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We elucidate that a staggered alignment of the magnetic toroidal dipole can give rise to spontaneous magnetization even under antiferromagnetic structures. We demonstrate the emergence of uniform magnetization by considering the collinear antiferromagnetic structure with the staggered magnetic toroidal dipole moment on a bilayer zigzag chain. Based on the model calculations, we show that the interplay between the collinear antiferromagnetic mean field and relativistic spin-orbit coupling plays an important role in inducing the magnetization.<\/jats:p>","DOI":"10.3390\/nano14211729","type":"journal-article","created":{"date-parts":[[2024,10,29]],"date-time":"2024-10-29T06:29:57Z","timestamp":1730183397000},"page":"1729","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Spontaneous Magnetization Induced by Antiferromagnetic Toroidal Ordering"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9186-6958","authenticated-orcid":false,"given":"Satoru","family":"Hayami","sequence":"first","affiliation":[{"name":"Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,29]]},"reference":[{"key":"ref_1","first-page":"318","article-title":"Multipole expansion in classical and quantum field theory and radiation","volume":"5","author":"Dubovik","year":"1975","journal-title":"Sov. 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