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Switchable geometric frustration in an artificial-spin-ice–superconductor heterosystem


Geometric frustration emerges when local interaction energies in an ordered lattice structure cannot be simultaneously minimized, resulting in a large number of degenerate states. The numerous degenerate configurations may lead to practical applications in microelectronics1, such as data storage, memory and logic2. However, it is difficult to achieve very high degeneracy, especially in a two-dimensional system3,4. Here, we showcase in situ controllable geometric frustration with high degeneracy in a two-dimensional flux-quantum system. We create this in a superconducting thin film placed underneath a reconfigurable artificial-spin-ice structure5. The tunable magnetic charges in the artificial-spin-ice strongly interact with the flux quanta in the superconductor, enabling switching between frustrated and crystallized flux quanta states. The different states have measurable effects on the superconducting critical current profile, which can be reconfigured by precise selection of the spin-ice magnetic state through the application of an external magnetic field. We demonstrate the applicability of these effects by realizing a reprogrammable flux quanta diode. The tailoring of the energy landscape of interacting ‘particles’ using artificial-spin-ices provides a new paradigm for the design of geometric frustration, which could illuminate a path to control new functionalities in other material systems, such as magnetic skyrmions6, electrons and holes in two-dimensional materials7,8, and topological insulators9, as well as colloids in soft materials10,11,12,13.

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Fig. 1: Reconfigurable potential landscapes and flux-quantum motion controlled by ASI.
Fig. 2: Switchable geometric frustration and crystallization.
Fig. 3: Geometrically frustrated local interactions and breakdown of long-range order.
Fig. 4: Reprogrammable flux-quantum rectifier.


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This work was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. Use of the Center for Nanoscale Materials, an Office of Science user facility, was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract number DE-AC02-06CH11357. Z.-L.X. and J.X. acknowledge National Science Foundation grant DMR-1407175.

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Authors and Affiliations



Y.-L.W., Z.-L.X., B.J. and W.-K.K. conceived and supervised the project. Y.-L.W., J.X., Z.-L.X. and W.-K.K. designed the experiments. X.M. and B.J. designed the simulations. Y.-L.W., J.X., R.D., L.E.O. and J.E.P. fabricated samples. Y.-L.W., J.X. and A.S. conducted the measurements. X.M. conducted the simulations. Y.-L.W., X.M. and J.X., analysed the data. Y.-L.W., X.M., J.X., Z.-L.X., B.J. and W.-K.K. co-wrote the manuscript. All authors contributed to the discussion of the data and commented on the manuscript.

Corresponding authors

Correspondence to Yong-Lei Wang, Zhi-Li Xiao or Boldizsar Janko.

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Supplementary information

Supplementary Information

Supplementary Figures 1–10, Supplementary Video Captions

Supplementary Video 1

d.c. transport property under type-II MC configuration at B/BΦ = 1.5

Supplementary Video 2

d.c. transport property under type-II MC configuration at B/BΦ = 0.5

Supplementary Video 3

d.c. transport property under type-II MC configuration at B/BΦ = 1.0

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Wang, YL., Ma, X., Xu, J. et al. Switchable geometric frustration in an artificial-spin-ice–superconductor heterosystem. Nature Nanotech 13, 560–565 (2018).

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