Spin density and spin torque induced by the D'yakonov-Perel' mechanism in magnetic semiconductor nanowires with a constriction

Abstract

The transport through a domain wall pinned at a nanoconstriction in (Ga,Mn)As wires is investigated theoretically using the Landauer-B\uttiker approach by considering the Rashba and Dresselhaus spin-orbit interactions. The local nonequilibrium spin densities produced by electrical spin injection at the nanoconstriction are calculated numerically along the nanowire. The adiabatic and nonadiabatic components of the spin-transfer torque, expressed in terms of the gradient of the spin current density, are also computed. An oscillatory behavior in the spin-transfer torque is observed for the systems containing atomically sharp domain walls, due to the strong reflections at the domain wall caused by the large magnetization gradient. It is demonstrated that the strength of the oscillations for nonadiabatic spin torque increases by the negative Rashba parameter ${\ensuremath{\alpha}}_{x}$, while it decreases with increasing positive values of ${\ensuremath{\alpha}}_{x}$. However, the nonadiabatic spin torque increases with $\left|{\ensuremath{\alpha}}_{y}\right|$, regardless of its sign. Furthermore, it is shown that the Dresselhaus coupling $\ensuremath{\beta}$ does not considerably alter the $z$ component of the spin torque, while the other two components are effectively changed by the Dresselhaus spin-orbit interaction.