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Crystallites of magnetic charges in artificial spin ice

Nature volume 500, pages 553–557 (2013)Cite this article

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Abstract

Artificial spin ice1 is a class of lithographically created arrays of interacting ferromagnetic nanometre-scale islands. It was introduced to investigate many-body phenomena related to frustration and disorder in a material that could be tailored to precise specifications and imaged directly. Because of the large magnetic energy scales of these nanoscale islands, it has so far been impossible to thermally anneal artificial spin ice into desired thermodynamic ensembles; nearly all studies of artificial spin ice have either treated it as a granular material activated by alternating fields2 or focused on the as-grown state of the arrays3. This limitation has prevented experimental investigation of novel phases that can emerge from the nominal ground states of frustrated lattices. For example, artificial kagome spin ice, in which the islands are arranged on the edges of a hexagonal net, is predicted to support states with monopolar charge order at entropies below that of the previously observed pseudo-ice manifold4. Here we demonstrate a method for thermalizing artificial spin ices with square and kagome lattices by heating above the Curie temperature of the constituent material. In this manner, artificial square spin ice achieves unprecedented thermal ordering of the moments. In artificial kagome spin ice, we observe incipient crystallization of the magnetic charges embedded in pseudo-ice, with crystallites of magnetic charges whose size can be controlled by tuning the lattice constant. We find excellent agreement between experimental data and Monte Carlo simulations of emergent charge–charge interactions.

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Figure 1: The artificial spin-ice lattices used in this study.
Figure 2: MFM images of annealed artificial square spin ice.
Figure 3: Magnitude of the correlation between islands as a function of island separation for annealed artificial square spin ice of all lattice spacings.
Figure 4: Emergent domains of ordered magnetic charges in artificial kagome spin ice.
Figure 5: Charge–charge correlation functions of annealed artificial kagome spin ice.

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References

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

    Article  ADS  CAS  Google Scholar 

  2. Ke, X. et al. Energy minimization and AC demagnetization in a nanomagnet array. Phys. Rev. Lett. 101, 037205 (2008)

    Article  ADS  CAS  Google Scholar 

  3. 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 (2011)

    Article  ADS  CAS  Google Scholar 

  4. 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  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  8. Ryzhkin, I. A. Magnetic relaxation in rare-earth oxide pyrochlores. J. Exp. Theor. Phys. 101, 481–486 (2005)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. Chern, G.-W., Mellado, P. & Tchernyshyov, O. Two-stage ordering of spins in dipolar spin ice on the kagome lattice. Phys. Rev. Lett. 106, 207202 (2011)

    Article  ADS  Google Scholar 

  11. Baxter, R. J. Exactly Solved Models in Statistical Mechanics (Academic, 1982)

    MATH  Google Scholar 

  12. Pollard, S. D., Volkov, V. & Zhu, Y. Propagation of magnetic charge monopoles and Dirac flux strings in an artificial spin-ice lattice. Phys. Rev. B 85, 180402(R) (2012)

    Article  ADS  Google Scholar 

  13. 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  CAS  Google Scholar 

  14. 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  CAS  Google Scholar 

  15. Nisoli, C. et al. Effective temperature in an interacting vertex system: theory and experiment on artificial spin ice. Phys. Rev. Lett. 105, 047205 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. 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  CAS  Google Scholar 

  19. Morgan, J. et al. Real and effective thermal equilibrium in artificial square spin ices. Phys. Rev. B 87, 024405 (2013)

    Article  ADS  Google Scholar 

  20. Kapaklis, V. et al. Melting artificial spin ice. New J. Phys. 14, 035009 (2012)

    Article  ADS  Google Scholar 

  21. Budrikis, Z. et al. Domain dynamics and fluctuations in artificial square ice at finite temperatures. New J. Phys. 14, 035014 (2012)

    Article  ADS  Google Scholar 

  22. Silva, R. C. et al. Thermodynamics of elementary excitations in artificial magnetic square ice. New J. Phys. 14, 015008 (2012)

    Article  ADS  Google Scholar 

  23. John Greaves, S. & Muraoka, H. Formation of thermally induced ground states in two-dimensional square spin ices. J. Appl. Phys. 112, 043909 (2012)

    Article  ADS  Google Scholar 

  24. Newman, M. E. J. & Barkema, G. T. Monte Carlo Methods in Statistical Physics (Clarendon, 1999)

    MATH  Google Scholar 

  25. Rougemaille, N. et al. Artificial kagome arrays of nanomagnets: a frozen dipolar spin ice. Phys. Rev. Lett. 106, 057209 (2011)

    Article  ADS  CAS  Google Scholar 

  26. Lammert, P. E. et al. Direct entropy determination and application to artificial spin ice. Nature Phys. 6, 786–789 (2010)

    Article  ADS  CAS  Google Scholar 

  27. Morrison, M. J., Nelson, T. R. & Nisoli, C. Unhappy vertices in artificial spin ice: degeneracy from vertex-frustration. New J. Phys. 15, 045009 (2013)

    Article  ADS  Google Scholar 

  28. Chern, G.-W., Morrison, M. J. & Nisoli, C. Engineering degeneracy: a critical ground state for artificial spin ice. Preprint at http://arxiv.org/abs/1210.8377 (2012)

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

    Article  ADS  CAS  Google Scholar 

  30. Porro, J. M. et al. Exploring thermally induced states in square artificial spin-ice arrays. New J. Phys. 15, 055012 (2013)

    Article  ADS  Google Scholar 

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Acknowledgements

This project was funded by the US Department of Energy, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under grant no. DE-SC0005313. Lithography was performed with the support of the National Nanotechnology Infrastructure Network. The work of C.N. and G.-W.C. was carried out under the auspices of the US Department of Energy at LANL under contract no. DE-AC52-06NA253962. Work at the University of Minnesota was supported by the NSF MRSEC under award DMR-0819885 and EU Marie Curie IOF project no. 299376. Certain theory elements were supported by the NSF MRSEC under award DMR-0820404.

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Author notes

  1. Sheng Zhang and Ian Gilbert: These authors contributed equally to this work.

Authors and Affiliations

  1. Department of Physics and Materials Research Institute, Pennsylvania State University, University Park, 16802, Pennsylvania, USA

    Sheng Zhang, Paul E. Lammert & Vincent H. Crespi

  2. Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, 61801, Illinois, USA

    Ian Gilbert & Peter Schiffer

  3. Theoretical Division, MS B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA,

    Cristiano Nisoli & Gia-Wei Chern

  4. Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, 55455, Minnesota, USA

    Michael J. Erickson, Liam O’Brien & Chris Leighton

  5. Department of Physics, Thin Film Magnetism Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK,

    Liam O’Brien

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  1. Sheng Zhang
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Contributions

P.S., C.L. and V.H.C. initiated this study and supervised the experiments, data analysis and simulations. Artificial spin-ice array fabrication, measurement and data analysis was performed by S.Z. and I.G. Thin film deposition and characterization was performed by L.O’B. and M.J.E. The thermal annealing process was refined and performed by L.O’B., M.J.E. and C.L. Simulations, some data analysis and theoretical interpretation were provided by C.N., G.-W.C. and P.E.L. I.G., C.N. and P.S. wrote the paper with input from all the co-authors. S.Z. and I.G. contributed equally to this work.

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Correspondence to Peter Schiffer.

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Zhang, S., Gilbert, I., Nisoli, C. et al. Crystallites of magnetic charges in artificial spin ice. Nature 500, 553–557 (2013). https://doi.org/10.1038/nature12399

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