Homogeneous and heterogeneous nucleation of skyrmions in thin layers of cubic helimagnets

Formation of isolated chiral skyrmions by homogeneous and heterogeneous nucleation has been studied in thin layers of cubic helimagnets via elongation of torons and chiral bobbers, respectively. Both torons and bobbers are localized in three dimensions, contain singularities, and, according to the theoretical analysis within the standard phenomenological models, can exist as metastable states in saturated and modulated phases of noncentrosymmetric ferromagnets. Their elongation into the defect-free skyrmion filament is facilitated by small anisotropic contributions making skyrmion cores negative with respect to the surrounding parental state. We show that isolated magnetic torons pose the same problem of compatibility with a surrounding phase as the torons in confinement-frustrated chiral nematics [I. I. Smalyukh et al., Nat. Mater. 9, 139 (2010)]. We underline the distinct features of magnetic and liquid-crystal torons and calculate phase diagrams indicating their stability regions.