Frustration and thermalization in an artificial magnetic quasicrystal


Artificial frustrated systems offer a playground to study the emergent properties of interacting systems. Most work to date has been on spatially periodic systems, known as artificial spin ices when the interacting elements are magnetic. Here we have studied artificial magnetic quasicrystals based on quasiperiodic Penrose tiling patterns of interacting nanomagnets. We construct a low-energy configuration from a step-by-step approach that we propose as a ground state. Topologically induced emergent frustration means that this configuration cannot be constructed from vertices in their ground states. It has two parts, a quasi-one-dimensional ‘skeleton’ that spans the entire pattern and is capable of long-range order, surrounding ‘flippable’ clusters of macrospins that lead to macroscopic degeneracy. Magnetic force microscopy imaging of Penrose tiling arrays revealed superdomains that are larger for more strongly coupled arrays, especially after annealing the array above its blocking temperature.

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Fig. 1: Penrose tiling pattern and the seven types of vertex found within it.
Fig. 2: The lowest energy configuration of each vertex and a low-energy state of the entire pattern.
Fig. 3: Ordered regions in the skeleton of an artificial magnetic quasicrystal.
Fig. 4: Populations of the energy levels of the seven vertex types.
Fig. 5: The blocking temperature and micromagnetic simulation results of the energy population distribution for type VII vertices.


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This research used resources of the Center for Functional Nanomaterials, which is a US DOE Office of Science Facility, at Brookhaven National Laboratory under Contract No. DE-SC0012704, and was also supported by the EPSRC (grant EP/L00285X/1). Z.B. was supported by the ERC Advanced Grant no. 291002 SIZEFFECTS.

Author information




C.H.M. conceived the project. A.S. fabricated the samples, using Penrose array designs made by G.B. and D.S. D.S. performed the MFM imaging and the a.c.-demagnetization and thermal annealling protocols, analysed the data (using software co-designed with G.B.) and theoretically derived the expected ground state. Z.B. performed the Monte Carlo simulations in consultation with D.S. S.A.M. performed the SQUID magnetometry measurements. C.H.M., G.B. and P.D.O. supervised the work. All authors discussed the data and commented on the manuscript.

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Correspondence to Christopher H. Marrows.

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Supplementary notes 1-7, Supplementary Figures 1-14, and Supplementary References 1-15

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Shi, D., Budrikis, Z., Stein, A. et al. Frustration and thermalization in an artificial magnetic quasicrystal. Nature Phys 14, 309–314 (2018).

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