Spin Drift Velocity, Polarization, and Current-Driven Domain-Wall Motion in (Ga,Mn)(As,P)

Current-driven domain-wall motion is studied in (Ga,Mn)(As,P) ferromagnetic semiconducting tracks with perpendicular anisotropy. A linear steady state flow regime is observed over a large temperature range of the ferromagnetic phase ($0.1T_c<T<T_c$). Close to 0 K, the domain-wall velocity is found to coincide with the spin drift velocity. This result is obtained below the intrinsic threshold for domain-wall motion which implies a nonadiabatic contribution to the spin transfer torque. The current spin polarization is deduced close to 0 K and to $T_c$. It suggests that the temperature dependence of the spin polarization can be inferred from the domain-wall dynamics.

Figure 1

Current-driven DW velocity $v$ measured at different temperatures $T$. Each point and its error bar correspond to the average and to the standard deviation calculated with more than 20 measurements, respectively. At $T=42.5\mathrm{K}$, larger error bars also reflect a slight asymmetry of DW displacements found as the current is reversed. Inset: Semilogarithmic plot of $v$ measured at 95 K for the lowest current densities.

Figure 2

Temperature variations of the current mobility (${\mu }_J=v/J$). The empty symbols correspond to three different current values: $13.3\pm 2.0\mathrm{GA}/{\mathrm{m}}^2$ (squares), $11.5\pm 1.8\mathrm{GA}/{\mathrm{m}}^2$ (triangles), and $7.0\pm 0.5\mathrm{GA}/{\mathrm{m}}^2$ (circles). The filled symbols correspond to the boundary between the pinning controlled and the flow linear regimes, deduced form the slope changes observed in Fig. 1. The flow linear regime is materialized by a shaded area.

Figure 3

Temperature variation of the spin polarization $P_c^{\mathrm{DW}}$ deduced from domain-wall dynamics (left scale: same legend as for Fig. 2) and of the magnetization $M_s$ (right scale: ⊙). Values of the spin polarization $P_c$ (left scale: down triangles) deduced from point-contact Andreev reflection measurements [10, 11, 12]. The crossed symbols (⊞) correspond to results obtained for $P_c^{\mathrm{DW}}$, with $({\mathrm{Ga}}_{0.93},{\mathrm{Mn}}_{0.07})\mathrm{As}$ $4\mu \mathrm{m}$ wide tracks.

Figure 4

Comparison between the experimental results and predictions for the domain-wall flow regimes. Filled (empty) symbols correspond to the flow (depinning) regime. Inset. Zoom for low values of the reduced spin drift velocity $u/v_w$.