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Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands

An Addendum to this article was published on 01 March 2007


Frustration, defined as a competition between interactions such that not all of them can be satisfied, is important in systems ranging from neural networks to structural glasses. Geometrical frustration, which arises from the topology of a well-ordered structure rather than from disorder, has recently become a topic of considerable interest1. In particular, geometrical frustration among spins in magnetic materials can lead to exotic low-temperature states2, including ‘spin ice’, in which the local moments mimic the frustration of hydrogen ion positions in frozen water3,4,5,6. Here we report an artificial geometrically frustrated magnet based on an array of lithographically fabricated single-domain ferromagnetic islands. The islands are arranged such that the dipole interactions create a two-dimensional analogue to spin ice. Images of the magnetic moments of individual elements in this correlated system allow us to study the local accommodation of frustration. We see both ice-like short-range correlations and an absence of long-range correlations, behaviour which is strikingly similar to the low-temperature state of spin ice. These results demonstrate that artificial frustrated magnets can provide an uncharted arena in which the physics of frustration can be directly visualized.

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Figure 1: Illustration of frustration on the square lattice used in these experiments.
Figure 2: AFM and MFM images of a frustrated lattice.
Figure 3: Statistics of moment configurations.


  1. 1

    Ramirez, A. P. in Handbook of Magnetic Materials Vol. 13 (ed. Buschow, K. J. H.) 423–520 (Elsevier Science, Amsterdam, 2001)

    Google Scholar 

  2. 2

    Moessner, R. Magnets with strong geometric frustration. Can. J. Phys. 79, 1283–1294 (2001)

    CAS  Article  ADS  Google Scholar 

  3. 3

    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)

    CAS  Article  ADS  Google Scholar 

  4. 4

    Siddharthan, R. et al. Ising pyrochlore magnets: low-temperature properties, “ice rules,” and beyond. Phys. Rev. Lett. 83, 1854–1857 (1999)

    CAS  Article  ADS  Google Scholar 

  5. 5

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

    CAS  Article  ADS  Google Scholar 

  6. 6

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

    CAS  Article  ADS  Google Scholar 

  7. 7

    Pauling, L. The Nature of the Chemical Bond 301–304 (Cornell Univ. Press, Ithaca, New York, 1945)

    Google Scholar 

  8. 8

    Snyder, J., Slusky, J. S., Cava, R. J. & Schiffer, P. How ‘spin ice’ freezes. Nature 413, 48–51 (2001)

    CAS  Article  ADS  Google Scholar 

  9. 9

    Snyder, J. et al. Low-temperature spin freezing in the Dy2Ti2O7 spin ice. Phys. Rev. B 69, 064414 (2004)

    Article  ADS  Google Scholar 

  10. 10

    Tsui, Y. K., Burns, C. A., Snyder, J. & Schiffer, P. Magnetic field induced transitions from spin glass to liquid to long range order in a 3D geometrically frustrated magnet. Phys. Rev. Lett. 82, 3532–3535 (1999)

    CAS  Article  ADS  Google Scholar 

  11. 11

    Gardner, J. S. et al. Cooperative paramagnetism in the geometrically frustrated pyrochlore antiferromagnet Tb2Ti2O7 . Phys. Rev. Lett. 82, 1012–1015 (1999)

    CAS  Article  ADS  Google Scholar 

  12. 12

    Davidovic, D. et al. Correlations and disorder in arrays of magnetically coupled superconducting rings. Phys. Rev. Lett. 76, 815–818 (1996)

    CAS  Article  ADS  Google Scholar 

  13. 13

    Hilgenkamp, H. et al. Ordering and manipulation of the magnetic moments in large-scale superconducting π-loop arrays. Nature 422, 50–53 (2003)

    CAS  Article  ADS  Google Scholar 

  14. 14

    Cowburn, R. P. & Welland, M. E. Room temperature magnetic quantum cellular automata. Science 287, 1466–1468 (2000)

    CAS  Article  ADS  Google Scholar 

  15. 15

    Ross, C. A. et al. Magnetic behaviour of lithographically patterned particle arrays (invited). J. Appl. Phys. 91, 6848–6853 (2002)

    CAS  Article  ADS  Google Scholar 

  16. 16

    Cowburn, R. P. Probing antiferromagnetic coupling between nanomagnets. Phys. Rev. B 65, 092409 (2002)

    Article  ADS  Google Scholar 

  17. 17

    Martin, J. I., Nogues, J., Liu, K., Vicent, J. L. & Schuller, I. K. Ordered magnetic nanostructures: fabrication and properties. J. Magn. Magn. Mater. 256, 449–501 (2003)

    CAS  Article  ADS  Google Scholar 

  18. 18

    Imrea, A., Csabaa, G., Bernstein, G. H., Porod, W. & Metlushko, V. Investigation of shape-dependent switching of coupled nanomagnets. Superlatt. Microstruct. 34, 513–518 (2003)

    Article  ADS  Google Scholar 

  19. 19

    Stamps, R. L. & Camley, R. E. Frustration and finite size effects of magnetic dot arrays. J. Magn. Magn. Mater. 177, 813–814 (1998)

    Article  ADS  Google Scholar 

  20. 20

    The Object Oriented MicroMagnetic Framework (OOMMF) project at ITL/NIST. (2005).

  21. 21

    Lieb, E. H. & Wu, F. Y. in Phase Transitions and Critical Phenomena (eds Domb, C. & Green, M. S.) Vol. I (Academic, London, 1972)

    Google Scholar 

  22. 22

    Melko, R. G., den Hertog, B. C. & Gingras, M. J. P. Long-range order at low temperatures in dipolar spin ice. Phys. Rev. Lett. 87, 067203 (2001)

    CAS  Article  ADS  Google Scholar 

  23. 23

    Zhitomirsky, M. E., Honecker, A. & Petrenko, O. A. Field induced ordering in highly frustrated antiferromagnets. Phys. Rev. Lett. 85, 3269–3272 (2001)

    Article  ADS  Google Scholar 

  24. 24

    Yang, X. M. et al. Fabrication of sub-50 nm critical feature for magnetic recording device using electron-beam lithography. J. Vac. Sci. Technol. B 21, 3017–3020 (2003)

    CAS  Article  Google Scholar 

  25. 25

    Lin, C. K., Wang, W., Hwu, H. & Chan, Y. Single step electron-beam lithography for asymmetric recess and gamma gate in high electron mobility transistor fabrication. J. Vac. Sci. Technol. B. 22, 1723–1726 (2004)

    CAS  Article  Google Scholar 

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We acknowledge financial support from the Army Research Office and the National Science Foundation MRSEC programme, and discussions with P. Crowell and P. Lammert. R.S.F. thanks the CNPq-Brazil for sponsorship.

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Correspondence to P. Schiffer.

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

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