$v$ to $v_{{\rm AP}\rightarrow{\rm P}}$, the AP state becomes unstable but there is no stable P state to switch to. This point is marked by an asterisk in Fig. \[fig5\](b). For $v>v_{{\rm AP}\rightarrow{\rm P}}$, the moment of the switching magnet is in a persistently time-dependent state. However, if $v$ is now decreased below $v_{{\rm P}\rightarrow{\rm AP}}$ the system homes in on the stable AP state and the overall behaviour is reversible, [*i.e.*]{} no switching and no hysteresis occur. When $h_{\rm
ext}>1$ similar behaviour, now involving the P state, occurs at negative bias, as shown in Fig. \[fig5\](b). The dashed curves in Fig. \[fig5\](b) show a hypothetical time-averaged resistance in the regions of time-dependent magnetisation. As discussed later time-resolved measurements of resistance suggest that several different types of dynamics can occur in these regions.

It is clear from Fig. \[fig5\](a) that the jump AP$\rightarrow$P always occurs for positive bias $v$, which corresponds to flow of electrons from the polarising to the switching magnet. This result depends on the assumption that $g_{\parallel}>0$; if $g_{\parallel}<0$ it is easy to see that the sense of the hysteresis loop is reversed and the jump P$\rightarrow$AP occurs for positive $v$. To our knowledge this reverse jump 