splitting, the torque is independent of the thickness of the switching magnet.

From the results of this simple model we can infer a general form of the spin-transfer torque ${\bf T}^{\rm s-t}$ which is independent of the choice of coordinate axes. Thus we write $$\label{torqueperp}
{\bf T}^{\rm s-t}={\bf T}_{\perp}+{\bf T}_{\parallel}$$ where $$\begin{aligned}
\label{torque2} {\bf T}_{\perp}&=&\left(g^{\rm ex}+g_{\perp} e
V_{\rm b}\right)({\bf
  m}\times{\bf p}) \nonumber\\
{\bf T}_{\parallel}&=&g_{\parallel} e V_{\rm b}{\bf m}\times({\bf
  p}\times{\bf m}).\end{aligned}$$ With the choice of axes in Fig. \[fig1\] ${\bf T}_{\parallel}$ corresponds to the $x$ component of torque, that is the component parallel to the plane containing the magnetisation directions ${\bf
m}$ and ${\bf p}$. Similarly ${\bf T}_{\perp}$ corresponds to the $y$ component of torque, this being perpendicular to the plane of ${\bf m}$ and ${\bf p}$. The modulus of both the vectors ${\bf
m}\times{\bf p}$ and ${\bf m}\times({\bf p}\times{\bf m})$ is $\sin\psi$, so that the factors $g^{\rm ex}$, $g_{\perp}$ and $g_{\parallel}$ are functions of $\psi$ which contain deviations from the simple $\sin\psi$ behaviour. The bias-independent term $g^{\rm ex}$ corresponds to the interlayer exchange coupling, as discussed above, and henceforth we assume that the spacer is thick enough for this term to be negligible. Sometimes the $\sin\psi$ factor accounts for most 