Magnetic vortex dynamics in the non-circular potential of a thin elliptic ferromagnetic nanodisk with applied fields

Abstract

Spontaneous vortex motion in thin ferromagnetic nanodisks of elliptical shape is dominated by a natural gyrotropic orbital part, whose resonance frequency omega(G) = (k) over bar /G depends on a force constant and gyrovector charge, both of which change with the disk size and shape and applied in-plane or out-of-plane fields. The system is analyzed via a dynamic Thiele equation and also using numerical simulations of the Landau-Lifshitz-Gilbert (LLG) equations for thin systems, including temperature via stochastic fields in a Langevin equation for the spin dynamics. A vortex is found to move in an elliptical potential with two principal axis force constants k(x) and k(y), whose ratio determines the eccentricity of the vortex motion, and whose geometric mean (k) over bar = root k(x)k(y) determines the frequency. The force constants can be estimated from the energy of quasi-static vortex configurations or from an analysis of the gyrotropic orbits. k(x) and k(y) get modified either by an applied field perpendicular to the plane or by an in-plane applied field that changes the vortex equilibrium location. Notably, an out-of-plane field also changes the vortex gyrovector G, which directly influences omega(G). The vortex position and velocity distributions in thermal equilibrium are found to be Boltzmann distributions in appropriate coordinates, characterized by the force constants.