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Skyrmions and hopfions in chiral magnetic crystals

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DNMW06 - Recent challenges in the mathematical design of new materials

Recent theoretical and experimental studies of chiral crystals have revealed a wide variety of new three-dimensional magnetic textures with non-trivial topology: skyrmion strings [1], their clusters, bundles and braids [2], as well as hopfions [3]. We discuss how these discoveries were made possible by combining micromagnetic simulations with Lorentz transmission electron microscopy or off-axis holography. We also pay special attention to the topology of these textures and new ways to classify them using homotopy groups [3,4]. [1] F.N. Rybakov, et al. PRL 115 , 117201 (2015). [2] F. Zheng, et al. Nat. Commun. 12, 5316 (2021). [3] F. Zheng, et al. Nature 623, 718 (2023). [4] F.N. Rybakov, et al. PRB 111 , 134417 (2025).

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