Fast domain-wall propagation in uniaxial nanowires with transverse fields

Under a magnetic field along its axis, domain-wall motion in a uniaxial nanowire is much slower than in the fully anisotropic case, typically by several orders of magnitude (the square of the dimensionless Gilbert damping parameter). However, with the addition of a magnetic field transverse to the wire, this behavior is dramatically reversed; up to a critical field strength, analogous to the Walker breakdown field, domain walls in a uniaxial wire propagate faster than in a fully anisotropic wire (without a transverse field). Beyond this critical field strength, precessional motion sets in, and the mean velocity decreases. Our results are based on leading-order analytic calculations of the velocity and critical field as well as numerical solutions of the Landau-Lifshitz-Gilbert equation.

Figure 1

Average DW velocity $V$ as a function of the driving field $|H_1|$ for three values of the transverse field $H_2$. The analytic formulas (solid curves) Eq. (30), for $|H_1|<H_{1,c}$, and Eq. (34), for $|H_1|>H_{1,c}$, are plotted against numerically computed values (open circles). For $H_2=0$, the analytic formula is exact.

Figure 2

DW velocity $V$ as a function of the driving field $|H_1|$ for $H_2=0.2$. The expressions for the small-transverse field Eq. (30) (red curve) and moderate-transverse field Eq. (40) (light blue curve) are plotted against numerically computed values (open circles).

Figure 3

The critical driving field $|H_{1,\mathrm{c}}|$ as a function of the transverse field $H_2$. A linear fit (blue curve) through the numerically computed data (blue diamonds) is plotted alongside the analytical result Eq. (29) (red curve).

Figure 4

The magnetization distribution, $\theta (x,t)$ and $\varphi (x,t)$, for two values of the driving field: $H_1=-0.01$ in (a) and (b) and $H_1=-0.05$ in (c) and (d). The transverse field is taken as $H_2=0.1$ throughout.