Optimization of the current pulse for spin-torque switches

We address optimization of the spin current intensity profile needed to achieve spin torque switching of a nanomagnet. For systems with Ohmic dissipation we prove that the optimal current drives the magnetization along the trajectory, which is exact time-reversed replica of the relaxation trajectory towards the equilibrium. In practice it means that the optimal current is very nearly {\em twice} the minimal critical current needed to switch the magnet. Pulse duration of such an optimal current is a slow logarithmic function of temperature and the required probability of switching.