Fast Domain Wall Propagation under an Optimal Field Pulse in Magnetic Nanowires

We investigate field-driven domain wall (DW) propagation in magnetic nanowires in the framework of the Landau-Lifshitz-Gilbert equation. We propose a new strategy to speed up the DW motion in a uniaxial magnetic nanowire by using an optimal space-dependent field pulse synchronized with the DW propagation. Depending on the damping parameter, the DW velocity can be increased by about 2 orders of magnitude compared to the standard case of a static uniform field. Moreover, under the optimal field pulse, the change in total magnetic energy in the nanowire is proportional to the DW velocity, implying that rapid energy release is essential for fast DW propagation.

Figure 1

A schematic diagram of two dynamically equivalent 1D magnetic nanowire structures. (a) Easy axis is along the wire axis ($z$ axis); (b) easy axis ($z$ axis) $\perp$ the wire axis ($x$ axis). The region between two dashed lines denotes the DW region.

Figure 2

The DW propagation velocity $v$ versus the parameter $u$ at the different damping values $\alpha =0.1$, 0.2, 0.5, and 0.8. The other parameters are chosen as $\Delta =20\mathrm{nm}$ and $H=100\mathrm{Oe}$.

Figure 3

The $x$, $y$, $z$ components of the optimal field pulse. The parameters are chosen as $\alpha =0.01$, $\Delta =20\mathrm{nm}$ for permalloy [6]. The field magnitude is $H=100\mathrm{Oe}$.