High domain wall velocities in in-plane magnetized (Ga,Mn)(As,P) layers

Field-induced domain wall (DW) propagation was evidenced in unpatterned layers of in-plane magnetized Ga${}_{1-x}$Mn${}_x$As${}_{1-y}$P${}_y$ using Kerr microscopy. Both stationary and precessional regimes were observed, and domain wall velocities of up to 500 m s${}^{-1}$ were measured, of the order of magnitude of those observed on in-plane magnetized metals. Taking advantage of the strain-dependent magnetocrystalline anisotropy in this dilute magnetic semiconductor, both out-of-plane and in-plane anisotropies were adjusted by varying the manganese and phosphorus concentrations. We demonstrate that these anisotropies are a critical parameter to obtain large velocities. These results are interpreted in the framework of the one-dimensional model for domain wall propagation.

Figure 1

(a) Design of the homemade cold finger and set of rotating microcoils giving $H_{\mathrm{pul}}$. (b) General top-view of the cold finger surrounded by the outer cryostat shield located between a set of rotating external coils giving $H_{\mathrm{ext}}$.

Figure 2

Methodology for DW velocity measurement, example on sample A4 at $T$ $=$ 25 K. (a) Snapshots taken in zero field after successive 400-ns pulses of a 6.9-mT field. (b) Dividing successive images yields the displacement after each pulse. (c) Linear regression leading to the DW velocity. Note that the fit has a negative $y$ intercept resulting from the finite rise time of the pulse and of the depinning field.

Figure 3

Domain wall velocity versus applied field in the [Mn]${}_{\mathrm{eff}}$ $=$ 3.7$\%$ series in order of decreasing lattice mismatch (slm) and uniaxial out-of-plane anisotropy. (a) A3, (b) B3, (c) C3. The lines are guides for the eyes.

Figure 4

(a) Domain wall velocity for the [Mn]${}_{\mathrm{eff}}$ $=$ 4.7$\%$ sample at $T$ =25, 60, and 85 K. (b) Modification of the domain profile with increasing field.

Figure 5

Computed 1D model $v\left(H\right)$ curves with the vertical arrows indicating the position of the Walker field. (a) Varying in-plane ($K_0$) and out-of-plane ($K_{\perp }$) anisotropies without pinning (following Ref. 3 with $\alpha$ $=$ 0.03, $A_{\mathrm{exc}}$ $=$ 10${}^{-13}$ J m${}^{-1}$, $M_s$ $=$ 36 kA m${}^{-1}$). (b) Possible modifications to the $v\left(H\right)$ curve when pinning is taken into account. The DW velocity may rejoin the intrinsic regime before Walker breakdown (dashed line) or afterwards (dotted line).