10 FIG. 5: (a) left axis (blue squares) frequency, right axis (green triangles) : integrated power as a function of the in plane magnetic field .(b) Atomic Force Microscopy topography image of the NiFe layer. Bottom : scan of the thickness as a function of the location. the grain boundaries that changes the pinning potential [30–32]. From this measurement, the number of material grains in the nanodot can be evaluated. We deduce a grain size of about 40 nm in agreement with the AFM measurements shown in Fig.5 (b). Interestingly, we find that when the resonance frequency is low (resp. high), the thermally induced vortex fluctuations are enhanced (resp. reduced) as shown in Fig.5 (a); this is because the stiffness of the potential well probed by the vortex core is reduced for lower frequency. The perspective opened by our results is very promising. From the application point of view, we have shown that the current-induced excitation of a vortex in a low resistivity MTJ showing a MR ratio of only 10 %, can already lead to microwave emissions combining large power (5 nW) and narrow linewidth (1 MHz). Furthermore the excellent fit between our experiments and the theory makes our results turn out as a textbook example of the physics of current-induced vortex gyrations. Interestingly, our work also indicates that the observation of sustained vortex gyration at zero magnetic field, required for targeted applications, is only possible either if an out-of-plane polarizer is used (as in this work by applying an out of plane field) or if the polarizer is non-uniform or dynamically excited [33, 34]. The quantitative agreement between our results and theory will also allow us to define the best conditions, in terms of device structure (for example tilted or out-of-plane polarizer) and materials parameters (lower R.A product and larger MR ratios), to improve