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swept from -8.1 to 8.1 kOe is presented as additional material. Large microwave power is detected in a very narrow field window between H$_{c}$ = 3.7 kOe and H$_{sw}$ = 4.3 kOe. We notice that H$_{sw}$ is reduced in the case of negative currents because the vortex core velocity is enhanced by spin transfer [28]. It implies that we have to increase the injected absolute value of the current in order to decrease H$_{c}$ and fulfill the condition H$_{c}$ < H$_{sw}$ . The counterpart of this additional experimental verification of the model, is that we must use a dc current that damages the junction quality leading to a decrease of the magnetoresistance ratio and therefore a smaller microwave output power compared to the case of positive currents. 

To extract some quantitative informations about the spin torque force, an expression of the critical current density J$_{c}$ for the onset of sustained vortex oscillations can be obtained by equalizing Eq. 2 and Eq.3. By this calculation, we predict that the ratio f/J$_{c}$ between the frequency and the critical current density should be proportional to the out-of-plane polarization p$_{z}$ : 

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In our magnetic system, the spin polarization is coming from the CoFeB layer of the synthetic antiferromagnet. Thus the evolution of p$_{z}$ with the out-of-plane magnetic field can be expressed by : p$_{z}$ = H$_{perp}$/M SAF s . The ratio f/J$_{c}$ is expected to vary linearly with H$_{perp}$ . In Fig.4, we plot the experimental values of f/J$_{c}$ vs. the out-of-plane magnetic field for 

