Topological Non-Identifiability in Stray Field Magnetometry

Topological Non-Identifiability in Stray Field Magnetometry | 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 Topological Non-Identifiability in Stray Field Magnetometry Shirsopratim Chattopadhyay, Aparajita Singha This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9343155/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 Inferring magnetic topology from stray field measurements is central to characterizing skyrmions, merons, and other topological textures. Yet, the uniqueness of such reconstructions remains poorly characterized. Here we use a computational framework to systematically demonstrate topological charge is not uniquely recoverable under realistic experimental magnetometry setups. We apply physics informed optimization to generate pairs of magnetization configurations with distinct topological charges (|ΔQ| ≈ 1,±0.5,±0.75) that produce nearly identical stray fields (Normalized Root Mean Square Error ~ 0.8–3% on average). Our approach jointly evolves magnetization pairs towards field degeneracy while preserving topological distinction. Across 100 randomized trials with varied initializations, we show rapid and reliable generation of adversarial pairs spanning skyrmions, merons, fractional defects and uniform domain textures. Multipole expansion analysis identifies the mathematical origin of this degeneracy: topologically distinct structures can share identical low-order magnetic charge distributions that dominate the far-field stray field profile. Our adversarial dataset enables rigorous assessment of magnetization reconstruction algorithms and highlights the need for measurement strategies capable of resolving topological ambiguity. Physical sciences/Materials science Physical sciences/Mathematics and computing Physical sciences/Physics Magnetometry topological magnetism inverse problems reconstruction physics informed optimization Full Text Additional Declarations No competing interests reported. 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. 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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-9343155","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":622570921,"identity":"f84f3ad6-5d99-49cd-aa12-3eff16dc648f","order_by":0,"name":"Shirsopratim Chattopadhyay","email":"","orcid":"","institution":"TU Dresden","correspondingAuthor":false,"prefix":"","firstName":"Shirsopratim","middleName":"","lastName":"Chattopadhyay","suffix":""},{"id":622570923,"identity":"69539923-339e-4be1-84c0-e411d8bfcce3","order_by":1,"name":"Aparajita Singha","email":"data:image/png;base64,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","orcid":"","institution":"TU Dresden","correspondingAuthor":true,"prefix":"","firstName":"Aparajita","middleName":"","lastName":"Singha","suffix":""}],"badges":[],"createdAt":"2026-04-07 10:08:47","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9343155/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9343155/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107484088,"identity":"27f8e4b6-6d12-4988-886a-00375687c766","added_by":"auto","created_at":"2026-04-22 02:30:43","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":657388,"visible":true,"origin":"","legend":"","description":"","filename":"TopologicalAmbiguitynpjCMrevised2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9343155/v1_covered_b5f68cc0-0e4e-493e-9592-2f5f59bd3c07.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Topological Non-Identifiability in Stray Field Magnetometry","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"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},"keywords":"Magnetometry, topological magnetism, inverse problems, reconstruction, physics informed optimization","lastPublishedDoi":"10.21203/rs.3.rs-9343155/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9343155/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eInferring magnetic topology from stray field measurements is central to characterizing skyrmions, merons, and other topological textures. 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