Spin transfer driven excitations in magnetic nanostructures are characterized by a relatively large microwave emission linewidth (10 -100 MHz). Here we investigate the role of thermal fluctuations as well as of the non-linear amplitude-phase coupling parameter and the amplitude relaxation rate to explain the linewidth broadening of in-plane precession modes induced in planar nanostructures. Experiments on the linewidth broadening performed on MgO based magnetic tunnel junctions are compared to the linewidth obtained from macrospin simulations and from evaluation of the phase variance. In all cases we find that the linewidth varies linearly with temperature when the amplitude relaxation rate is of the same order as the linewidth and when the amplitude-phase coupling parameter is relatively small. The small amplitude-phase coupling parameter means that the linewidth is dominated by direct phase fluctuations and not by amplitude fluctuations, explaining thus its linear dependence as a function of temperature.
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