FIG. 4: ratio of frequency over critical current density as a function of the out of plane magnetic field for both sweep directions (red symbols : negative to positive, blue symbols : positive to negative). The black lines correspond to the calculations using equation 4. increasing (blue squares) and decreasing (red squares) values of the field. The expected linear variation of f/J$_{c}$ with H$_{perp}$ is clearly confirmed by the experiments. In Fig.4, we also plot in plain lines the result from an analytical calculation using Eq. 4 taking M NiFe s = 9.0 kOe, M SAF s = 10.3 kOe, α = 0.01, η = 1.48 and P$_{spin}$ = 0.53. We emphasize that this value of P$_{spin}$ is consistent with the MR ratios in conventional CoFeB/MgO/CoFeB MTJs in which spin polarization P$_{spin}$ = 0.5 - 0.6 for the CoFeB/MgO interface is found using the simple Jullieres model. The excellent agreement between the experimental results and the theoretical predictions on the whole field range reveals that not only a qualitative but also a quantitative understanding of the spin transfer vortex dynamics has been achieved. The location of the vortex core inside the nanodot can also strongly influence its dy- namical properties. This core position can be controlled by the application on an in-plane magnetic field H$_{in}$ that forces the vortex to move perpendicularly to the field [29]. In ad- dition, it provides a tool to investigate the role of the material grains on the motion of the vortices but also potentially to increase the accessible frequencies. In Fig.5 (a), we display the measurement of the gyrotropic mode frequency as a function of H$_{in}$ . We observe an os- cillating behavior of the frequency while the magnetic vortex is traveling from the center of the dot where it nucleates, to the edge of the disk where it annihilates. Such large frequency variations are due to the modification of the magnetization and/or the local anisotropies at 9