Wire edge dependent magnetic domain wall creep

While edge pinning is known to play an important role in sub-$\mu \mathrm{m}$ wires, we demonstrate that strong deviations from the universal creep law can occur in 1 to $20\mu \mathrm{m}$ wide wires. Magnetic imaging shows that edge pinning translates into a marked bending of domain walls at low drive and is found to depend on the wire fabrication process and aging. Edge pinning introduces a reduction of domain wall velocity with respect to full films which increasingly dominates the creep dynamics as the wire width decreases. We show that the deviations from the creep law can be described by a simple model including a counter magnetic field which links the width of the wire to the edge dependent pinning strength. This counter field defines a key nonuniversal contribution to creep motion in patterned structures.

Figure 1

ln(DW velocity) vs ${\mu }_0{\mathrm{H}}^{-1/4}$ in a $200\mu \mathrm{m}$ wire. The insets show (left) the same plot in a linear scale highlighting the position of H${}_{\mathrm{dep}}$ and (right) the DW profile at low drive (0.33 mT $\approx {\mathit{H}}_{\mathrm{dep}}/24$).

Figure 2

ln(DW velocity) vs ${\mu }_0{\mathrm{H}}^{-1/4}$ for different wire widths. Deviations from the creep model ($\mu =1/4$) are observed as the wire width and driving field decrease. In the high field region the fitting line corresponds to the depinning model; at low drive a modified creep model including a counter field is also plotted.

Figure 3

(a) ln(DW velocity) vs ${\mu }_0{\mathrm{H}}^{-1/4}$ for different $20\mu \mathrm{m}$ wire series. The magnitude of the deviation depends on the different fabrication processes (A and B) and aging (C). Note that wire A belongs to the variable width series presented in Fig. 2. (b) SEM images and (c) AFM scans of each wire presented in (a).

Figure 4

Wires A, B, and C showing DW displacements under ${\mathit{H}}_{\mathrm{dep}}/20$ (a) and ${\mathit{H}}_{\mathrm{dep}}*5$ (b). The DW curvature seen in the creep regime is highly suppressed beyond ${\mathit{H}}_{\mathrm{dep}}$.

Figure 5

(a) Graphic representation of a DW displacement $\mathrm{\Delta }x$ in the absence (top) and presence (bottom) of edge pinning. (b) ${\mathit{H}}_{\mathrm{edge}}$ as a function of the inverse wire width $1/w$ showing the variable width series including wire A and wires B and C. The inset shows a zoom-in of the large wire width region.

Figure 6

Dependence of the single creep exponent $\mu$ on wire widths between $200\mu \mathrm{m}$ and $1\mu \mathrm{m}$ for the wire series A. (inset) ln(DW velocity) vs ${\mu }_0{\mathrm{H}}^{-\mu }$ for wire widths of $1\mu \mathrm{m}$ (circles, $\mu =0.56$), $5\mu \mathrm{m}$ (triangles, $\mu =0.35$), and $200\mu \mathrm{m}$ (squares, $\mu =0.25$), and the respective fitting curves (solid lines).

Figure 7

Scaled ln(DW velocity) vs ${\mu }_0{\mathrm{H}}^{-1/4}$ for (a) all wire widths and for (b) the $20\mu \mathrm{m}$ wire series.

Figure 8

DW velocity difference between the measured velocity and the pure creep model for (a) all wire widths and (b) the $20\mu \mathrm{m}$ wire series with respect to the pure creep model dynamics. $\ln (\mathrm{\Delta }\mathrm{DW}$ velocity) vs ${\mu }_0{\mathrm{H}}^{-0.38}$ shows a linear trend.