  To verify the exact underlying mechanism of ultrafast vortex-core reversal as
well as the vortex state stability we conducted numerical calculations of the
dynamic evolution of magnetic vortices in Permalloy cylindrical nanodots under
an oscillating in-plane magnetic field over a wide range of the frequency and
amplitude. The calculated results reveal different kinds of the non-trivial
dynamic responses of vortices to the driving external field. In particular, the
results offer insight into the 10 ps scale underlying physics of the ulrafast
vortex-core reversals driven by small amplitude (~10 Oe) in-plane fields. This
work also provides fundamentals of how to manipulate effectively the dynamical
switching of the vortex-core orientation.
