  Frequency of free magnetic vortex precession in circular soft ferromagnetic
nano-cylinders (magnetic dots) of various sizes is an important parameter, used
in design of spintronic devices (such as spin-torque microwave
nano-oscillators) and characterization of magnetic nanostructures. Here, using
a recently developed collective-variable approach to non-linear dynamics of
magnetic textures in planar nano-magnets, this frequency and its
amplitude-dependent shift are computed analytically and plotted for the full
range of cylinder geometries. The frequency shift is positive in large planar
dots, but becomes negative in smaller and more elongated ones. At certain dot
dimensions a zero frequency shift is realized, which can be important for
enhancing frequency stability of magnetic nano-oscillators.
