Relation between microscopic interactions and macroscopic properties in ferroics


The driving force in materials to spontaneously form states with magnetic or electric order is of fundamental importance for basic research and device technology. The macroscopic properties and functionalities of these ferroics depend on the size, distribution and morphology of domains; that is, of regions across which such uniform order is maintained1. Typically, extrinsic factors such as strain profiles, grain size or annealing procedures control the size and shape of the domains2,3,4,5, whereas intrinsic parameters are often difficult to extract due to the complexity of a processed material. Here, we achieve this separation by building artificial crystals of planar nanomagnets that are coupled by well-defined, tuneable and competing magnetic interactions6,7,8,9. Aside from analysing the domain configurations, we uncover fundamental intrinsic correlations between the microscopic interactions establishing magnetically compensated order and the macroscopic manifestations of these interactions in basic physical properties. Experiment and simulations reveal how competing interactions can be exploited to control ferroic hallmark properties such as the size and morphology of domains, topological properties of domain walls or their thermal mobility.

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Fig. 1: Model of a ferroic crystal with zero net magnetization and two competing microscopic interactions.
Fig. 2: Phase diagram revealing the correlation between short-range and long-range order.
Fig. 3: Correlation between short-range order and domain formation.
Fig. 4: Macroscopic physical properties determined by the microscopic interactions.

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The programme codes that support the figures and other findings of this study can be found here ( Additional data and information are available from the corresponding authors upon reasonable request.


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We thank T. Lottermoser, S. Vélez Centoral, A. Cano and T. Weber for discussions. M.F. acknowledges funding by the Swiss National Science Foundation (project no. 200021-175926). J.L. and M.F. acknowledge funding by the ETH Research grant no. ETH-28 14-1 ‘Resonant optical magnetoelectric effect in magnetic nanostructures’. A.B. and M.F. acknowledge funding by the European Research Council (advanced grant no. 694955–INSEETO). N.L. and L.J.H. acknowledge funding by the Swiss National Science Foundation (project no. 200021-155917).

Author information




All authors contributed to the discussion and interpretation of the study. J.L., A.B. and M.F. wrote the manuscript with input from all coauthors. C.D. and N.L. fabricated the nanomagnetic structures. J.L. performed magnetic force microscopy experiments. A.B. and P.M.D. performed the Monte Carlo simulations. M.F. and L.J.H. supervised the study.

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Correspondence to Jannis Lehmann or Amadé Bortis or Manfred Fiebig.

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Peer review information Nature Nanotechnology thanks Will Branford, Olena Gomonay and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Lehmann, J., Bortis, A., Derlet, P.M. et al. Relation between microscopic interactions and macroscopic properties in ferroics. Nat. Nanotechnol. (2020).

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