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We investigate the dependence of the N\'eel skyrmion size and stability onperpendicular magnetic field in ultrathin circular magnetic dots without-of-plane anisotropy and interfacial Dzyaloshinskii-Moriya exchangeinteraction. Our results show the existence of two distinct dependencies of theskyrmion radius on the applied field and dot size. In the case of skyrmionsstable at zero field, their radius strongly increases with the field appliedparallel to the skyrmion core until skyrmion reaches the metastability regionand this dependence slows down. More common metastable skyrmions demonstrate aweaker increase of their size as a function of the field until some criticalfield value at which these skyrmions drastically increase in size showing ahysteretic behavior with coexistence of small and large radius skyrmions andsmall energy barriers between them. The first case is also characterized by astrong dependence of the skyrmion radius on the dot diameter, while in thesecond case this dependence is very weak.

Distinct magnetic field dependence of N\'eel skyrmion sizes in ultrathin nanodots