Interaction modifiers in artificial spin ices

Abstract

The modification of geometry and interactions in two-dimensional magnetic nanosystems has enabled a range of studies addressing the magnetic order1,2,3,4,5,6, collective low-energy dynamics7,8 and emergent magnetic properties5, 9,10 in, for example, artificial spin-ice structures. The common denominator of all these investigations is the use of Ising-like mesospins as building blocks, in the form of elongated magnetic islands. Here, we introduce a new approach: single interaction modifiers, using slave mesospins in the form of discs, within which the mesospin is free to rotate in the disc plane11. We show that by placing these on the vertices of square artificial spin-ice arrays and varying their diameter, it is possible to tailor the strength and the ratio of the interaction energies. We demonstrate the existence of degenerate ice-rule-obeying states in square artificial spin-ice structures, enabling the exploration of thermal dynamics in a spin-liquid manifold. Furthermore, we even observe the emergence of flux lattices on larger length scales, when the energy landscape of the vertices is reversed. The work highlights the potential of a design strategy for two-dimensional magnetic nano-architectures, through which mixed dimensionality of mesospins can be used to promote thermally emergent mesoscale magnetic states.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Schematics of the SASI and mSASI lattices shown together with their vertex types.
Fig. 2: Real-space magnetic imaging and vertex populations.
Fig. 3: Magnetic spin structure factor and autocorrelation.
Fig. 4: Emergent flux lattice ordering.

References

  1. 1.

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

    ADS  Article  Google Scholar 

  2. 2.

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

    Article  Google Scholar 

  3. 3.

    Morgan, J. P., Stein, A., Langridge, S. & Marrows, C. H. Thermal ground-state ordering and elementary excitations in artificial magnetic square ice. Nat. Phys. 7, 75–79 (2011).

    Article  Google Scholar 

  4. 4.

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

    ADS  Article  Google Scholar 

  5. 5.

    Gilbert, I. et al. Emergent ice rule and magnetic charge screening from vertex frustration in artificial spin ice. Nat. Phys. 10, 670–675 (2014).

    Article  Google Scholar 

  6. 6.

    Gilbert, I. et al. Emergent reduced dimensionality by vertex frustration in artificial spin ice. Nat. Phys. 12, 162–165 (2016).

    Article  Google Scholar 

  7. 7.

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

    Article  Google Scholar 

  8. 8.

    Kapaklis, V. et al. Thermal fluctuations in artificial spin ice. Nat. Nanotech 9, 1–6 (2014).

    Article  Google Scholar 

  9. 9.

    Perrin, Y., Canals, B. & Rougemaille, N. Extensive degeneracy, Coulomb phase and magnetic monopoles in an artificial realization of the square ice model. Nature 540, 410–413 (2016).

    ADS  Article  Google Scholar 

  10. 10.

    Canals, B. et al. Fragmentation of magnetism in artificial kagome dipolar spin ice. Nat. Commun. 7, 11446 (2016).

    ADS  Article  Google Scholar 

  11. 11.

    Arnalds, U. B. et al. Thermal transitions in nano-patterned XY-magnets. Appl. Phys. Lett. 105, 042409 (2014).

    ADS  Article  Google Scholar 

  12. 12.

    Arnalds, U. B. et al. Thermalized ground state of artificial kagome spin ice building blocks. Appl. Phys. Lett. 101, 112404 (2012).

    ADS  Article  Google Scholar 

  13. 13.

    Andersson, M. S. et al. Thermally induced magnetic relaxation in square artificial spin ice. Sci. Rep. 6, 37097 (2016).

    ADS  Article  Google Scholar 

  14. 14.

    Morley, S. A. et al. Vogel-Fulcher-Tammann freezing of a thermally fluctuating artificial spin ice probed by x-ray photon correlation spectroscopy. Phys. Rev. B 95, 104422 (2017).

    ADS  Article  Google Scholar 

  15. 15.

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

    ADS  Article  Google Scholar 

  16. 16.

    Lieb, E. H. Residual entropy of square ice. Phys. Rev. 162, 162–172 (1967).

    ADS  Article  Google Scholar 

  17. 17.

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

    ADS  Article  Google Scholar 

  18. 18.

    Chern, G. W., Reichhardt, C. & Nisoli, C. Realizing three-dimensional artificial spin ice by stacking planar nano-arrays. Appl. Phys. Lett. 104, 013101 (2014).

    ADS  Article  Google Scholar 

  19. 19.

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

    Article  Google Scholar 

  20. 20.

    Henley, C. L. Power-law spin correlations in pyrochlore antiferromagnets. Phys. Rev. B 71, 014424 (2005).

    ADS  Article  Google Scholar 

  21. 21.

    Henley, C. L. The “Coulomb phase” in frustrated systems. Annu. Rev. Condens. Matter Phys. 1, 179–210 (2010).

    ADS  Article  Google Scholar 

  22. 22.

    Fennell, T., Bramwell, S. T., McMorrow, D. F., Manuel, P. & Wildes, A. R. Pinch points and Kasteleyn transitions in kagome ice. Nat. Phys. 3, 566–572 (2007).

    Article  Google Scholar 

  23. 23.

    Bramwell, S. T. in Introduction to Frustrated Magnetism (eds Lacroix, C., Mendels, P. & Mila, F.) (Springer, Berlin, Heidelberg, 2011).

  24. 24.

    Nisoli, C. Nano-ising. New J. Phys. 18, 021007 (2016).

    Article  Google Scholar 

  25. 25.

    Edwards, S. F. & Anderson, P. W. Theory of spin glasses. J. Phys. F. 5, 965–974 (1975).

    ADS  Article  Google Scholar 

  26. 26.

    Zhou, D., Wang, F., Li, B., Lou, X. & Han, Y. Glassy spin dynamics in geometrically frustrated buckled colloidalcrystals. Phys. Rev. X 7, 021030 (2017).

    Google Scholar 

  27. 27.

    Perrin, Y. Artificial Frustrated Arrays. PhD thesis, Univ. Grenoble Alpes (2016).

  28. 28.

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

    ADS  Article  Google Scholar 

  29. 29.

    Morgan, J. P. et al. Magnetic hysteresis of an artificial square ice studied by in-plane Bragg x-ray resonant magnetic scattering. AIP Adv. 2, 022163 (2012).

    ADS  Article  Google Scholar 

  30. 30.

    Sendetskyi, O. et al. Magnetic diffuse scattering in artificial kagome spin ice. Phys. Rev. B 93, 224413 (2016).

    ADS  Article  Google Scholar 

  31. 31.

    Nisoli, C., Kapaklis, V. & Schiffer, P. Deliberate exotic magnetism via frustration and topology. Nat. Phys. 13, 200–203 (2017).

    Article  Google Scholar 

  32. 32.

    Papaioannou, E. T., Kapaklis, V., Taroni, A., Marcellini, M. & Hjörvarsson, B. Dimensionality and confinement effects in δ-doped Pd(Fe) layers. J. Phys. Condens. Matter 22, 236004 (2010).

    ADS  Article  Google Scholar 

  33. 33.

    Vansteenkiste, A., Leliaert, J., Dvornik, M., Garcia-Sanchez, F. & Van Waeyenberge, B. The design and verification of Mumax3. AIP Adv. 4, 107133 (2014).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank S. T. Bramwell and P. C. W. Holdsworth for valuable discussions. The authors acknowledge support from the Knut and Alice Wallenberg Foundation project 'Harnessing light and spins through plasmons at the nanoscale' (2015.0060), the Swedish Research Council and the Swedish Foundation for International Cooperation in Research and Higher Education. The patterning was performed at the Center for Functional Nanomaterials, Brookhaven National Laboratory, supported by the US Department of Energy, Office of Basic Energy Sciences, under contract no. DE-SC0012704. This research used resources of the Advanced Light Source, which is a DOE Office of Science User Facility under contract no. DE-AC02-05CH11231. This work is part of a project which has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 737093. U.B.A. acknowledges funding from the Icelandic Research Fund grant nos 141518 and 152483.

Author information

Affiliations

Authors

Contributions

H.S. and A.S. fabricated the sample. E.Ö., H.S., U.B.A. and V.K. performed the PEEM–XMCD experiments. E.Ö., I.-A.C., H.S., V.K. and B.H. analysed the data and contributed to theory development. E.Ö., I.-A.C. V.K. and B.H. wrote the manuscript. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Erik Östman.

Ethics declarations

Competing financial interests

The authors declare no competing financial interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary figures 1–16, Supplementary references 1–3

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Östman, E., Stopfel, H., Chioar, I. et al. Interaction modifiers in artificial spin ices. Nature Phys 14, 375–379 (2018). https://doi.org/10.1038/s41567-017-0027-2

Download citation

Further reading