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Emergent ice rule and magnetic charge screening from vertex frustration in artificial spin ice


Artificial spin ice comprises a class of frustrated arrays of interacting single-domain ferromagnetic nanostructures. Previous studies of artificial spin ice have focused on simple lattices based on natural frustrated materials. Here we experimentally examine artificial spin ice created on the shakti lattice, a structure that does not directly correspond to any known natural magnetic material. On the shakti lattice, none of the near-neighbour interactions is locally frustrated, but instead the lattice topology frustrates the interactions leading to a high degree of degeneracy. We demonstrate that the shakti system achieves a physical realization of the classic six-vertex model ground state. Furthermore, we observe that the mixed coordination of the shakti lattice leads to crystallization of effective magnetic charges and the screening of magnetic excitations, underscoring the importance of magnetic charge as the relevant degree of freedom in artificial spin ice and opening new possibilities for studies of its dynamics.

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Figure 1: Sketches of several different artificial spin-ice lattices.
Figure 2: Experimental realization of the shakti lattice.
Figure 3: Mapping the shakti lattice to the six-vertex model.
Figure 4: Vertex population fractions for the shakti lattice.
Figure 5: Charge ordering in the shakti lattices.
Figure 6: Evidence of magnetic charge screening in the long-island shakti lattice.


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This project was funded by the US Department of Energy, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under Grant No. DE-SC0010778. Lithography was performed in part with the support of the National Nanotechnology Infrastructure Network. The work of G-W.C. and C.N. was carried out under the auspices of the US Department of Energy at LANL under contract no. DE-AC52-06NA253962. Work performed at the University of Minnesota was supported by EU Marie Curie IOF project no. 299376.

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C.N. and P.S. designed this study and supervised the experiments, simulations and data analysis. Artificial spin-ice samples were fabricated by I.G. and S.Z. Thin-film deposition and thermal annealing was done by L.O’B. Magnetic force microscopy and data analysis was performed by I.G. with assistance from B.F. Simulations and theoretical interpretation was given by G-W.C. and C.N. The paper was written by I.G., G-W.C., C.N. and P.S. with input from all of the co-authors.

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Correspondence to Peter Schiffer.

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The authors declare no competing financial interests.

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

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