvin temperatures, but their real-space observation has remained elusive. Here we report on direct, real-space observations of emergent monopoles and their associated Dirac strings in two-dimensional (2D) artificial kagome spin ice at room temperature using synchrotron X-ray photoemission electron microscopy. Magnetization reversal proceeds through the nucleation and avalanche-type dissociation of monopole–antimonopole pairs along 1D Dirac strings. This is in sharp contrast to conventional domain growth in 2D systems, providing a striking example of dimensional reduction due to frustration. The observed hysteresis, monopole densities and 1D Dirac-string avalanches are quantitatively explained by Monte Carlo simulations.

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

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Emergent monopoles and associated Dirac strings in artificial kagome spin ice.
Figure 2: Identification of monopoles during magnetization reversal.
Figure 3: Creation and separation of monopole–antimonopole pairs and growth of Dirac strings.
Figure 4: Hysteresis and avalanches—experimental results.
Figure 5: Hysteresis, avalanches and disorder—Monte-Carlo simulations.

References

  1. Dirac, P. A. M. Quantised singularities in the electromagnetic field. Proc. R. Soc. Lond. A 133, 60–72 (1931).

    Article  ADS  Google Scholar 

  2. ’t Hooft, G. Magnetic monopoles in unified gauge theories. Nucl. Phys. B 79, 276–284 (1974).

    Article  ADS  MathSciNet  Google Scholar 

  3. Polyakov, A. M. Particle spectrum in quantum field theory. JETP Lett. 20, 194–195 (1974).

    ADS  Google Scholar 

  4. Goldhaber, A. S. & Trower, W. P. Magnetic monopoles. Am. J. Phys. 58, 429–439 (1990).

    Article  ADS  Google Scholar 

  5. Abbiendi, G. et al. Search for Dirac magnetic monopoles in e+e collisions with the OPAL detector at LEP2. Phys. Lett. B 663, 37–42 (2008).

    Article  ADS  Google Scholar 

  6. Castelnovo, C., Moessner, R. & Sondhi, S. L. Magnetic monopoles in spin ice. Nature 451, 42–45 (2008).

    Article  ADS  Google Scholar 

  7. Harris, M. J., Bramwell, S. T., McMorrow, D. F., Zeiske, T. & Godfrey, K. W. Geometrical frustration in the ferromagnetic pyrochlore Ho2Ti2O7 . Phys. Rev. Lett. 79, 2554–2557 (1997).

    Article  ADS  Google Scholar 

  8. Bramwell, S. T. & Gingras, M. J. P. Spin ice state in frustrated magnetic pyrochlore materials. Science 294, 1495–1501 (2001).

    Article  ADS  Google Scholar 

  9. Ramirez, A. P., Hayashi, A., Cava, R. J., Siddharthan, R. & Shastry, B. S. Zero-point entropy in ‘spin ice’. Nature 399, 333–335 (1999).

    Article  ADS  Google Scholar 

  10. Pauling, L. The structure and entropy of ice and of other crystals with some randomness of atomic arrangement. J. Am. Chem. Soc. 57, 2680–2684 (1935).

    Article  Google Scholar 

  11. Tchernyshyov, O. Magnetism: Freedom for the poles. Nature 451, 22–23 (2008).

    Article  ADS  Google Scholar 

  12. Balents, L. Spin liquids in frustrated magnets. Nature 464, 199–208 (2010).

    Article  ADS  Google Scholar 

  13. Heeger, A. J., Kivelson, S., Schrieffer, J. R. & Su, W. P. Solitons in conducting polymers. Rev. Mod. Phys. 60, 781–850 (1988).

    Article  ADS  Google Scholar 

  14. Faddeev, L. D. & Takhtajan, L. A. What is the spin of a spin-wave? Phys. Lett. A 85, 375–377 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  15. Lake, B., Tennant, D. A., Frost, C. D. & Nagler, S. E. Quantum criticality and universal scaling of a quantum antiferromagnet. Nature Mat. 4, 329–334 (2005).

    Article  ADS  Google Scholar 

  16. Braun, H. B. et al. Emergence of soliton chirality in a quantum antiferromagnet. Nature Phys. 1, 159–163 (2005).

    Article  ADS  Google Scholar 

  17. dePicciotto, R. et al. Direct observation of a fractional charge. Nature 389, 162–164 (1997).

    Article  ADS  Google Scholar 

  18. Dolev, M., Heiblum, M., Umansky, V., Stern, A. & Mahalu, D. Observation of a quarter of an electron charge at the ν=5/2 quantum Hall state. Nature 452, 829–835 (2008).

    Article  ADS  Google Scholar 

  19. Jaubert, L. D. C. & Holdsworth, P. C. W. Signature of magnetic monopole and Dirac string dynamics in spin ice. Nature Phys. 5, 258–261 (2009).

    Article  ADS  Google Scholar 

  20. Morris, D. J. P. et al. Dirac strings and magnetic monopoles in spin ice Dy2Ti2O7 . Science 326, 411–414 (2009).

    Article  ADS  Google Scholar 

  21. Fennell, T. et al. Magnetic Coulomb phase in the spin ice Ho2Ti2O7 . Science 326, 415–417 (2009).

    Article  ADS  Google Scholar 

  22. Bianchi, A. D. et al. Superconducting vortices in CeCoIn5: Toward the Pauli-limiting field. Science 319, 177–180 (2008).

    Article  ADS  Google Scholar 

  23. Laver, M. & Forgan, E. M. Magnetic flux lines in type-II superconductors and the hairy ball theorem. Nature Comm. 1, 1–4 (2010).

    Article  Google Scholar 

  24. Nelson, D. R. Defects and Geometry in Condensed Matter Physics 303 (Cambridge Univ. Press, 2002).

    Google Scholar 

  25. Kadowaki, H. et al. Observation of magnetic monopoles in spin ice. J. Phys. Soc. Jpn 78, 103706 (2009).

    Article  ADS  Google Scholar 

  26. 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 

  27. 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 

  28. Mengotti, E. et al. Building blocks of an artificial kagome spin ice: Photoemission electron microscopy of arrays of ferromagnetic islands. Phys. Rev. B 78, 144402 (2008).

    Article  ADS  Google Scholar 

  29. Remhof, A. et al. Magnetostatic interactions on a square lattice. Phys. Rev. B 77, 134409 (2008).

    Article  ADS  Google Scholar 

  30. Möller, G. & Moessner, R. Artificial square ice and related dipolar nanoarrays. Phys. Rev. Lett. 96, 237202 (2006).

    Article  ADS  Google Scholar 

  31. Wills, A. S., Ballou, R. & Lacroix, C. Model of localized highly frustrated ferromagnetism: The kagome spin ice. Phys. Rev. B 66, 144407 (2002).

    Article  ADS  Google Scholar 

  32. Tabata, Y. et al. Kagome ice state in the dipolar spin ice Dy2Ti2O7 . Phys. Rev. Lett. 97, 257205 (2006).

    Article  ADS  Google Scholar 

  33. Fennell, T., Bramwell, S. T., McMorrow, D. F., Manuel, P. & Wildes, A. R. Pinch points and Kasteleyn transitions in kagome ice. Nature Phys. 3, 566–571 (2007).

    Article  ADS  Google Scholar 

  34. Möller, G. & Moessner, R. Magnetic multipole analysis of kagome and artificial spin-ice dipolar arrays. Phys. Rev. B 80, 140409 (2009).

    Article  ADS  Google Scholar 

  35. Chern, G. W., Mellado, P. & Tchernyshyov, O. Two-stage ordering of spins in dipolar spin ice on kagome. Preprint at http://arxiv.org/abs/0906.4781 (2009).

  36. Im, M. Y., Fischer, P., Kim, D. H. & Shin, S. C. Direct observation of individual Barkhausen avalanches in nucleation-mediated magnetization reversal processes. Appl. Phys. Lett. 95, 182504 (2009).

    Article  ADS  Google Scholar 

  37. Sethna, J. P. et al. Hysteresis and hierarchies: Dynamics of disorder-driven first-order phase transformations. Phys. Rev. Lett. 70, 3347 (1993).

    Article  ADS  Google Scholar 

  38. Sethna, J. P., Dahmen, K. A. & Myers, C. R. Crackling noise. Nature 410, 242–250 (2001).

    Article  ADS  Google Scholar 

  39. Sethna, J. P., Dahmen, K. A. & Perkovic, O. Random-field Ising models of hysteresis. Preprint at http://arxiv.org/abs/0406320 (2004).

  40. Chubykalo, O. A., González, J. M. & González, J. Avalanches as propagating domain walls in a micromagnetic model. Physica D 113, 382–386 (1998).

    Article  ADS  Google Scholar 

  41. Schumann, A., Sothmann, B., Szary, P. & Zabel, H. Charge ordering of magnetic dipoles in artificial honeycomb patterns. Appl. Phys. Lett. 97, 022509 (2010).

    Article  ADS  Google Scholar 

  42. Stöhr, J. et al. Element-specific magnetic microscopy with circularly polarized X-rays. Science 259, 658–661 (1993).

    Article  ADS  Google Scholar 

  43. Christensen, K. & Moloney, N. R. Complexity and Criticality (Imperial College Press, 2005).

    Book  Google Scholar 

Download references

Acknowledgements

The authors would like to thank: M. Horisberger, E. Deckardt, A. Weber, C. David, A. Steger, L. Le Guyader, A. Kleibert, J. Raabe, D. Eastwood and D. Atkinson for their help. We also acknowledge helpful discussions with V. Lobaskin, W. Nahm and M. Sigrist. This work was supported by the Swiss National Science Foundation and the Science Foundation of Ireland (08/RFP/PHY1532 and 05/IN1/I853), and part of this work was carried out at the Swiss Light Source, Paul Scherrer Institute, Villigen, Switzerland. We also acknowledge receipt of an HEA Ireland equipment fund.

Author information

Authors and Affiliations

Authors

Contributions

Sample preparation: E.M.; measurements: E.M., A.F.R.; analysis and interpretation: E.M., L.J.H., H.B.B.; theory and simulations: R.V.H., H.B.B.; preparation of the manuscript: E.M., L.J.H., H.B.B.; supervision of the project: L.J.H., H.B.B., F.N. All authors discussed the results and implications, and commented on the manuscript at all stages.

Corresponding authors

Correspondence to Laura J. Heyderman or Hans-Benjamin Braun.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 1991 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Mengotti, E., Heyderman, L., Rodríguez, A. et al. Real-space observation of emergent magnetic monopoles and associated Dirac strings in artificial kagome spin ice. Nature Phys 7, 68–74 (2011). https://doi.org/10.1038/nphys1794

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys1794

This article is cited by

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