Current-induced fingering instability in magnetic domain walls

The shape instability of magnetic domain walls under current is investigated in a ferromagnetic (Ga,Mn)(As,P) film with perpendicular anisotropy. Domain wall motion is driven by the spin transfer torque mechanism. A current density gradient is found either to stabilize domains with walls perpendicular to current lines or to produce fingerlike patterns, depending on the domain wall motion direction. The instability mechanism is shown to result from the nonadiabatic contribution of the spin transfer torque mechanism.

Figure 1

Current-induced modification of the magnetic domain pattern. (a) Sample description. (b) Magnetic-field-driven domain pattern corresponding to the initial magnetic state. (c), (d) Modification of the domain pattern due to a dc current. The current flows from the narrow to the semicircular electrode $\left(j>0\right)$ for 60 s. Its amplitude was (c) $I=2.16$ mA and (d) $I=2.98$ mA. The domain pattern is observed by magneto-optical Kerr microscopy. The two gray levels reflect the two opposite magnetization directions perpendicular to the (Ga,Mn)(As,P) film. $T=95$ K.

Figure 2

Instability of magnetic DW produced by a gradient of current density. Left frames: Stability of a domain wall (dotted arcs) placed perpendicularly to a current density gradient. A small tilt of an elementary wall length (blue segments) produces an asymmetry of the forces due to spin transfer (thin black arrows). A current flow (thick green arrows) in the direction of the narrow electrode $(j>0$, top frame) tends to destabilize the initial orientation while it tends to be stabilized for $j<0$ (bottom frame). (a)–(d) DW shape instability for $j>0$. (a) Initial state. (b)–(d) A 60 s dc current flow produces a finger growth towards the narrow electrode. Increasing the current magnitude $\mathrm{[}I=0.70$, 1.10, and 1.20 mA for (b)–(d), respectively] enhances the distance at which the semicircular DWs become unstable. (e)–(g) Stable radial DW growth for $j<0$. The sample that is initially in an homogeneous magnetic state is submitted to a current pulse of amplitude $-1.547$ mA of increasing duration $\mathrm{[}1\mu \mathrm{s},10\mu \mathrm{s}$, and $100\mu \mathrm{s}$ for (e)–(g), respectively]. The propagation front remains almost semicircular. The weak anisotropy of magnetic domain growth is most probably associated with the in-plane anisotropy of the (Ga,Mn)(As,P) single crystal. $T=95$ K.

Figure 3

Fingerlike magnetic domain growth resulting from domain wall instability. The images were obtained for a constant current $(I=-1.55$ mA) directed towards the narrow electrode $\left(j<0\right)$ and for different durations [(a) $100\mu \mathrm{s}$, (b) 690 ms, and (c) 29.7 s]. $T=95$ K. (d) Square of the critical instability radius as a function of the bias current. The line corresponds to the best fit of the theoretical prediction.