ext}|<1$ and $|h_{\rm ext}|>1$.

![Bias-field stability diagram for $g_{\perp}(\psi)=0$, $g_{\parallel}(\psi)>0$. A small downward slope of the lines $V_{{\rm
  AP}\rightarrow{\rm P}}$,$V_{{\rm P}\rightarrow{\rm AP}}$ (see Eq. (\[crbias\])) is not shown.[]{data-label="fig4"}](Fig4.eps){width="13cm"}

Consider first the case $|h_{\rm ext}|<1$. Suppose we start in the AP state with a bias $v=0$ which is gradually increased to $v_{{\rm
    AP}\rightarrow P}$. At this point the AP state becomes unstable and the system switches to the P state as $v$ increases further. On reducing $v$ the hysteresis loop is completed via a switch back to the AP state at the negative bias $v_{{\rm P}\rightarrow AP}$. The hysteresis loop is shown in Fig. \[fig5\](a). The increase in resistance R between the P and AP states is the same as would be produced by varying the applied field in a GMR experiment.

![(a) Hysteresis loop of resistance vs bias for $|h_{\rm
    ext}|<1$; (b) Reversible behaviour (no hysteresis) for $|h_{\rm
    ext}|<-1$ (upper curve) and $h_{\rm ext}>1$ (lower curve). The dashed lines represent hypothetical behaviour of average resistance in regions of Fig. \[fig4\] marked “both unstable” where no steady states exist.[]{data-label="fig5"}](Fig5.eps){width="13cm"}

Now consider the case $h_{\rm ext}<-1$. Starting again in the AP state at $v=0$ we see from Fig. \[fig4\] that, on increasing 