Spin transfer and spin-orbit torques in in-plane magnetized (Ga,Mn)As tracks

Current-driven domain wall motion is investigated experimentally in in-plane magnetized (Ga,Mn)As tracks. The wall dynamics is found to differ in two important ways with respect to perpendicularly magnetized (Ga,Mn)As: the wall mobilities are up to ten times higher and the walls move in the same direction as the hole current. We demonstrate that these observations cannot be explained by spin-orbit field torques (Rashba and Dresselhaus types) but are consistent with nonadiabatic spin transfer torque enhanced by the strong spin-orbit coupling of (Ga,Mn)As. This mechanism opens the way to domain wall motion driven by bulk rather than interfacial spin-orbit coupling as in ultrathin ferromagnet/heavy metal multilayers.

Figure 1

(a),(b) Two track configurations and device schematics: the hole current (red arrows) flows either parallel (${\mathrm{C}}_{//}$) or perpendicular (${\mathrm{C}}_{\perp }$) to the magnetization (dark arrows) whose easy direction is along the crystallographic axis $\left[1\overline{1}0\right]$. With the reservoir grounded, the hole current direction shown in this schematics therefore results from a negative potential applied to the opposite tip of the track. The hydrogenated (Ga,Mn)As:H has turned paramagnetic, thus defining the stripe. (c),(g),(j) Phenomenology of current-induced DW motion. The effective spin-orbit field (${\vec{H}}_{SO}$) is the sum of the Rashba and the Dresselhaus contributions (see text). (d)–(f) and (h),(i) Longitudinal Kerr microscopy images (divided by a reference image taken after saturation) showing domain wall displacements under the application of successive current pulses ($1,2$, etc.). The white dotted lines are guides for the eyes and the black dashed ones materialize the edges of the track and reservoir. (d)–(f) $2\mu \mathrm{m}$ wide ${\mathrm{C}}_{//}$ track, 70 ns long current pulses of $J=24.5\mathrm{GA}{\mathrm{m}}^{-2}$ under ${\mu }_{0}H=1.1$ mT ($T_{\mathrm{eff}}=40$ K). (h) $10\mu \mathrm{m}$ wide ${\mathrm{C}}_{\perp }$ track, 120 ns long current pulses of $J=14.9\mathrm{GA}{\mathrm{m}}^{-2}$, no applied field ($T_{\mathrm{eff}}=80$ K). A domain is easily nucleated in the middle of the track under current by ${\vec{H}}_{SO}$ (pulses $1$ and 5). (i) $2\mu \mathrm{m}$ wide ${\mathrm{C}}_{\perp }$ track, 100 ns long current pulses of $J=23.5\mathrm{GA}{\mathrm{m}}^{-2}$ under ${\mu }_{0}H=1.3$ mT ($T_{\mathrm{eff}}=50$ K).

Figure 2

Estimation of the current-induced STT-like and FL-like contributions in the $2\mu \mathrm{m}$ wide ${\mathrm{C}}_{\perp }$ track, at $T_{\mathrm{eff}}=83$ K. (a) Normalized hysteresis cycles under continuous current $J=\pm 8.3\mathrm{GA}{\mathrm{m}}^{-2}$, and without current. They are obtained by taking longitudinal Kerr images as the field is cycled, and averaging the signal over the entire surface of the track. Hysteresis cycles averaged on the reservoir under current coincide with those averaged on the track without current. (b) The DW depinning field out of a given trap $H_{\mathrm{dep}}\left(J\right)$ is monitored as a function of current density and compared to the one without applied current $H_{\mathrm{dep}}(J=0)$. The difference is indicated in the $y$ axis. The four schematics represent the physical situations encountered in the four corresponding quadrants of the plot, with the same arrow legend as in Fig. 1.

Figure 3

Domain-wall velocity: (a) velocity versus field curves (${\mathrm{C}}_{//}$ and ${\mathrm{C}}_{\perp } 2\mu \mathrm{m}$ wide tracks) at constant temperature and current density. (b) Velocity versus current density for tracks ${\mathrm{C}}_{//}$ ($2\mu \mathrm{m}$ wide, ${\mu }_{0}H=1.1$ and 1.2 mT) and ${\mathrm{C}}_{\perp }$ ($2\mu \mathrm{m}$ wide, ${\mu }_{0}H=1.3$ mT, and $10\mu \mathrm{m}$ wide, no field). Measurements taken at $T_{\mathrm{eff}}=49\pm 1$ K for the $2\mu \mathrm{m}$ wide tracks, and at $T_{\mathrm{eff}}=77\pm 2$ K for the $10\mu \mathrm{m}$ wide one.

Figure 4

Micromagnetic simulations ($T=60$ K micromagnetic parameters of the sample, and $T=0$ in mumax code [42]) for both track configurations. (a) Static domain wall width. Smaller DW widths translate into smaller mobilities under field. (b) Field-driven DW propagation, subtracting surface magnetic charges at wire ends to simulate infinite wire. The best agreement with measurements on unpatterned samples [39] was obtained with $\alpha =0.025$. The precessional regime is reached at a few mT, in the plateau of the curve.

Figure 5

Effective fields acting on the magnetization (blue arrows) involved in the fieldlike torque (green hollowed arrows) and the Slonczweski-like torque (black hollowed arrows), ${\vec{H}}_{SL}\propto {\vec{H}}_{so}\times \vec{M}$. Their effect on ${\mathrm{C}}_{//}$ (a),(c) and ${\mathrm{C}}_{\perp }$ (b),(d) configurations, and supposing Néel (a),(b) or Bloch (c),(d) domain walls are represented using dashed contours if the field is only efficient in the precessional regime, or continuous contours if it is efficient in the stationary regime. The direction of the hole current is indicated by a red arrow and the dotted contours materialize the plane of rotation of the magnetization in the domain wall. The direction of ${\vec{H}}_{so}$ has only been inferred experimentally in (b).

Figure 6

$2\mu \mathrm{m}$ wide ${\mathrm{C}}_{//}$ tracks: (a) position of the DW versus current pulse number at fixed applied field ${\mu }_{0}H=0.7$ mT and $T_{\mathrm{eff}}\approx 62\mathrm{K}$, pulse duration $\tau =100$ ns. Pinned (magenta), depinning (blue), and depinned (black) regimes are clearly identified for increasing current densities. No pr1opagation or depinning are observed for negative values of the current. (b) Domain wall velocity determination from the averaged domain-wall displacement, at fixed applied field ${\mu }_{0}H=1.3$ mT, $J=21.75$ GA ${\mathrm{m}}^{-2}$, and $T_{\mathrm{eff}}\approx 49\mathrm{K}$.