A tunable magnetic metamaterial based on the dipolar four-state Potts model


Metamaterials, tunable artificial materials, are useful playgrounds to investigate magnetic systems. So far, artificial Ising spin systems have revealed features such as emergent magnetic monopoles1,2 and charge fragmentation3. Here we present a metasystem composed of a lattice of dipolarly coupled nanomagnets. The magnetic spin of each nanomagnet is constrained to lie along a body diagonal, which yields four possible spin states. We show that the magnetic ordering of this metasystem (antiferromagnetic, ferromagnetic or spin ice like) is determined by the spin states orientation relative to the underlying lattice. The dipolar four-state Potts model explains our experimental observations and sheds light on the role of symmetry, as well as short- and long-range dipolar magnetic interactions, in such non-Ising spin systems.

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Fig. 1: Four-state Potts model based on an artificial spin system.
Fig. 2: Distribution of different magnetic orders in an artificial four-state Potts model.
Fig. 3: Modelling of the dependence of spin configurations on angle between spins and underlying lattice α.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.


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The authors thank N. Rougemaille and B. Canals for fruitful discussions. This work was supported by the Agence Nationale de la Recherche through project number ANR12-BS04-009 ‘Frustrated’ and partially supported by the French PIA project ‘Lorraine Université d’Excellence’ ANR15-IDEX-04-LUE.

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D.Louis, T.H., M.H. and F.M. prepared the samples. MFM measurements were carried out by D.Louis, D.Lacour and M.H., and D.Louis, D.Lacour and F.M. analysed the data. D.Louis, F.M. and V.L. carried out theory and simulations. All authors discussed the results and implications at all stages and prepared the manuscript.

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Correspondence to F. Montaigne.

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Louis, D., Lacour, D., Hehn, M. et al. A tunable magnetic metamaterial based on the dipolar four-state Potts model. Nature Mater 17, 1076–1080 (2018). https://doi.org/10.1038/s41563-018-0199-x

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