001018431 001__ 1018431 001018431 005__ 20240403082800.0 001018431 0247_ $$2doi$$a10.1038/s41586-023-06658-5 001018431 0247_ $$2ISSN$$a0028-0836 001018431 0247_ $$2ISSN$$a1476-4687 001018431 0247_ $$2datacite_doi$$a10.34734/FZJ-2023-04806 001018431 0247_ $$2pmid$$a37993571 001018431 0247_ $$2WOS$$aWOS:001169158300012 001018431 037__ $$aFZJ-2023-04806 001018431 082__ $$a500 001018431 1001_ $$0P:(DE-Juel1)165965$$aZheng, Fengshan$$b0$$eCorresponding author$$ufzj 001018431 245__ $$aHopfion rings in a cubic chiral magnet 001018431 260__ $$aLondon [u.a.]$$bNature Publ. Group$$c2023 001018431 3367_ $$2DRIVER$$aarticle 001018431 3367_ $$2DataCite$$aOutput Types/Journal article 001018431 3367_ $$0PUB:(DE-HGF)16$$2PUB:(DE-HGF)$$aJournal Article$$bjournal$$mjournal$$s1700821254_5332 001018431 3367_ $$2BibTeX$$aARTICLE 001018431 3367_ $$2ORCID$$aJOURNAL_ARTICLE 001018431 3367_ $$00$$2EndNote$$aJournal Article 001018431 520__ $$aMagnetic skyrmions and hopfions are topological solitons1—well-localized field configurations that have gained considerable attention over the past decade owing to their unique particle-like properties, which make them promising objects for spintronic applications. Skyrmions2,3 are two-dimensional solitons resembling vortex-like string structures that can penetrate an entire sample. Hopfions4,5,6,7,8,9 are three-dimensional solitons confined within a magnetic sample volume and can be considered as closed twisted skyrmion strings that take the shape of a ring in the simplest case. Despite extensive research on magnetic skyrmions, the direct observation of magnetic hopfions is challenging10 and has only been reported in a synthetic material11. Here we present direct observations of hopfions in crystals. In our experiment, we use transmission electron microscopy to observe hopfions forming coupled states with skyrmion strings in B20-type FeGe plates. We provide a protocol for nucleating such hopfion rings, which we verify using Lorentz imaging and electron holography. Our results are highly reproducible and in full agreement with micromagnetic simulations. We provide a unified skyrmion–hopfion homotopy classification and offer insight into the diversity of topological solitons in three-dimensional chiral magnets. 001018431 536__ $$0G:(DE-HGF)POF4-5211$$a5211 - Topological Matter (POF4-521)$$cPOF4-521$$fPOF IV$$x0 001018431 536__ $$0G:(EU-Grant)856538$$a3D MAGiC - Three-dimensional magnetization textures: Discovery and control on the nanoscale (856538)$$c856538$$fERC-2019-SyG$$x1 001018431 536__ $$0G:(GEPRIS)403503315$$aDFG project 403503315 - Grenzflächenstabilisierte Skyrmionen in Oxidstrukturen für die Skyrmionik (403503315)$$c403503315$$x2 001018431 588__ $$aDataset connected to CrossRef, Journals: juser.fz-juelich.de 001018431 7001_ $$0P:(DE-Juel1)145390$$aKiselev, Nikolai S.$$b1$$eCorresponding author 001018431 7001_ $$0P:(DE-HGF)0$$aRybakov, Filipp N.$$b2$$eCorresponding author 001018431 7001_ $$0P:(DE-HGF)0$$aYang, Luyan$$b3 001018431 7001_ $$0P:(DE-Juel1)195974$$aShi, Wen$$b4$$ufzj 001018431 7001_ $$0P:(DE-Juel1)130548$$aBlügel, Stefan$$b5 001018431 7001_ $$0P:(DE-Juel1)144121$$aDunin-Borkowski, Rafal E.$$b6 001018431 773__ $$0PERI:(DE-600)1413423-8$$a10.1038/s41586-023-06658-5$$gVol. 623, no. 7988, p. 718 - 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