Two Circular-Rotational Eigenmodes in Vortex Gyrotropic Motions in Soft Magnetic Nanodots

TL;DR

This paper identifies two fundamental circular eigenmodes in vortex gyrotropic motion within soft magnetic nanodots, explaining the dynamics through superposition and resonance characteristics influenced by vortex polarization.

Contribution

It reveals the existence of two circular-rotational eigenmodes in vortex gyrotropic motion, providing a comprehensive understanding of vortex core dynamics in magnetic nanodots.

Findings

Two eigenmodes (CW and CCW) are fundamental in vortex gyrotropic motion.

Superposition of eigenmodes explains steady-state vortex motion.

Resonance characteristics depend on vortex polarization and field frequency.

Abstract

We found, by micromagnetic numerical and analytical calculations, that the clockwise (CW) and counterclockwise (CCW) circular-rotational motions of a magnetic vortex core in a soft magnetic circular nanodot are the elementary eigenmodes existing in the gyrotropic motion with respect to the corresponding CW and CCW circular-rotational-field eigenbasis. Any steady-state vortex gyrotropic motions driven by a linearly polarized oscillating in-plane magnetic field in the linear regime can be perfectly understood according to the superposition of the two circular eigenmodes, which show asymmetric resonance characteristics reflecting the vortex polarization. The relative magnitudes in the amplitude and phase between the CCW and CW eigenmodes determine the elongation and orientation of the orbital trajectories of the vortex core motions, respectively, which trajectories vary with the polarization and chirality of the given vortex as well as the field frequency across the resonance frequency.