Magnetically controlled geometry of flexible ferromagnetic rings

We propose a minimal extension of the anisotropic Heisenberg model in order to describe flexible magnetic wires (rings) [1]. Flexible ferromagnetic wires are spin-chain magnets, in which the magnetic and mechanical subsystems are coupled. The coupling between the magnetic and mechanical subsystems is driven by uniaxial anisotropy with the easy-axis oriented along the tangential direction. First, we show that depending on the magnetic and elastic parameters and the size of the system one can obtain two different states: the onion state with the quasi-uniform magnetization is typical for small enough rings, while the vortex state with the magnetization oriented tangential to the wire is preferable for large systems. Second, we demonstrate that according to the system symmetry there can appear normal modes with zero frequency (i. e. zero modes) on the background of equilibrium states. [1] Yu. Gaididei et al, arXiv:1809.10622 (2018).