Orbit-like trajectory of the vortex core in ferrimagnetic dots close to the compensation point

In physics, conserved quantities are key to understand and describe physical phenomena. These conserved quantities are related to Noether's theorem and Lagrangian description in both classical mechanics and field theory. In this article we have found the equation of the vortex core trajectory in ferrimagnets close to the compensation point in terms of two conserved physical quantities, namely the energy, E, and a vector perpendicular to the orbit plane, A→=−L→+G→|r→_c|²∕2 where G→, L→ and r→_c are the topological gyrovector, the angular momentum and the position of the vortex core, respectively. We found 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, 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.