Tuning Coupled Toroidic and Polar Orders in a Bilayer Antiferromagnet

Tuning Coupled Toroidic and Polar Orders in a Bilayer Antiferromagnet | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Tuning Coupled Toroidic and Polar Orders in a Bilayer Antiferromagnet Liuyan Zhao, Chuangtang Wang, Xiaoyu Guo, Zixin Zhai, Meixin Cheng, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7811382/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Magnetic toroidal order features a loop-like arrangement of magnetic dipole moments, thus breaking both spatial inversion (P) and time-reversal (T) symmetries while preserving their combined PT symmetry. This PT symmetry enables a linear magnetoelectric effect, allowing the coupling between magnetic toroidicity and electric polarity. However, the detection and control of two-dimensional (2D) magnetic toroidal order and the investigation of its linear magnetoelectric response remain largely unexplored. Here, using bilayer CrSBr as a platform, which hosts an in-plane layer antiferromagnetic (AFM) order and simultaneously exhibits a magnetic toroidal order, we show compelling evidence for tuning this 2D magnetic toroidicity and its induced electric polarity through magnetic-field-dependent second harmonic generation (SHG). Under an out-of-plane magnetic field, we decompose the SHG signal into a time-reversal-odd component that scales with the magnetic toroidal moment and a time-reversal-even component that is proportional to the electric polarization. When sweeping the magnetic field from positive to negative values, we observe that the magnetic toroidicity retains its sign but diminishes in magnitude at higher fields while the electric polarity flips its sign and increases in strength at increasing fields below a critical threshold. When applying an in-plane electric field along the Néel vector direction, together with an out-of-plane field, we find that the magnetic toroidal and electric polar domains are moved in a locked fashion. These findings underscore the promise of 2D magnetic toroidal order in realizing giant linear magnetoelectric effects, opening exciting possibilities for next-generation electronic, magnetic, optical, and photonic devices enabled by 2D magnetoelectrics. Physical sciences/Physics/Condensed-matter physics/Magnetic properties and materials Physical sciences/Materials science/Nanoscale materials/Two-dimensional materials Full Text Additional Declarations There is NO Competing Interest. Supplementary Files Supplementarymaterial.pdf Supplementary Material Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7811382","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":534060366,"identity":"0aa736e0-ada2-46aa-97ff-22f33689f0cd","order_by":0,"name":"Liuyan 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This PT symmetry enables a linear magnetoelectric effect, allowing the coupling between magnetic toroidicity and electric polarity. However, the detection and control of two-dimensional (2D) magnetic toroidal order and the investigation of its linear magnetoelectric response remain largely unexplored. Here, using bilayer CrSBr as a platform, which hosts an in-plane layer antiferromagnetic (AFM) order and simultaneously exhibits a magnetic toroidal order, we show compelling evidence for tuning this 2D magnetic toroidicity and its induced electric polarity through magnetic-field-dependent second harmonic generation (SHG). Under an out-of-plane magnetic field, we decompose the SHG signal into a time-reversal-odd component that scales with the magnetic toroidal moment and a time-reversal-even component that is proportional to the electric polarization. When sweeping the magnetic field from positive to negative values, we observe that the magnetic toroidicity retains its sign but diminishes in magnitude at higher fields while the electric polarity flips its sign and increases in strength at increasing fields below a critical threshold. When applying an in-plane electric field along the Néel vector direction, together with an out-of-plane field, we find that the magnetic toroidal and electric polar domains are moved in a locked fashion. These findings underscore the promise of 2D magnetic toroidal order in realizing giant linear magnetoelectric effects, opening exciting possibilities for next-generation electronic, magnetic, optical, and photonic devices enabled by 2D magnetoelectrics.","manuscriptTitle":"Tuning Coupled Toroidic and Polar Orders in a Bilayer Antiferromagnet","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-24 05:16:26","doi":"10.21203/rs.3.rs-7811382/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f6678b01-c846-4f4a-875f-20a05969a6bb","owner":[],"postedDate":"October 24th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":56786443,"name":"Physical sciences/Physics/Condensed-matter physics/Magnetic properties and materials"},{"id":56786444,"name":"Physical sciences/Materials science/Nanoscale materials/Two-dimensional materials"}],"tags":[],"updatedAt":"2025-12-04T07:41:02+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-24 05:16:26","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7811382","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7811382","identity":"rs-7811382","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}