Transitions of the magnetization in the presence of a polarized current

Transitions of the magnetization out of a metastable state to a more stable one in the presence of a polarized current is considered. We derive an effective Lagrangian to represent the equation of motion of the magnetization, and with the method of path integral we derive the imaginary-time action and the rate of transitions out of the metastable state. As the current can be varied, its presence allows one to study transitions of the magnetization with or without dissipation. The rates of quantum and thermal transitions are given for various regimes of temperature. Results for cubic and tetragonal ferromagnets are given as examples.