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Interaction modifiers in artificial spin ices


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.

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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.


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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.

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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.

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Correspondence to Erik Östman.

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Supplementary figures 1–16, Supplementary references 1–3

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Östman, E., Stopfel, H., Chioar, IA. et al. Interaction modifiers in artificial spin ices. Nature Phys 14, 375–379 (2018).

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