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Thermal fluctuations in artificial spin ice

Nature Nanotechnology volume 9, pages 514–519 (2014)Cite this article

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Abstract

Artificial spin ice systems have been proposed as a playground for the study of monopole-like magnetic excitations1,2, similar to those observed in pyrochlore spin ice materials3. Currents of magnetic monopole excitations have been observed4, demonstrating the possibility for the realization of magnetic-charge-based circuitry. Artificial spin ice systems that support thermal fluctuations can serve as an ideal setting for observing dynamical effects such as monopole propagation and as a potential medium for magnetricity investigations1,2. Here, we report on the transition from a frozen to a dynamic state in artificial spin ice with a square lattice. Magnetic imaging is used to determine the magnetic state of the islands in thermal equilibrium. The temperature-induced onset of magnetic fluctuations and excitation populations are shown to depend on the lattice spacing and related interaction strength between islands. The excitations are described by Boltzmann distributions with their factors in the frozen state relating to the blocking temperatures of the array. Our results provide insight into the design of thermal artificial spin ice arrays where the magnetic charge density and response to external fields can be studied in thermal equilibrium.

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Figure 1: Geometry and magnetic imaging.
Figure 2: Determination of vertex states from magnetic imaging.
Figure 3: Effect of inter-island interactions on the onset of vertex state fluctuations.
Figure 4: Temperature dependence of magnetic fluctuations.
Figure 5: Thermal distributions, fluctuations and energy statistics of vertex states.

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Acknowledgements

The authors acknowledge support from the Knut and Alice Wallenberg Foundation, the Swedish Research Council, the Swedish Foundation for International Cooperation in Research and Higher Education and the Swiss National Science Foundation. The Advanced Light Source (ALS) is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy (contract no. DE-AC02-05CH11231). The authors thank A. Young of the ALS for support during the PEEM experiments and A. Weber for development of the patterning processes and sample manufacture. The authors are also grateful to V. Guzenko for support with electron-beam lithography. V.K. would like to thank P.E. Jönsson for discussions.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120, Uppsala, Sweden

    Vassilios Kapaklis, Unnar B. Arnalds & Björgvin Hjörvarsson

  2. Laboratory for Micro- and Nanotechnology, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland

    Alan Farhan, Rajesh V. Chopdekar & Laura J. Heyderman

  3. Department of Materials, Laboratory for Mesoscopic Systems, ETH Zurich, CH-8093 Zurich, Switzerland

    Alan Farhan & Laura J. Heyderman

  4. Swiss Light Source, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland

    Rajesh V. Chopdekar & Ana Balan

  5. Lawrence Berkeley National Laboratory (LBNL), 1 Cyclotron Road, Berkeley, 94720, California, USA

    Andreas Scholl

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Contributions

B.H. and L.J.H. initiated the work. V.K., U.B.A., A.F., R.V.C., A.B. and A.S. performed the PEEM-XMCD imaging. V.K. and U.B.A. analysed the data. V.K., U.B.A. and B.H. wrote the paper. All authors discussed the results and commented on the manuscript.

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Correspondence to Vassilios Kapaklis.

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The authors declare no competing financial interests.

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Kapaklis, V., Arnalds, U., Farhan, A. et al. Thermal fluctuations in artificial spin ice. Nature Nanotech 9, 514–519 (2014). https://doi.org/10.1038/nnano.2014.104

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