The stability of steady motion of magnetic domain wall: Role of higher-order spin-orbit torques

Abstract

The steady motion of magnetic domain wall driven by spin-orbit torques is investigated analytically in the heavy/ferromagnetic metal nanowires for three cases with a current transverse to the in-plane and perpendicular easy axis, and along the in-plane easy axis. By the stability analysis of Walker wall profile, we find that if including the higher-order spin-orbit torques, the Walker breakdown can be avoided in some parameter regions of spin-orbit torques with a current transverse to or along the in-plane easy axis. However, in the case of perpendicular anisotropy, even considering the higher-order spin-orbit torques, the velocity of domain wall cannot be efficiently enhanced by the current. Furthermore, the direction of wall motion is dependent on the configuration and chirality of domain wall with a current along the in-plane easy axis or transverse to the perpendicular one. Especially, the direction of motion can be controlled by the initial chirality of domain wall. So, if only involving the spin-orbit mechanism, it is preferable to adopt the scheme of a current along the in-plane easy axis for enhancing the velocity and controlling the direction of domain wall.