Current-driven vortex domain wall dynamics by micromagnetic simulations

Current-driven vortex wall dynamics is studied by means of a two-dimensional analytical model and micromagnetic simulation. By constructing a trial function for the vortex wall in the magnetic wire, we analytically solve for domain wall velocity and deformation in the presence of the current-induced spin torque. A critical current for the domain wall transformation from the vortex wall to the transverse wall is calculated. A comparison between the field- and current-driven wall dynamics is carried out. Micromagnetic simulations are performed to verify our analytical results.

Figure 1

Magnetization patterns of (a) a transverse wall and (b) a vortex wall, without an applied current or field. (c) Schematic model for the vortex wall (b): a vortex wall is modeled by two TWs and a vortex core, shown in gray areas. The vortex core is at the center of the wire and $\pm x_0$ are the positions of the centers of the TWs. $R$ is the outer radius of the vortex core, $w$ is the wall width of two TW walls, and $y_0$ is the half-width of the wire. (d) The magnetization pattern of the vortex wall in the presence of the current, which is calculated by micromagnetic simulation in Sec. 3. The parameters are the spin torque $b_J=25\mathrm{m}∕\mathrm{s}$, damping parameter $\alpha =0.05$, and nonadiabaticity coefficient $\xi =0.04$. (e) The schematic model for the vortex wall (d). $\delta y$ is the displacement of the vortex toward the edge of the wire. The wall structure is not symmetrical, and one TW is expanded and the other is compressed.

Figure 2

The dependence of (a) the $x$ component of the initial velocity $v_{x_0}$ and (b) the $y$-component displacement $\delta y$ as a function of the nonadiabaticity parameter $\xi$ for two different polarity VWs $(p=\pm 1)$. We have used $b_J=25\mathrm{m}∕\mathrm{s}$ and $\alpha =0.05$. The straight lines are simple data fits.

Figure 3

Steady state velocity of TW and VW as a function of (a) the damping parameter, and (b) the nonadiabaticity parameter. The current density is $b_J=25\mathrm{m}∕\mathrm{s}$. The straight lines are simple data fits.

Figure 4

Steady state velocities of both TW and VW as functions of (a) the magnetic field and (b) the damping parameter. The current density is $b_J=25\mathrm{m}∕\mathrm{s}$. The straight lines are simple data fits.