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The homogeneous energy functional resulting from our analysis provides an effective description of most of the magnetic composites of interest nowadays. Although our study covers more general scenarios than the micromagnetic one, it builds on the phenomenological considerations of Dzyaloshinskii on the existence of helicoidal textures, as a result of possible instabilities of ferromagnetic structures under small relativistic spin\u2013lattice or spin\u2013spin interactions. In particular, we provide the first quantitative counterpart to Dzyaloshinskii\u2019s predictions on helical structures.<\/jats:p>","DOI":"10.1007\/s00332-019-09606-8","type":"journal-article","created":{"date-parts":[[2020,1,8]],"date-time":"2020-01-08T07:02:51Z","timestamp":1578466971000},"page":"1229-1262","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Homogenization of Chiral Magnetic Materials: A Mathematical Evidence of Dzyaloshinskii\u2019s Predictions on Helical Structures"],"prefix":"10.1007","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1715-5004","authenticated-orcid":false,"given":"E.","family":"Davoli","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G.","family":"Di Fratta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,1,8]]},"reference":[{"key":"9606_CR1","doi-asserted-by":"publisher","first-page":"2225","DOI":"10.1098\/rspa.2006.1655","volume":"462","author":"E Acerbi","year":"2006","unstructured":"Acerbi, E., Fonseca, I., Mingione, G.: Existence and regularity for mixtures of micromagnetic materials. 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