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Poling of an artificial magneto-toroidal crystal


Although ferromagnetism is known to be of enormous importance, the exploitation of materials with a compensated (for example, antiferromagnetic) arrangement of long-range ordered magnetic moments is still in its infancy. Antiferromagnetism is more robust against external perturbations, exhibits ultrafast responses of the spin system1 and is key to phenomena such as exchange bias2,3, magnetically induced ferroelectricity4 or certain magnetoresistance phenomena5. However, there is no conjugate field for the manipulation of antiferromagnetic order, hindering both its observation and direct manipulation. Only recently, direct poling of a particular antiferromagnet was achieved with spintronic approaches6. An interesting alternative to antiferromagnetism is ferrotoroidicity—a recently established fourth form of ferroic order7,8. This is defined as a vortex-like magnetic state with zero net magnetization, yet with a spontaneously occurring toroidal moment9. As a hallmark of ferroic order, there must be a conjugate field that can manipulate the order parameter. For ferrotoroidic materials, this is a toroidal field—a magnetic vortex field violating both space-inversion and time-reversal symmetry analogous to the toroidal moment10. However, the nature and generation of the toroidal field remain elusive for conventional crystalline systems. Here, we demonstrate the creation of an artificial crystal11,12 consisting of mesoscopic planar nanomagnets with a magneto-toroidal-ordered ground state. Effective toroidal fields of either sign are applied by scanning a magnetic tip over the crystal. Thus, we achieve local control over the orientation of the toroidal moment despite its zero net magnetization.

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Fig. 1: Artificial magneto-toroidal crystal.
Fig. 2: Magnetization curve and ferrotoroidic ground state.
Fig. 3: Generation of a toroidal poling field at the mesoscale.
Fig. 4: Experimental demonstration of magneto-toroidal poling.

Data availability

The data that support the figures within this paper and other findings of this study are available from the corresponding authors upon reasonable request.


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We thank S. Gliga for initial discussions. This work was funded by an ETH Research Grant (grant number ETH-28 14-1 ‘Resonant optical magnetoelectric effect in magnetic nanostructures’ (to J.L. and M.F.)).

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Authors and Affiliations



All authors contributed to the discussion and interpretation of the experiment. J.L., C.D. and M.F. wrote the manuscript with input from all co-authors. C.D. fabricated the nanomagnetic structures. J.L. performed the LMOKE and MFM experiments and micromagnetic calculations. P.M.D. and J.L. developed the theoretical description. M.F. and L.J.H. supervised the study.

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Correspondence to Jannis Lehmann or Manfred Fiebig.

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Lehmann, J., Donnelly, C., Derlet, P.M. et al. Poling of an artificial magneto-toroidal crystal. Nature Nanotech 14, 141–144 (2019).

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