  We theoretically study domain wall oscillations upon the injection of a dc
current through a geometrically constrained wire with perpendicular magnetic
anisotropy. The oscillation frequency spectrum can be tuned by the injected
current density, but additionally by the application of an external magnetic
field independent of the power. The results of analytical calculations are
supported by micromagnetic simulations based on the Landau-Lifshitz-Gilbert
equation. The simple concept of our localized steady-state oscillator might
prove useful as a nanoscale microwave generator with possible applications in
telecommunication or for rf-assisted writing in magnetic hard drives.
