{"quality_controlled":"1","volume":34,"date_published":"2024-01-23T00:00:00Z","scopus_import":"1","article_processing_charge":"No","title":"Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions","citation":{"short":"E. Davoli, L. D’Elia, J. Ingmanns, Journal of Nonlinear Science 34 (2024).","chicago":"Davoli, Elisa, Lorenza D’Elia, and Jonas Ingmanns. “Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” <i>Journal of Nonlinear Science</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00332-023-10005-3\">https://doi.org/10.1007/s00332-023-10005-3</a>.","apa":"Davoli, E., D’Elia, L., &#38; Ingmanns, J. (2024). Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. <i>Journal of Nonlinear Science</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00332-023-10005-3\">https://doi.org/10.1007/s00332-023-10005-3</a>","ama":"Davoli E, D’Elia L, Ingmanns J. Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. <i>Journal of Nonlinear Science</i>. 2024;34(2). doi:<a href=\"https://doi.org/10.1007/s00332-023-10005-3\">10.1007/s00332-023-10005-3</a>","ieee":"E. Davoli, L. D’Elia, and J. Ingmanns, “Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions,” <i>Journal of Nonlinear Science</i>, vol. 34, no. 2. Springer Nature, 2024.","ista":"Davoli E, D’Elia L, Ingmanns J. 2024. Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. 34(2), 30.","mla":"Davoli, Elisa, et al. “Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” <i>Journal of Nonlinear Science</i>, vol. 34, no. 2, 30, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00332-023-10005-3\">10.1007/s00332-023-10005-3</a>."},"intvolume":"        34","publication_identifier":{"eissn":["1432-1467"],"issn":["0938-8974"]},"article_number":"30","language":[{"iso":"eng"}],"day":"23","author":[{"full_name":"Davoli, Elisa","first_name":"Elisa","last_name":"Davoli"},{"full_name":"D’Elia, Lorenza","first_name":"Lorenza","last_name":"D’Elia"},{"full_name":"Ingmanns, Jonas","id":"71523d30-15b2-11ec-abd3-f80aa909d6b0","first_name":"Jonas","last_name":"Ingmanns"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2306.05151","open_access":"1"}],"abstract":[{"lang":"eng","text":"We perform a stochastic homogenization analysis for composite materials exhibiting a random microstructure. Under the assumptions of stationarity and ergodicity, we characterize the Gamma-limit of a micromagnetic energy functional defined on magnetizations taking value in the unit sphere and including both symmetric and antisymmetric exchange contributions. This Gamma-limit corresponds to a micromagnetic energy functional with homogeneous coefficients. We provide explicit formulas for the effective magnetic properties of the composite material in terms of homogenization correctors. Additionally, the variational analysis of the two exchange energy terms is performed in the more general setting of functionals defined on manifold-valued maps with Sobolev regularity, in the case in which the target manifold is a bounded, orientable smooth surface with tubular neighborhood of uniform thickness. Eventually, we present an explicit characterization of minimizers of the effective exchange in the case of magnetic multilayers, providing quantitative evidence of Dzyaloshinskii’s predictions on the emergence of helical structures in composite ferromagnetic materials with stochastic microstructure."}],"oa":1,"year":"2024","status":"public","article_type":"original","_id":"14884","acknowledgement":"All authors acknowledge support of the Austrian Science Fund (FWF) through the SFB project F65. The research of E. Davoli and L. D’Elia has additionally been supported by the FWF through grants V662, Y1292, and P35359, as well as from OeAD through the WTZ grant CZ09/2023.","department":[{"_id":"JuFi"}],"doi":"10.1007/s00332-023-10005-3","oa_version":"Preprint","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2024-02-05T08:54:44Z","type":"journal_article","publication":"Journal of Nonlinear Science","issue":"2","month":"01","date_created":"2024-01-28T23:01:42Z","publication_status":"epub_ahead","publisher":"Springer Nature","external_id":{"arxiv":["2306.05151"]}}