Abstract
One of the two key requirements of n-dimensional ferroic systems is the spontaneous formation of homogeneously ordered areas, called domains, separated one from another by distinct (\(n-1\))-dimensional entities, called domain walls, see Sect. 2.1.4 on page 16. These walls constitute natural interfaces within the system between two or more energetically degenerate realisations of a particular order. For the artificial nanomagnetic arrays investigated throughout this work, the spontaneous formation of long-range order connected to an order parameter is a hallmark for their classification as primary ferroic order [1]. Suitable symmetry groups allowing for toroidal order have already been identified a few decades ago and are listed in Sect. 2.1.6 on page 19. The nanomagnetic arrays that have been investigated here, see Fig. 4.1 on page 83, fall in one of these groups, setting the basis for their further scrutiny not only on the macroscopic but also on the microscopic scale.
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Notes
- 1.
Defects that are located close to the edges of some arrays prevented a comparative analysis of whole arrays.
- 2.
Remember that this asymmetric exchange interaction necessitates a non-centrosymmetric material, whereas the particular symmetry violation predetermines the sign of this energy spitting.
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Lehmann, J. (2022). Domains in Artificial Magneto-Toroidal Crystals. In: Toroidal Order in Magnetic Metamaterials. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-85495-9_5
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