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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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.
The authors declare no competing interests.
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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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