Figure 2

Vortex dynamical properties vs. DC current excitation. (a) The absolute values of the vortex gyrotropic frequency \(f^{\mathrm{STVO}}\) and (b) the vortex reduced position s as a function of the DC current density \(J_{\mathrm{dc}}\). The colours black, red and blue correspond to simulations without AOF (\(\mathrm{noOe}\)), with AOF and \(C = +1\) (\(C^{+}\)) and with AOF and \(C = -1\) (\(C^{-}\)), respectively. The frequency is fitted with a linear function of \(J_{\mathrm{dc}}\) in the first resonant regime (\(J_{\mathrm{dc}}< J_{\mathrm{c}1}\)) for each configuration. The resulting fits are plotted with grey dashed lines. The critical current \(J_{\mathrm{c}1}\) is extracted from \(s(J_{\mathrm{dc}})\) and gives rise to the first green \(J_{\mathrm{c}1}\)-line. The \(J_{\mathrm{c}1}\)-line represents the transition between the first resonant regime and the steady-state oscillating regime. The \(J_{\mathrm{c}1}\)-line links the \(f^{\mathrm{STVO}}(J_{\mathrm{c}1})\) points originating from the micromagnetic data and is also well approximated by the analytical counterpart \(f^{\mathrm{STVO}} = J_{\mathrm{dc}}\cdot \kappa ^{\mathrm{ST}}_{\perp }/ (2\pi D)\). The \(J_{\mathrm{c}1}\) and \(J_{\mathrm{c}2}\) values are plotted across both sub-figures by corresponding dash-dotted lines. The \(J_{\mathrm{c}2}\)-line represents the transition from the steady-state oscillating regime to the second resonant regime as for \(J_{\mathrm{dc}}>J_{\mathrm{c}2}\), the vortex core polarity switches from \(P=-1\) to \(P=+1\) and \(J_{\mathrm{dc}}P p_z\) becomes positive.