  We report direct imaging by means of x-ray photoemission electron microscopy
of the dynamics of magnetic vortices confined in micron-size circular Permalloy
dots that are 30 nm thick. The vortex core positions oscillate on a 10-ns
timescale in a self-induced magnetostatic potential well after the in-plane
magnetic field is turned off. The measured oscillation frequencies as a
function of the aspect ratio (thickness/radius) of the dots are in agreement
with theoretical calculations presented for the same geometry.
