  Axisymmetric solitonic states (chiral skyrmions) have been predicted
theoretically more than two decades ago. However, until recently they have been
observed in a form of skyrmionic condensates (hexagonal lattices and other
mesophases). In this paper we report experimental and theoretical
investigations of isolated chiral skyrmions discovered in PdFe/Ir(111) bilayers
two years ago (Science 341 , 636 (2013)). The results of spin-polarized
scanning tunneling microscopy analyzed within the continuum and discrete models
provide a consistent description of isolated skyrmions in thin layers. The
existence region of chiral skyrmions is restricted by strip-out instabilities
at low fields and a collapse at high fields. We demonstrate that the same
equations describe axisymmetric localized states in all condensed matter
systems with broken mirror symmetry, and thus our findings establish basic
properties of isolated skyrmions common for chiral liquid crystals, different
classes of noncentrosymmetric magnets, ferroelectrics, and multiferroics.
