Giant Current-Driven Domain Wall Mobility in (Ga,Mn)As

We study theoretically hole current-driven domain wall dynamics in (Ga,Mn)As. We show that the spin-orbit coupling causes significant hole reflection at the domain wall, even in the adiabatic limit when the wall is much thicker than the Fermi wavelength, resulting in spin accumulation and mistracking between current-carrying spins and the domain wall magnetization. This increases the out-of-plane nonadiabatic spin-transfer torque and consequently the current-driven domain wall mobility by 3 to 4 orders of magnitude. Trends and magnitude of the calculated domain wall current mobilities agree with experimental findings.

Figure 1

(a)–(c) Distributions of transverse propagating modes in (Ga,Mn)As for different magnetization directions shown by the arrows. White (gray) color indicates that two (one) spin channels are open for transport. (d) Distribution of transverse conducting channels through an adiabatic Bloch domain wall in (Ga,Mn)As. Arrows show the magnetization directions itinerant holes encounter while traversing a Bloch wall. For an adiabatic domain wall, transverse modes in (a) that do not exist in (d) are totally reflected by the wall. Such reflections increase the out-of-plane torque on the domain wall, which subsequently increases the domain wall drift velocity. The plots are created using Eq. (3) with ${\gamma }_1=6.8$, ${\gamma }_2=2.7$, $h_{\mathrm{ex}}/{ϵ}_0=1.5$, ${ϵ}_F/{ϵ}_0=2.25$.

Figure 2

Steady-state snapshots. (a) and (b) exchange field ($h_x/{ϵ}_0$ and $h_z/{ϵ}_0$), spin per conducting hole ($⟨S_x⟩$ and $⟨S_z⟩$), and absolute values of spin-torque per conducting hole $|\mathcal{T}|$ as functions of position, for (a) vanishing and (b) finite spin-orbit coupling. (c) Absolute values of the out-of-plane torque $|{\mathcal{T}}_y|$ versus position for ${\gamma }_2=0$ (thick solid line), ${\gamma }_2=0.5$ (dashed line), and $\gamma =2$ (symbol $+$). For all plots, $h_{\mathrm{pd}}=0.001$ and ${\lambda }_w/{\lambda }_0=2$.

Figure 3

Domain wall displacement as a function of time for (a) zero spin-orbit coupling for different domain wall widths, and (b) fixed domain wall width for varying hole spin-orbit coupling strengths. For both plots, $h_{\mathrm{pd}}=0.001$.

Figure 4

(a) Domain wall drift velocity as a function of $h_{\mathrm{pd}}$ for varying spin-orbit couplings ${\gamma }_2$. Note that the scale of the horizontal axis is different for each spin-orbit coupling, done to collect all graphs into a single plot. (b) Current-driven domain wall mobility ${\mu }_I$ and spatial total of the absolute values of the out-of-plane torque $⟨|{\mathcal{T}}_y|⟩$ as functions of spin-orbit coupling. For both plots, ${\lambda }_w/{\lambda }_0=2$. Lines are guides for the eye.