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Classical topological order in the kinetics of artificial spin ice


Systems of interacting nanomagnets known as artificial spin ice1,2,3,4 have allowed the design, realization and study of geometrically frustrated exotic collective states5,6,7,8,9,10 that are absent in natural magnets. We have experimentally measured11,12 the thermally induced moment fluctuations in the Shakti geometry of artificial spin ice. We show that its disordered moment configuration is a topological phase described by an emergent dimer-cover model13 with excitations that can be characterized as topologically charged defects. Examination of the low-energy dynamics of the system confirms that these effective topological charges have long lifetimes associated with their topological protection, that is, they can be created and annihilated only as charge pairs with opposite sign and are kinetically constrained. This manifestation of classical topological order14,15,16,17,18,19 demonstrates that geometrical design in nanomagnetic systems can lead to emergent, topologically protected kinetics that can limit pathways to equilibration and ergodicity.

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Fig. 1: The Shakti lattice.
Fig. 2: Excitations above the ground state.
Fig. 3: The dimer model.
Fig. 4: Stability of topological charges.


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The work of Y.L., J.S., D.G. and P.S. was funded by the US Department of Energy, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under grant no. DE-SC0010778. The work of C.N. and F.C. was carried out under the auspices of the NNSA of the US DOE at LANL under contract no. DE-AC52-06NA25396. C.N. wishes to thank the LDRD office for support and C. Castelnovo (University of Cambridge) for very useful discussions. The work of M.S. and K.D. was supported by the NSF through grant CBET 1336634. The work of A.M.A. and J.D.W. was supported by the NSF through grant DMR-1507048. This research used resources of the Advanced Light Source, which is a DOE Office of Science User Facility under contract no. DE-AC02-05CH11231.

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Y.L. and J.S. prepared the lithographic patterns and performed the PEEM experiments with A.S. J.D.W. and A.M.A. prepared the permalloy deposition for the samples. Y.L. and D.G. digitalized the experimental images, analysed the data and rendered the data graphically. F.C. performed the numerical analysis and contributed to the theoretical interpretation. M.S. and K.D. assisted in data analysis. C.N. developed the topological framework for interpretation of the data. P.S. supervised the experimental work and coordinated the entire project.

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Correspondence to Peter Schiffer.

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Lao, Y., Caravelli, F., Sheikh, M. et al. Classical topological order in the kinetics of artificial spin ice. Nature Phys 14, 723–727 (2018).

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