Shape transformations of flexible ferromagnetic ribbons

We propose a minimal extension of the anisotropic 2D Heisenberg model in order to describe flexible magnetic systems with coupled magnetic and mechanical subsystems[1,2]. The coupling between the magnetic and mechanical subsystems is driven by uniaxial anisotropy with the easy-axis normal or tangential to the magnetic film and by the Dzyaloshinskii--Moriya interaction (DMI). We show that the presence of DMI results in a spontaneous deformation of a flexible magnetic ribbon. The final state is characterized by the geometrical chirality whose sign is determined by the sign of the DMI constant. Depending on the mechanical, magnetic, and geometric parameters of the system one can obtain two different states: a twisted-state with zero curvature of the central line is typical for small DMI constants and narrow ribbons, while a DNA-like state with nonzero curvature of its central line is preferable for large DMI constants and wider ribbons. All these states can be efficiently controlled by magnetic fields opening new possibilities in the development of nanorobots in the context of organicelectronics and spintronics.
[1] Yu. Gaididei et al, Phys. Rev. B 99, 014404, (2019).
[2] K. V. Yershov et al, Phys. Rev. B 100, 140407(R), (2019).