Interplay of Linear and Nonlinear Localization Mechanisms in Spin-Torque Oscillators with a Field Well

The magnetization dynamics in a spin-torque oscillator with nonuniform profile of a static magnetic field creating a field well is studied by analytic calculations and numerical simulations. It is demonstrated that, in the case of sufficiently deep and narrow field well, the linear localization in the field well dominates the nonlinear self-localization, despite a negative nonlinear frequency shift. A change of the localization mechanism results in a qualitatively different dependence of the generation power on the driving current. For the dominant linear localization, the soft generation mode is realized, while, for the nonlinear self-localization, we observe a hard mode of auto-oscillator excitation. Simultaneously, a difference in the profiles of the excited spin-wave mode can become evident and distinguishable in experiments only in the case of a nonsymmetric field well.