{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T08:45:13Z","timestamp":1740127513647,"version":"3.37.3"},"reference-count":37,"publisher":"AIP Publishing","issue":"8","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2020,8,1]]},"abstract":"<jats:p>We summarize our experimental findings in the arrays of Ni80Fe20 circular nanodots with diameter 300\u2009nm and thickness 20\u2009nm\u2009\u2264\u2009L\u2009\u2264\u2009100\u2009nm, probed by broadband ferromagnetic resonance spectroscopy in the absence of external magnetic field. Spin excitation modes related to the vortex core gyrotropic dynamics were observed in the gigahertz frequency range. Micromagnetic simulations revealed that they are flexure oscillations of the vortex core string with n\u2009=\u20090, 1, 2 nodes along the dot thickness. It was found that for L\u2009&amp;gt;\u200970\u2009nm the intensity of more complicated n\u2009=\u20091 vortex gyrotropic mode is unexpectedly higher than the one of the lowest n\u2009=\u20090 gyrotropic mode. This behavior was clarified on the basis of the inhomogeneous vortex mode phase profiles extracted from micromagnetic simulations and calculated analytically. Precise measurements of the dependence of resonance frequency of the vortex n\u2009=\u20090 mode on the dot thickness demonstrated a clear maximum around L\u2009=\u200970\u2009nm, that was theoretically explained by introducing a vortex mass, which is a result of the vortex distortion due to interaction with spin waves having azimuthal indices m\u2009=\u2009\u00b11. Finally, several azimuthal spin-wave modes having curled structure at the dot top and bottom faces were found in the spectrum of the dots with thicknesses L\u2009\u2265\u200940\u2009nm.<\/jats:p>","DOI":"10.1063\/10.0001555","type":"journal-article","created":{"date-parts":[[2020,8,27]],"date-time":"2020-08-27T12:24:38Z","timestamp":1598531078000},"page":"863-868","update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Non-uniform along thickness spin excitations in magnetic vortex-state nanodots"],"prefix":"10.1063","volume":"46","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7081-581X","authenticated-orcid":false,"given":"G. N.","family":"Kakazei","sequence":"first","affiliation":[{"name":"Institute of Physics for Advanced Materials, Nanotechnology and Photonics (IFIMUP), Departamento de F\u00edsica e Astronomia, Universidade do Porto 1 , Porto 4169-007, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0096-9052","authenticated-orcid":false,"given":"K. Y.","family":"Guslienko","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica de Materiales, Universidad del Pa\u00eds Vasco 2 , San Sebasti\u00e1n 20018, Spain"},{"name":"IKERBASQUE, the Basque Foundation for Science 3 , Bilbao 48013, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8811-6232","authenticated-orcid":false,"given":"R. V.","family":"Verba","sequence":"additional","affiliation":[{"name":"Institute of Magnetism NAS of Ukraine and MES of Ukraine 4 , Kyiv 03142, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9917-9156","authenticated-orcid":false,"given":"J.","family":"Ding","sequence":"additional","affiliation":[{"name":"Information Storage Materials Laboratory, Department of Electrical and Computer Engineering, National University of Singapore 5 , Singapore 117576, Singapore"}]},{"given":"X. M.","family":"Liu","sequence":"additional","affiliation":[{"name":"Information Storage Materials Laboratory, Department of Electrical and Computer Engineering, National University of Singapore 5 , Singapore 117576, Singapore"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9724-2468","authenticated-orcid":false,"given":"A. 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