It is particularly evident in the example of ferromagnetism, which has been recognised and used by mankind for over 2500 years, that ferroic materials, i.e., materials that show spontaneous magnetic, electric or elastic order are invaluable for modern condensed-matter research and device applications. Most of the practical value of ferroics results from their characteristic to form domains that are regions with a different yet uniform orientation of a magnetisation, electric polarisation, etc. Their size and reverseability determine the feasibility of a ferroic material for digital data storage, as a sensor, for power generation, and much more. Often, extrinsic effects such as impurities, grains or mechanical strain determine the domain formation and, thus, macroscopic properties of a ferroic. The relation of those properties to the intrinsic microscopic interactions providing the fundamental frame within which a domain size and stability can vary in the first place, are largely unknown, however.

In our paper we describe the construction of a simple ferroic model system and reveal a correlation between the intrinsic microscopic interactions underlying the ferroic order and the formation and resilience of the corresponding domains. Key for accessing these correlations is our use of an artificial nanoscale model system that enables us to design a well-defined set of microscopic interactions and avoids any type of extrinsic perturbation. Our system is based on periodic arrangements of submicrometre-sized bars of a magnetic material in which interactions between parallel and perpendicular magnetic moments can be distinguished as the main coupling parameters, see the left side of the Figure above. The two coupling parameters can be tuned by varying these geometric parameters throughout a series of grown arrays. Domain- and domain-wall structures are studied by magnetic force microscopy and Monte Carlo simulations. We show how the domain size, morphology and stability are controlled across orders of magnitude by tuning the ratio of the two competing coupling parameters. Furthermore, we find that their interplay gives rise to the formation of topological magnetic defects within the domain walls.

The use of (magnetic) metamaterials to model complex ordered phases of matter provides a fascinating degree of freedom to access phenomena and relationships that are otherwise difficult to uncover. The relevance of this study is furthermore given by the current interest in novel types of ferroic states and domains, especially because ferroic order constitutes one of the core pillars of modern computing and memory schemes.

To the Article: https://doi.org/10.1038/s41565-020-0763-9

Text: Jannis Lehmann, Manfred Fiebig