Current-driven domain wall dynamics in spin-valve nanostrips with parallel, perpendicular, and tilted polarizers

Current-driven domain wall dynamics is studied theoretically in the spin-valve nanostrips with parallel, perpendicular and tilted polarizers by Lagrangian formalism. In this description, the Slonczewski and field-like spin-transfer torques act as a Coulomb-type dissipation and an effective magnetic field, respectively. Considering a Walker profile, the wall behavior is governed by the dynamic equations about the center position, the out-of-plane angle, and the width of walls. It is found that the wall precesses after the steady motion breaks down for the parallel polarizer. The field-like spin-transfer torque favors a rapid increase of the steady velocity. The average velocity in the precession is nearly proportional to the current density. On the other hand, there is no precession for the perpendicular and tilted polarizers. Under the perpendicular polarizer, the wall stops when increasing current density. Moreover, there exist hysteresis and tri-stability for a large spin polarization. Under the tilted polarizer, it can be observed hysteretic, linear and nonlinear dependence of the wall velocity on the increasing current density. In the hysteresis, the wall experiences a switching of polarity or a reversal of motion.