Direct observation of internal vortex domain-wall dynamics

The motion of domain walls is influenced by their internal structure and their structural changes during motion. The macroscopic motion is well understood but the internal dynamics during motion have not been experimentally studied in detail. We study vortex domain walls excited by nanosecond long magnetic field pulses in a pinning potential and above the pinning threshold. The dynamic response is imaged by transmission x-ray microscopy and the structural changes are analyzed. From the directly observed inertial behavior of the wall the domain-wall mass equivalent is estimated. During motion, oscillations of both the vortex core around the center of the domain wall and the domain-wall width are observed. The wall shows a fully elastic behavior by compression and overexpansion when being pushed by the field.

Figure 1

(a) Experimental setup with a 2 $\mu$m wide stripline across a kinked permalloy nanowire. An external magnetic field $H_{\text{sat}}$ is used to create a vortex domain wall next to the kink that is excited by the Oersted field $H_{\text{Oersted}}$ of a current pulse. The ingoing ($-$20 dB pick off) and outgoing pulses are monitored by an oscilloscope. (b) Time-resolved sequence of scanning transmission x-ray micrographs of an excited domain wall over a period of 15 ns. (c) Measured minimal field pulse strength (crosses) for depinning a domain wall from the kink in dependence of the pulse length and an exponentially decaying fit (dashed black line).

Figure 2

Measured position of the vortex core of a domain wall excited by (a) 2 ns and (b) 3 ns long field pulses for various field strengths. The domain wall either stays pinned and oscillates or is depinned and moves outwards until the field pulse ends and the restoring potential returns it to its initial position. The solid lines are guides to the eye.

Figure 3

Positions of depinned domain walls over time after excitement by (a) 2 ns long and (b) 3 ns long field pulses. The position of the vortex core is shown in black, the averaged center of the domain wall in solid red. The red dots show the upper and lower edge of the domain wall. The strength of the pulse is plotted on the right and the position on the left axis. The domain-wall mass equivalent is shown over time in (c). In the shaded areas the applied definition is not valid.

Figure 4

(a) Width of depinned domain walls excited by 2 ns long (blue) and 3 ns long pulses (red, black). The pulses are indicated by the gray and blue shaded areas. (b) Position of the vortex core for the same domain walls. The shaded area indicates the outward motion until the turning point.

Figure 5

(a) Widths of the upper (black line) and lower (gray line) half of the domain wall shown in red in Fig. 3. (b) Velocity (red line) and total width (green line) of the domain wall during the motion. The width is plotted on the left and the velocity on the right axis.