  Here, we predict the effect of the spontaneous deformation of a flexible
ferromagnetic ribbon induced by Dzyaloshinskii-Moriya interaction (DMI). The
geometrical form of the deformation is determined both by the type of DMI and
by the equilibrium magnetization of the stripe. We found three different
geometrical phases, namely (i) the DNA-like deformation with the stripe central
line in the form of a helix, (ii) the helicoid deformation with the straight
central line and (iii) cylindrical deformation. In the main approximation the
magnitude of the DMI-induced deformation is determined by the ratio of the DMI
constant and the Young's modulus. It can be effectively controlled by the
external magnetic field, what can be utilized for the nanorobotics
applications. All analytical calculations are confirmed by numerical
simulations.
