Magnetic vortex resonance in patterned ferromagnetic dots

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 mu m and thickness 20 and 40 nm, patterned via electron-beam lithography onto microwave coplanar 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 disks of 2.2- and 1.1-mu m-diameter with thickness 40 nm, respectively. A resonance peak at 83 MHz was detected for 20-nm thick, 2-mu m-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.