to be approximately $\sin\psi$. This torque is due to exchange coupling, analogous to an RKKY coupling, between the two magnetic layers. This coupling oscillates as a function of spacer thickness and tends to zero as the thickness tends to infinity. For finite bias $V_{\rm B}$ the second term in the integrand of Eq. (\[landau33\]) comes into play. In general this leads to finite $x$ and $y$ components of ${\bf T}^{\rm s-t}$ proportional to $V_{\rm b}$ (for small $V_{\rm b}$) whereas $T_{z}^{\rm s-t}=0$. However for the special model considered here with infinite exchange splitting in both ferromagnets it turns out that $T_y^{\rm s-t}=0$. For this model the only non-zero component of ${\bf T}^{\rm s-t}$ proportional to $V_{\rm b}$ is found to be $$\label{torquex}
T_x^{\rm s-t}=\frac{\hbar j^{\rm c}}{2|e|}\tan\frac{\psi}{2}$$ where $j^{\rm c}$ is the charge current given by Eq. (\[current\]).

Slonczewski [@3] originally obtained this result for the analogous parabolic band model. From Eqs. (\[torquex\]), (\[current\]) and (\[T\]) it follows that $T_{x}^{\rm s-t}$ contains an important factor $\sin\psi$ although this does not represent the whole angle dependence. Clearly, from Eq. (\[torquex\]), the torque proportional to bias remains finite for arbitrarily large spacer thickness, in the ballistic limit. For this model, with infinite exchange 