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Thermal ground-state ordering and elementary excitations in artificial magnetic square ice


Recent advances in nanotechnology allow model systems to be constructed, in which frustrated interactions can be tuned at will, such as artificial spin ice. The symmetry of the square ice lattice leads to the emergence of a long-range-ordered ground state from the manifold of frustrated states. However, it is experimentally very difficult to access using the effective thermodynamics of rotating-field demagnetization protocols, because the energy barriers to thermal equilibrium are extremely large. Here we study an as-fabricated sample that approaches the ground state very closely. We identify the small localized departures from the ground state as elementary excitations of the system, at frequencies that follow a Boltzmann law. We therefore identify the state we observe as the frozen-in residue of true thermodynamics that occurred during the fabrication of the sample. The relative proportions of different excitations are suggestive of monopole interactions during thermalization.

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Figure 1: Artificial square ice of single-domain nanobar magnets.
Figure 2: MFM images of a 400-nm-pitch as-grown square ice array.
Figure 3: Elementary excitations above the GS of square ice.
Figure 4: Statistics of square ice excitations.


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This work was supported financially by EPSRC and the STFC Centre for Materials Physics and Chemistry. The research was carried out in part at the Center for Functional Nanomaterials, Brookhaven National Laboratory, which is supported by the US Department of Energy, Office of Basic Energy Sciences, under Contract No. DE-AC02-98CH10886.

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J.P.M. and A.S. conducted sample fabrication. J.P.M conducted the MFM, data processing, calculations and analysis. C.H.M. and S.L. supervised the work, and contributed to discussion and direction. All authors discussed the results and commented on the manuscript.

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Correspondence to Christopher H. Marrows.

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The authors declare no competing financial interests.

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Morgan, J., Stein, A., Langridge, S. et al. Thermal ground-state ordering and elementary excitations in artificial magnetic square ice. Nature Phys 7, 75–79 (2011).

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