Gyrotropic linear and nonlinear motions of a magnetic vortex in soft magnetic nanodots

The authors investigated the gyrotropic linear and nonlinear motions of a magnetic vortex in soft magnetic cylindrical nanodots under in-plane oscillating magnetic fields of different frequencies and amplitudes, by employing both micromagnetic simulations and the numerical solutions of Thiele's equation of motion [Phys. Rev. Lett. 30, 230 (1973)]. Not only noncircular elliptical vortex-core orbital trajectories in the linear regime but also complex trajectories including stadiumlike shape in the nonlinear regime were observed from the micromagnetic simulations and were in excellent agreement with the numerical solutions of the analytical equations of motion. It was verified that the numerical solutions of Thiele's equation are promisingly applicable in order to predict and describe well such complex vortex gyrotropic linear and nonlinear motions in both the initial transient and later steady states. These results enrich the fundamental understanding of the linear and nonlinear motions of vortices in confined magnetic elements in response to oscillating driving forces.