  We report a high-resolution experimental detection of the resonant behavior
of magnetic vortices confined in small disk-shaped ferromagnetic dots. The
samples are magnetically soft Fe-Ni disks of diameter 1.1 and 2.2 um, and
thickness 20 and 40 nm patterned via electron beam lithography onto microwave
co-planar waveguides. The vortex excitation spectra were probed by a vector
network analyzer operating in reflection mode, which records the derivative of
the real and the imaginary impedance as a function of frequency. The spectra
show well-defined resonance peaks in magnetic fields smaller than the
characteristic vortex annihilation field. Resonances at 162 and 272 MHz were
detected for 2.2 and 1.1 um disks with thickness 40 nm, respectively. A
resonance peak at 83 MHz was detected for 20-nm thick, 2-um diameter disks. The
resonance frequencies exhibit weak field dependence, and scale as a function of
the dot geometrical aspect ratio. The measured frequencies are well described
by micromagnetic and analytical calculations that rely only on known properties
of the dots (such as the dot diameter, thickness, saturation magnetization, and
exchange stiffness constant) without any adjustable parameters. We find that
the observed resonance originates from the translational motion of the magnetic
vortex core.
