Orbit-like trajectory of the vortex core in a magnetic nanodot

TL;DR

This paper derives the vortex core trajectory in magnetic nanodots using conserved quantities, revealing orbit-like paths in the absence of dissipation and inward or outward motion with damping.

Contribution

It introduces a new analytical description of vortex core motion based on conserved physical quantities, linking trajectory behavior to dissipation and magnetic field effects.

Findings

Vortex core follows orbit-like trajectories in ideal conditions.

Dissipation causes the vortex to move towards or away from the center.

Trajectory bounds depend on energy and conserved vector A.

Abstract

In physics, conserved quantities are key to understanding and describing physical phenomena. These conserved quantities are related to Noether's theorem and the Lagrangian description both in classical mechanics and in field theory. In this article we have found the equation of the vortex core trajectory in terms of two conserved physical quantities, namely the energy, $E$, and a vector perpendicular to the orbit plane, $\vec{A} = -\vec{L} + \vec{G} \, |\vec{r}_c|^2/2$ where $\vec{G}$, $\vec{L}$ and $\vec{r}_c$ are the topological gyrovector, the angular momentum and the position of the vortex core, respectively. We find that in the absence of a dissipative term, for small deviations of the vortex core, the trajectory is bounded between two concentric circles. On the contrary, under the action of a dissipative term proportional to the damping coefficient, $\vec{A}$ is no longer conservative and the vortex core moves either towards the center or out of the cylinder, depending on the circularity of the magnetic vortex and the intensity of the magnetic field applied in the plane of the cylinder.