Figure 3

Magnetisation of the magnetic dot at the beginning (initial state) and at the end (final state) of the micromagnetic simulations. The x-y component of the magnetisation is represented by green (clockwise chirality) or orange (counterclockwise chirality) arrows while the z component is represented by a colour code, i.e., dark blue for \(m_z=-1\), white for \(m_z=0\), and dark red for \(m_z=+1\). The vortex core is initially placed at \(x=1\) nm and \(y=0\) nm for \(J_{\mathrm{dc}}< J_{\mathrm{c}1}\) and at \(x=80\) nm and \(y=0\) nm for \(J_{\mathrm{dc}}> J_{\mathrm{c}2}\). The initial state of the vortex is \(C=-1\) and \(P=-1\). To simplify the visualisation, the arrows represent the averaged magnetisation over multiple cells. (a) For \(C^{-}\) and \(J_{\mathrm{dc}}=\) 5.0 MA/cm\(^2\), the vortex final state is damped back to the dot centre as at least one of the conditions for steady-state oscillations is not fulfilled, namely \(J_{\mathrm{dc}}< J_{\mathrm{c}1}\). Here, the chirality and the polarity do not change. (b) For \(C^{-}\) and \(J_{\mathrm{dc}}>J_{\mathrm{c}2}\) with \(J_{\mathrm{dc}}=\) 8.8 MA/cm\(^2\), only the vortex core polarity switches from \(P=-1\) (blue) to \(P=+1\) (red). Here, the same chirality as in the beginning nucleates. (c) For \(C^{-}\) and \(J_{\mathrm{dc}}=\) 9.0 MA/cm\(^2\), both the vortex core polarity switches from \(P=-1\) (blue) to \(P=+1\) (red) and the vortex chirality switches as it is initially clockwise (\(C=-1\)) and becomes counterclockwise (\(C=+1\)) at the end of the simulation.