Field-driven domain-wall dynamics in (Ga,Mn)As films with perpendicular anisotropy

We combine magneto-optical imaging and a magnetic-field pulse technique to study domain-wall dynamics in a ferromagnetic (Ga,Mn)As layer with perpendicular easy axis. Contrary to ultrathin metallic layers, the depinning field is found to be smaller than the Walker field, thereby allowing for the observation of the steady and precessional flow regimes. The domain-wall width and damping parameters are determined self-consistently. The damping, 30 times larger than the one deduced from ferromagnetic resonance, is shown to essentially originate from the nonconservation of the magnetization modulus. An unpredicted damping resonance and a dissipation regime associated with the existence of horizontal Bloch lines are also revealed.

Figure 1

Magnetic field dependence of the DW velocity at $T=80\text{K}$. The error bars represent the standard deviation of the velocity distribution. Inset: low-field region in semilogarithmic scale with a fit (dashed line) according to the creep model (Ref. 12). Labels (a)–(c) refer to the corresponding images in the creep, depinning, and flow regimes, respectively. Images (b) and (c) are differential images showing the DW displacement as indicated by black arrows.

Figure 2

(Color online) Temperature dependence of the DW field-velocity curves. Each curve is upshifted by $10\text{m}{\text{s}}^{-1}$ with respect to the previous one. Inset: temperature dependence of the resonance field $H_p$ and damping $\delta \alpha$ of the velocity peak indicated by arrows.

Figure 3

(Color online) Comparison between theoretical predictions and experimental results (black circles). Dashed blue lines in (a): linear velocity in the steady and precessional regimes with mobility ${\mu }_{st}$ and ${\mu }_{\text{prec}}$, respectively. Solid blue curves in (b): velocity in the steady regime (below $H_W$) and in the unstable precessional regime (above $H_W$) calculated using the experimentally determined values of $\Delta$ and $\alpha$ (this work), and $M_s$ (Ref. 21); dotted red line: linear fit of the velocity in the Bloch line regime.

Figure 4

(Color online) (a) Comparison between the DW parameter $\Delta$ obtained from DW dynamics (full circles) and the boundaries for $\Delta$ obtained from domain theory (open symbols) (Ref. 21). (b) Temperature dependence of the DW damping parameter $\alpha$.