6 stabilized. The frequency of the excitations increases linearly with the field independently on the current I$_{dc}$ , as expected for small amplitude uniform precessions from the FMR Kittel formula. In this large field region, the slope is close to the expected value of 2.8 GHz/kOe and the intercept with the zero-frequency axis occurs at 7.7 kOe, which corresponds to M NiFe s = 9 kOe after taking into account the demagnetizing factors. For | H$_{perp}$ | between 6.5 and 7.5 kOe, one clearly sees in Fig.2 (a) a slight deviation from the Kittel mode, reflecting the onset of a weak inhomogeneity that is suppressed when I$_{dc}$ increases. Such behavior is well reproduced by the micromagnetic simulations of the frequency versus out-of-plane magnetic field presented in Fig.3 by introducing a small tilt (1 $^{◦}$) of H$_{perp}$ from the normal direction. In both zone I and VI, as mentioned before, very low power emissions are measured in agreement with what is generally observed for uniform magnetization oscillations of the free layer. The transition between the uniform magnetization and the vortex configurations (zone II) occurs at H$_{perp}$ = - 6.1 kOe (resp. transition from vortex to uniform configuration, zone V, at H$_{perp}$ = 6.1 kOe). It is characterized by a dip in frequency as can be seen from the curve at I$_{dc}$ = 1 mA in Fig.2. This dip is well reproduced by the micromagnetic simulations shown in Fig.3, and is related to a modification of the shape of the vortex core that results into a softening of the mode. In this field range of large emission, the simulations for I$_{dc}$ = 3.2 mA are in good agreement with the experimental results. We find that the combined action of the spin transfer torque and the Oersted field strongly modifies the evolution of the frequency and maintains the vortex present at larger H$_{perp}$ (see additional materials for the observation of the gradual disappearance of the frequency dip as the current is increased). In the experiment and simulations, we see that several large- amplitude non-uniform oscillating modes are successively excited when changing the field. Note that such sequential transition of modes is not detectable by measuring the device resistance versus field. Below the critical field | H$_{c}$ | , only thermally excited vortex motion associated with a very small power is observed and in consequence the two frequency curves at different I$_{dc}$ are superimposed. While increasing H$_{perp}$ from - 4.5 kOe to + 4.9 k0e, i.e. zones III and IV, after a small increase of the frequency, the general trend is a decrease of the gyrotropic frequency (see Fig.2, top panel) as already observed in vortex resonance induced by ac field by De Loubens et al (see Eq.2 in Ref.[27]) due to the field dependence of the vortex stiffness. The deviation from the expected linear behavior of the frequency vs.