Phase-diagram of condensed and isolated skyrmions in chiral magnetic films

Skyrmions in chiral magnetic films exist either in the isolated phase, confined within the sample, or the condensed phase, occupying it entirely. The stability of magnetic structures in generic perpendicularly magnetized chiral magnetic films is fully determined by, $${\kappa }$$ and $${\kappa }^{{\prime} }$$ , measuring relative interaction strengths preferring curling and collinear structures, rather than individual material parameters. The phase diagram of skyrmion should span the isolated and condensed phases rather than skyrmion crystal and helical/conical states as in the conventional diagrams. Here, we provide a comprehensive skyrmion phase diagram between isolated and condensed phases in the $$\kappa {\kappa }^{{\prime} }$$ -plane. In the absence of magnetic crystalline anisotropy, perpendicular magnetic field is used to drive the transition from condensed to isolated skyrmions, where $${\kappa }^{{\prime} }$$ solely determines the (meta)stable structures and $$| {\kappa }^{{\prime} }| =4$$ separates isolated skyrmions, including circular and polygonal skyrmions, from condensed skyrmions, including skyrmion crystal and helical states. $$| {\kappa }^{{\prime} }| =4$$ , aligns with $$\kappa = 1$$ , which separate these phases in the absence of a perpendicular magnetic field when $${\kappa }$$ solely determines (meta)stable structures. Our phase diagram provides a versatile framework for exploring skyrmion behavior across different chiral magnetic films. The study investigates the stability of skyrmion phases in chiral magnetic films using a phase-diagram based on the parameters κ and $$\kappa ^{\prime}$$ , which quantify the relative strengths of interactions favouring curling and collinear structures. Isolated skyrmion, including circular and polygonal types, are distinguished from condensed skyrmion phases.