Helicity of magnetic vortices and skyrmions in soft ferromagnetic nanodots and films biased by stray radial fields

The Portuguese team acknowledges the Network of Extreme Conditions Laboratories and Portuguese Foundation of Science and Technology for support through Projects No. NORTE-01-0145-FEDER-022096, No. MIT-EXPL/IRA/0012/2017, No. PTDC/FISMAC/31302/2017, No. POCI-0145-FEDER-030085(NOVAMAG), No. PTDC/FIS-MAC/31302/2017, andNo. EXPL/IF/00541/2015 (S.A.B.) and Grant No.SFRH/BPD/90471/2012 (A.H.-R.). Work was also supported by the Ministry of Education and Science of Ukraine, Project No. 0118U004007 (R.V.V., B.A.I.); IKERBASQUE (the Basque Foundation for Science) (K.Y.G.); the Spanish Ministry of Economy, Industry and Competitiveness, Grant No. FIS2016-78591-C3-3-R (K.Y.G.); the European Union Horizon 2020 Research and Innovation Programme under Marie Sklodowska-Curie Grants No. 644348 (R.V.V., B.A.I., K.Y.G.), No. H2020-MSCA-RISE-2016-734801 (D.N., G.N.K.), and No. H2020-MSCA-IF-2016-74695 (A.H.-R.); the Program of NUST “MISiS,” Grant No. K2-2019-006, implemented by Russian Federation government Decree No. 211 dated 16 March 2013 (B.A.I.); the Spanish Ministry for Science, Innovation and Universities, for funding through the “Ramon y Cajal” Program No. RYC-2017-22820 (D.N.); and European Cooperation in Science and Technology, Projects No. CA16218 “NANOCOHYBRI” (G.N.K.) and No. CA17123 “MAGNETOFON” (B.A.I).