Near-Field Interaction between Domain Walls in Adjacent Permalloy Nanowires

The magnetostatic interaction between two oppositely charged transverse domain walls (TDWs) in adjacent Permalloy nanowires is experimentally demonstrated. The dependence of the pinning strength on wire separation is investigated for distances between 13 and 125 nm. The results can be described fully by considering the distribution of magnetic charge within rigid, isolated TDWs. Alternative DW internal structure cannot reproduce this observed dependence. Modeling suggests the TDW internal structure is not appreciably disturbed, and remains rigid although the pinning strength is significant.

Figure 1

(a) SEM image of a typical structure showing two $10\mu \mathrm{m}$ long $U$-shaped Py nanowires separated by an edge to edge distance $d=100\mathrm{nm}$. The asterisks indicate the positions where the MOKE laser spot is focused. (b) Schematic of oppositely charged TDWs created in “$A$” corners moving, under field $H$, along wires separated by $d$.

Figure 2

Open circles: Experimental dependence of DW transmission field $H_D$ on wire separation $d$. Gray line, average wire propagation field $H_P$. Modeled depinning fields considering charge distribution of the DWs with wide-wide (HHD, TTD; upper long dashed line), wide-narrow (HHU, TTD or HHD TTU; dotted line) or narrow-narrow (HHU, TTU; lower dashed and dotted line) sides closest. Solid black line, wide-wide interaction with a fitting scale factor of 0.54. Inset: Example MOKE observed hysteresis loop of a nanowire. Switching occurs at $H_D$, in this case 70 Oe, due to depinning from the DW-DW potential well.

Figure 3

Potential well obtained when laterally separating a pair of oppositely charged TDWs by $x$ for the case $d=10\mathrm{nm}$, from rigid charge model. The nearest sides of the TDWs are wide-wide (black line), wide-narrow (gray line), and narrow-narrow (light gray line).