Magnetization induced shape transformations in flexible ferromagnetic rings

TL;DR

This paper investigates how magnetization influences shape changes in flexible ferromagnetic rings, revealing phase transitions between vortex and onion states through analytical and numerical methods.

Contribution

It introduces a minimal model for deformable ferromagnetic rings and maps their phase diagram, linking magnetic states with mechanical deformations.

Findings

Vortex state with zero magnetic moment forms in large rings.

Small rings exhibit an onion state with elliptical deformation.

Phase transition occurs between vortex and onion states based on parameters.

Abstract

Flexible ferromagnetic rings are spin-chain magnets, in which the magnetic and mechanical subsystems are coupled. The coupling is achieved through the tangentially oriented anisotropy axis. The possibility to operate the mechanics of the nanomagnets by controlling their magnetization is an important issue for the nanorobotics applications. A minimal model for the deformable curved anisotropic Heisenberg ferromagnetic wire is proposed. An equilibrium phase diagram is constructed for the closed loop geometry: (i) A vortex state with vanishing total magnetic moment is typical for relatively large systems; in this case the wire has the form of a regular circle. (ii) A topologically trivial onion state with the planar magnetization distribution is realized in small enough systems; magnetic loop is elliptically deformed. By varying geometrical and elastic parameters a phase transition between the vortex and onion states takes place. The detailed analytical description of the phase diagram is well confirmed by numerical simulations.