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:

Freezing and thawing of artificial ice by thermal switching of geometric frustration in magnetic flux lattices

Nature Nanotechnology volume 9, pages 710–715 (2014)Cite this article

Subjects

Abstract

The problem of an ensemble of repulsive particles on a potential-energy landscape is common to many physical systems and has been studied in multiple artificial playgrounds. However, the latter usually involve fixed energy landscapes, thereby impeding in situ investigations of the particles’ collective response to controlled changes in the landscape geometry. Here, we experimentally realize a system in which the geometry of the potential-energy landscape can be switched using temperature as the control knob. This realization is based on a high-temperature superconductor in which we engineer a nanoscale spatial modulation of the superconducting condensate. Depending on the temperature, the flux quanta induced by an applied magnetic field see either a geometrically frustrated energy landscape that favours an ice-like flux ordering, or an unfrustrated landscape that yields a periodic flux distribution. This effect is reflected in a dramatic change in the superconductor's magneto-transport. The thermal switching of the energy landscape geometry opens new opportunities for the study of ordering and reorganization in repulsive particle manifolds.

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: Square ice and thermal switching of geometrical frustration.
Figure 2: Nanoscale modulation of the superconducting critical temperature.
Figure 3: Field-matching effects in the magneto-resistance.
Figure 4: Temperature crossover from the geometrically frustrated landscape to the unfrustrated energy landscape.
Figure 5: Analysis of the stability of the vortex ice.

Similar content being viewed by others

References

  1. Daldini, O., Martinoli, P., Olsen, J. & Berner, G. Vortex-line pinning by thickness modulation of superconducting films. Phys. Rev. Lett. 32, 218–221 (1974).

    Article  CAS  Google Scholar 

  2. Fiory, A. T., Hebard, A. F. & Somekh, S. Critical currents associated with the interaction of commensurate flux-line sublattices in a perforated Al film. Appl. Phys. Lett. 32, 73–75 (1978).

    Article  CAS  Google Scholar 

  3. Pruymboom, A., Kes, P. H., van der Drift, E. & Radelaar, S. Flux-line shear through narrow constraints in superconducting films. Phys. Rev. Lett. 60, 1430–1434 (1988).

    Article  CAS  Google Scholar 

  4. Otani, Y., Pannetier, B., Nozières, J. P. & Givord, D. Magnetostatic interactions between magnetic arrays and superconducting thin films. J. Magn. Magn. Mater. 126, 622–625 (1993).

    Article  CAS  Google Scholar 

  5. Baert, M., Metlushko, V., Jonckheere, R., Moshchalkov, V. V. & Bruynseraede, Y. Composite flux-line lattices stabilized in superconducting films by a regular array of artificial defects. Phys. Rev. Lett. 74, 3269–3272 (1995).

    Article  CAS  Google Scholar 

  6. Harada, K. et al. Direct observation of vortex dynamics in superconducting films with regular arrays of defects. Science 274, 1167–1170 (1996).

    Article  CAS  Google Scholar 

  7. Metlushko, V. V et al. Supermatching vortex phases in superconducting thin films with antidot lattices. Europhys. Lett. 41, 333–338 (1998).

    Article  CAS  Google Scholar 

  8. Metlushko, V. et al. Interstitial flux phases in a superconducting niobium film with a square lattice of artificial pinning centers. Phys. Rev. B 60, R12585–R12588 (1999).

    Article  CAS  Google Scholar 

  9. Reichhardt, C. & Grønbech-Jensen, N. Critical currents and vortex states at fractional matching fields in superconductors with periodic pinning. Phys. Rev. B 63, 054510 (2001).

    Article  Google Scholar 

  10. Field, S. B. et al. Vortex configurations, matching, and domain structure in large arrays of artificial pinning centers. Phys. Rev. Lett. 88, 067003 (2002).

    Article  CAS  Google Scholar 

  11. Misko, V. R., Savel'ev, S. & Nori, F. Critical currents in superconductors with quasiperiodic pinning arrays: one-dimensional chains and two-dimensional Penrose lattices. Phys. Rev. B 74, 024522 (2006).

    Article  Google Scholar 

  12. Villegas, J. E., Montero, M. I., Li, C-P. & Schuller, I. K. Correlation length of quasiperiodic vortex lattices. Phys. Rev. Lett. 97, 027002 (2006).

    Article  CAS  Google Scholar 

  13. Sochnikov, I., Shaulov, A., Yeshurun, Y., Logvenov, G. & Bozović, I. Large oscillations of the magnetoresistance in nanopatterned high-temperature superconducting films. Nature Nanotech. 5, 516–519 (2010).

    Article  CAS  Google Scholar 

  14. Reichhardt, C. & Olson Reichhardt, C. J. Moving vortex phases, dynamical symmetry breaking, and jamming for vortices in honeycomb pinning arrays. Phys. Rev. B 78, 224511 (2008).

    Article  Google Scholar 

  15. Field, S., Witt, J., Nori, F. & Ling, X. Superconducting vortex avalanches. Phys. Rev. Lett. 74, 1206–1209 (1995).

    Article  CAS  Google Scholar 

  16. Lee, C-S., Janko, B., Derenyi, I. & Barabasi, A-L. Reducing vortex density in superconductors using the ‘ratchet effect’. Nature 400, 337–340 (1999).

    Article  CAS  Google Scholar 

  17. Villegas, J. E. et al. A superconducting reversible rectifier that controls the motion of magnetic flux quanta. Science 302, 1188–1191 (2003).

    Article  CAS  Google Scholar 

  18. Jaksch, D., Bruder, C., Cirac, J. I., Gardiner, C. W. & Zoller, P. Cold bosonic atoms in optical lattices. Phys. Rev. Lett. 81, 3108–3111 (1998).

    Article  CAS  Google Scholar 

  19. Korda, P. T., Spalding, G. C. & Grier, D. G. Evolution of a colloidal critical state in an optical pinning potential landscape. Phys. Rev. B 66, 024504 (2002).

    Article  Google Scholar 

  20. Sampaio, J., Cros, V., Rohart, S., Thiaville, A. & Fert, A. Nucleation, stability and current-induced motion of isolated magnetic skyrmions in nanostructures. Nature Nanotech. 8, 839–844 (2013).

    Article  CAS  Google Scholar 

  21. Dunkel, J. et al. Fluid dynamics of bacterial turbulence. Phys. Rev. Lett. 110, 228102 (2013).

    Article  Google Scholar 

  22. Frauenfelder, H., Sligar, S. G. & Wolynes, P. G. The energy landscapes and motions of proteins. Science 254, 1598–1603 (1991).

    Article  CAS  Google Scholar 

  23. Bonsall, L. & Maradudin, A. A. Some static and dynamical properties of a two-dimensional Wigner crystal. Phys. Rev. B 15, 1959–1973 (1977).

    Article  CAS  Google Scholar 

  24. Crassous, A. et al. Nanoscale electrostatic manipulation of magnetic flux quanta in ferroelectric/superconductor BiFeO3/YBa2Cu3O7–δ heterostructures. Phys. Rev. Lett. 107, 247002 (2011).

    Article  Google Scholar 

  25. 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  CAS  Google Scholar 

  26. 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  CAS  Google Scholar 

  27. 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  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  31. Libál, A., Reichhardt, C. & Olson Reichhardt, C. J. Realizing colloidal artificial ice on arrays of optical traps. Phys. Rev. Lett. 97, 228302 (2006).

    Article  Google Scholar 

  32. 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  CAS  Google Scholar 

  33. Bhat, V. S. et al. Controlled magnetic reversal in permalloy films patterned into artificial quasicrystals. Phys. Rev. Lett. 111, 077201 (2013).

    Article  CAS  Google Scholar 

  34. Qi, Y., Brintlinger, T. & Cumings, J. Direct observation of the ice rule in an artificial kagome spin ice. Phys. Rev. B 77, 094418 (2008).

    Article  Google Scholar 

  35. 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 (2010).

    Article  Google Scholar 

  36. Morgan, J. P., Stein, A., Langridge, S. & Marrows, C. H. Thermal ground-state ordering and elementary excitations in artificial magnetic square ice. Nature Phys. 7, 75–79 (2010).

    Article  Google Scholar 

  37. Farhan, A. et al. Exploring hyper-cubic energy landscapes in thermally active finite artificial spin-ice systems. Nature Phys. 9, 375–382 (2013).

    Article  CAS  Google Scholar 

  38. Marrows, C. Artificial spin ice: The heat is on. Nature Phys. 9, 324–325 (2013).

    Article  CAS  Google Scholar 

  39. Farhan, A. et al. Direct observation of thermal relaxation in artificial spin ice. Phys. Rev. Lett. 111, 057204 (2013).

    Article  CAS  Google Scholar 

  40. Zhang, S. et al. Crystallites of magnetic charges in artificial spin ice. Nature 500, 553–557 (2013).

    Article  CAS  Google Scholar 

  41. Libál, A., Olson Reichhardt, C. J. & Reichhardt, C. Creating artificial ice states using vortices in nanostructured superconductors. Phys. Rev. Lett. 102, 237004 (2009).

    Article  Google Scholar 

  42. Latimer, M. L., Berdiyorov, G. R., Xiao, Z. L., Peeters, F. M. & Kwok, W. K. Realization of artificial ice systems for magnetic vortices in a superconducting MoGe thin film with patterned nanostructures. Phys. Rev. Lett. 111, 067001 (2013).

    Article  CAS  Google Scholar 

  43. Swiecicki, I. et al. Strong field-matching effects in superconducting YBa2Cu3O7−δ films with vortex energy landscapes engineered via masked ion irradiation. Phys. Rev. B 85, 224502 (2012).

    Article  Google Scholar 

  44. Trastoy, J. et al. Unusual magneto-transport of YBa2Cu3O7− δ films due to the interplay of anisotropy, random disorder and nanoscale periodic pinning. New J. Phys. 15, 103022 (2013).

    Article  Google Scholar 

  45. Blatter, G., Feigel'man, M. V., Geshkenbein, V. B., Larkin, A. I. & Vinokur, V. M. Vortices in high-temperature superconductors. Rev. Mod. Phys. 66, 1125 (1994).

    Article  CAS  Google Scholar 

  46. Wördenweber, R., Kes, P. H. & Tsuei, C. C. Peak and history effects in two-dimensional collective flux pinning. Phys. Rev. B 33, 3172–3180 (1986).

    Article  Google Scholar 

  47. Henderson, W., Andrei, E. Y., Higgins, M. J. & Bhattacharya, S. Metastability and glassy behavior of a driven flux-line lattice. Phys. Rev. Lett. 77, 2077–2080 (1996).

    Article  CAS  Google Scholar 

  48. Tonomura, A. et al. Observation of individual vortices trapped along columnar defects in high-temperature superconductors. Nature 412, 620–622 (2001).

    Article  CAS  Google Scholar 

  49. Auslaender, O. M. et al. Mechanics of individual isolated vortices in a cuprate superconductor. Nature Phys. 5, 35–39 (2008).

    Article  Google Scholar 

  50. Lesueur, J., Nedellec, P., Bernas, H., Burger, J. P. & Dumoulin, L. Depairing-like variation of Tc in YBa2Cu3O7−δ . Phys. C Supercond. 167, 1–5 (1990).

    Article  CAS  Google Scholar 

  51. Bergeal, N. et al. Using ion irradiation to make high-Tc Josephson junctions. J. Appl. Phys. 102, 083903 (2007).

    Article  Google Scholar 

  52. Reichhardt, C., Groth, J., Olson, C., Field, S. & Nori, F. Spatiotemporal dynamics and plastic flow of vortices in superconductors with periodic arrays of pinning sites. Phys. Rev. B 54, 16108–16115 (1996).

    Article  CAS  Google Scholar 

  53. Velez, M., Hoffmann, A., Schuller, I. K. & Vicent, J. L. Artificially induced reconfiguration of the vortex lattice by arrays of magnetic dots. Phys. Rev. Lett. 83, 1022–1025 (1999).

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the French Agence Nationale de la Recherche (grant MASTHER, no. 2011-BS03-008-02), COST Action MP1201 “NanoSC” and the Ville de Paris Emergence Programme. J.T. acknowledges the support of Fundación Barrié (Galicia, Spain).

Author information

Authors and Affiliations

  1. Unité Mixte de Physique CNRS/Thales, 1 ave. A. Fresnel, 91767, Palaiseau, France

    J. Trastoy, R. Bernard, J. Briatico & Javier E. Villegas

  2. Université Paris Sud, 91405, Orsay, France

    J. Trastoy, R. Bernard, J. Briatico & Javier E. Villegas

  3. LPEM, ESPCI-CNRS-UPMC, 10 rue Vauquelin, Paris, 75231, France

    M. Malnou, N. Bergeal & J. Lesueur

  4. CNRS, Phynano Team, Laboratoire de Photonique et de Nanostructures, route de Nozay, 91460, Marcoussis, France

    C. Ulysse & G. Faini

Authors
  1. J. Trastoy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Malnou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. Ulysse
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R. Bernard
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. N. Bergeal
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. G. Faini
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. J. Lesueur
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. J. Briatico
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Javier E. Villegas
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

J.E.V. conceived the experiments. R.B. and J.T. grew the YBCO films. C.U. performed electron-beam lithography. J.T. carried out the rest of the sample fabrication steps, and performed magneto-transport and vortex energy calculations. M.M. and N.B. realized the ion damage simulations. J.T. and J.E.V. analysed the results and wrote the paper. All authors contributed to the discussion of the results and revised the manuscript.

Corresponding author

Correspondence to Javier E. Villegas.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary Information (PDF 1582 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Trastoy, J., Malnou, M., Ulysse, C. et al. Freezing and thawing of artificial ice by thermal switching of geometric frustration in magnetic flux lattices. Nature Nanotech 9, 710–715 (2014). https://doi.org/10.1038/nnano.2014.158

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nnano.2014.158

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