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Spin-transfer torques in magnetic nanocontacts can lead to self-sustainedmagnetization oscillations that involve large-amplitude gyrotropic vortexmotion. This dynamics consists of a steady state orbit around the nanocontact,which is made possible because the intrinsic magnetic damping is compensated byspin torques. In this article, we present an analytical theory of the powerspectrum of these oscillations based on a rigid-vortex model. The appearance ofvortex oscillations in nanocontacts is not associated with a Hopf bifurcation:there is no critical current and the only precondition for steady-stateoscillations at finite currents is the existence of a vortex in the system, incontrast with conventional spin-torque oscillators that involve large-anglemagnetization precession. The oscillation frequency is found to depend linearlyon the applied current and inversely proportional to the orbital radius. Bysolving the associated Langevin problem for the vortex dynamics, the lineshapeand linewidth for the power spectrum are also obtained. Under typicalexperimental conditions, a Lorentzian lineshape with a current-independentlinewidth is predicted. Good quantitative agreement between the theory andrecent experiments is shown.

Theory of the power spectrum of spin-torque nanocontact vortex oscillators