Conservative effects in spin-transfer-driven magnetization dynamics

It is shown that under certain conditions spin transfer results in conservative magnetization dynamics. This dynamics occurs along closed precessional-type trajectories, and it admits a special integral of motion which is reduced to the usual magnetic energy when the spin current is reduced to zero. The existence of this conservative dynamics is due to the symmetry properties of the magnetization dynamics equation with respect to simultaneous inversions of magnetization and time. When an external dc magnetic field is applied parallel to the spin polarization, the conservative magnetization dynamics is transformed into relaxations. It is demonstrated that there exists such a state function (Lyapunov function) that monotonically either increases or decreases during these relaxations, depending on the directions of the injected current and applied dc magnetic field. These results hold in the absence of intrinsic (thermal) damping. When the intrinsic damping is included in the description, mutual compensation between field-induced and damping-induced nonconservative effects may occur, which may eventually lead to the appearance of limit cycles, that is, of magnetization self-oscillations.