{"title":"Renormalised energy between boundary vortices in thin-film micromagnetics with Dzyaloshinskii-Moriya interaction","authors":"","doi":"10.1016/j.na.2024.113622","DOIUrl":null,"url":null,"abstract":"<div><p>We consider a three-dimensional micromagnetic model with Dzyaloshinskii-Moriya interaction in a thin-film regime for boundary vortices. In this regime, we prove a dimension reduction result: the nonlocal three-dimensional model reduces to a local two-dimensional Ginzburg–Landau type model in terms of the averaged magnetisation in the thickness of the film. This reduced model captures the interaction between boundary vortices (so-called renormalised energy), that we determine by a <span><math><mi>Γ</mi></math></span>-convergence result at the second order and then we analyse its minimisers. They nucleate two boundary vortices whose position depends on the Dzyaloshinskii-Moriya interaction.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0362546X2400141X/pdfft?md5=909aaa9112d6eb58c619099b93d70d70&pid=1-s2.0-S0362546X2400141X-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Theory Methods & Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0362546X2400141X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a three-dimensional micromagnetic model with Dzyaloshinskii-Moriya interaction in a thin-film regime for boundary vortices. In this regime, we prove a dimension reduction result: the nonlocal three-dimensional model reduces to a local two-dimensional Ginzburg–Landau type model in terms of the averaged magnetisation in the thickness of the film. This reduced model captures the interaction between boundary vortices (so-called renormalised energy), that we determine by a -convergence result at the second order and then we analyse its minimisers. They nucleate two boundary vortices whose position depends on the Dzyaloshinskii-Moriya interaction.
期刊介绍:
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