  Spin-transfer torques in magnetic nanocontacts can lead to self-sustained
magnetization oscillations that involve large-amplitude gyrotropic vortex
motion. This dynamics consists of a steady state orbit around the nanocontact,
which is made possible because the intrinsic magnetic damping is compensated by
spin torques. In this article, we present an analytical theory of the power
spectrum of these oscillations based on a rigid-vortex model. The appearance of
vortex oscillations in nanocontacts is not associated with a Hopf bifurcation:
there is no critical current and the only precondition for steady-state
oscillations at finite currents is the existence of a vortex in the system, in
contrast with conventional spin-torque oscillators that involve large-angle
magnetization precession. The oscillation frequency is found to depend linearly
on the applied current and inversely proportional to the orbital radius. By
solving the associated Langevin problem for the vortex dynamics, the lineshape
and linewidth for the power spectrum are also obtained. Under typical
experimental conditions, a Lorentzian lineshape with a current-independent
linewidth is predicted. Good quantitative agreement between the theory and
recent experiments is shown.
