Effects of Disorder and Internal Dynamics on Vortex Wall Propagation

Experimental measurements of domain wall propagation are typically interpreted by comparison to reduced models that ignore both the effects of disorder and the internal dynamics of the domain wall structure. Using micromagnetic simulations, we study vortex wall propagation in magnetic nanowires induced by fields or currents in the presence of disorder. We show that the disorder leads to increases and decreases in the domain wall velocity depending on the conditions. These results can be understood in terms of an effective damping that increases as disorder increases. As a domain wall moves through disorder, internal degrees of freedom get excited, increasing the energy dissipation rate.

Figure 1

(a) A typical vortex wall structure in a wire with 200 nm width and 20 nm thickness. The color indicates the in-plane angle of the magnetization, and the arrows indicate the approximate magnetization direction. (b) Schematic trajectories of field-induced vortex wall propagation in ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ film for ${\mu }_{0}H=3\mathrm{mT}$ above the critical field along the $x$ direction with disorder $\mathcal{D}=0$ and 0.05. Here the total simulation time is 100 ns. Points that the vortex core pass through are black (dark blue) or gray (orange) depending on whether the vortex core has its magnetization into or out of the plane. Insets show the domain wall displacement as a function of time.

Figure 2

Energy dissipation rate along $x$ for ${\mu }_{0}H=3\mathrm{mT}$ with disorder (a) $\mathcal{D}=0$ and (b) $\mathcal{D}=0.05$. Insets show contributions from spin wave and vortex to the energy dissipation rate, which were obtained by separating regions near a vortex core with a diameter of 400 nm, as shown in Fig. 1a.

Figure 3

Domain wall velocity as a function of applied field for disorder $\mathcal{D}=0$, 0.025, and 0.05. Error bars indicate 1 standard deviation statistical uncertainty.

Figure 4

Domain wall velocity (a) as a function of disorder and (b) as a function of the damping constant for $J=2\times {10}^{13}\mathrm{A}/{\mathrm{m}}^2$ with $\beta$ as a parameter.

Figure 5

Effective damping ${\alpha }_{\mathrm{eff}}$ as a function of disorder $\mathcal{D}$ for field-induced and current-induced vortex wall propagation.