It was shown by micromagnetic simulation that a current-driven in-plane magnetized magnetic nano-contact, besides a quasi-linear propagating ("Slonczewski") spin wave mode, can also support a nonlinear self-localized spin wave "bullet" mode that exists in a much wider range of bias currents. The frequency of the "bullet" mode lies below the spectrum of linear propagating spin waves, which makes this mode evanescent and determines its spatial localization. The threshold current for the excitation of the self-localized "bullet" is substantially lower than for the linear propagating mode, but finite-amplitude initial perturbations of magnetization are necessary to generate a "bullet" in our numerical simulations, where thermal fluctuations are neglected.Consequently, in these simulations the hysteretic switching between the propagating and localized spin wave modes is found when the bias current is varied.

We demonstrate that high-frequency cooperative dynamics of an array of coupled nonlinear spintorque nano-oscillators (STNO) can be controlled by introduction of an additional external phase shift β c between the microwave current, which couples STNOs, and the total array microwave voltage. When this external phase shift β c compensates the intrinsic phase shift β 0 , caused by the STNO nonlinearity, a phase-locking regime with increased output power and vanishing inhomogeneous linewidth broadening is achieved. In the opposite case, when external and intrinsic phase shifts are added, the STNO array demonstrates a frustration regime with low output power and wide and noisy frequency spectrum.

It is shown that in a spin-torque microwave oscillator based on a magnetic nanocontact, the nature of the microwave spin wave mode generated at the threshold critically depends on the angle between the external bias magnetic field and the plane of the free layer. When the external bias field is rotating from normal to in-plane orientation, an abrupt transition from a propagating cylindrical wave with the frequency higher than the frequency of the linear ferromagnetic resonance ͑FMR͒ to a self-localized standing nonlinear spin wave "bullet" with the frequency lower than the FMR frequency takes place at a certain intermediate angle cr . This transition manifests itself as an abrupt jump ͑of the order of several gigahertz͒ in the generated microwave frequency. This mechanism of mode switching might explain abrupt jumps of the generated microwave frequency observed in recent experiments on spin-torque oscillators.

The nature of spin wave modes excited by spin-polarized direct current in a spin-torque autooscillator based on a magnetic nanocontact was studied by a micromagnetic simulation in the case when the external bias magnetic field was rotated from the in-plane to perpendicular-to-plane orientation. In qualitative agreement with the weakly-nonlinear analytical theory it was found, that at a certain critical angle, an abrupt switching from the self-localized nonlinear "bullet' mode to a propagating quasi-linear Slonczewski mode takes place, and is accompanied by an upward jump in generated microwave frequency. It was, also, found that the analytical theory overestimates the magnitude of a critical magnetization angle, corresponding to the mode switching, and that the magnitude of the frequency jump caused by the mode switching is inversely proportional to the nanocontact radius.