# Spontaneous deformation of flexible ferromagnetic ribbons induced by Dzyaloshinskii-Moriya interaction

## TL;DR

This paper predicts how Dzyaloshinskii-Moriya interaction causes spontaneous deformation in flexible ferromagnetic ribbons, revealing three distinct geometrical phases controllable by magnetic fields, with potential applications in nanorobotics.

## Contribution

It introduces a theoretical framework for understanding DMI-induced deformations in ferromagnetic ribbons and identifies three unique geometrical phases based on DMI and magnetization.

## Key findings

- Identified three deformation phases: helix, helicoid, and cylindrical.
- Deformation magnitude depends on DMI to Young's modulus ratio.
- External magnetic fields can control the deformation.

## Abstract

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.