  Vortex states in magnetic nanodisks are essentially affected by
surface/interface induced Dzyaloshinskii-Moriya interactions. Within a
micromagnetic approach we calculate the equilibrium sizes and shape of the
vortices as functions of magnetic field, the material and geometrical
parameters of nanodisks. It was found that the Dzyaloshinskii-Moriya coupling
can considerably increase sizes of vortices with "right" chirality and suppress
vortices with opposite chirality. This allows to form a bistable system of
homochiral vortices as a basic element for storage applications.
