Current-induced motion of a transverse magnetic domain wall in the presence of spin Hall effect

We theoretically study the current-induced dynamics of a transverse magnetic domain wall in bi-layer nanowires consisting of a ferromagnet on top of a nonmagnet having strong spin-orbit coupling. Domain wall dynamics is characterized by two threshold current densities, $J_{th}^{WB}$ and $J_{th}^{REV}$, where $J_{th}^{WB}$ is a threshold for the chirality switching of the domain wall and $J_{th}^{REV}$ is another threshold for the reversed domain wall motion caused by spin Hall effect. Domain walls with a certain chirality may move opposite to the electron-flow direction with high speed in the current range $J_{th}^{REV} < J < J_{th}^{WB}$ for the system designed to satisfy the conditions $J_{th}^{WB} > J_{th}^{REV}$ and \alpha > \beta, where \alpha is the Gilbert damping constant and \beta is the nonadiabaticity of spin torque. Micromagnetic simulations confirm the validity of analytical results.