Influence of magnetic viscosity on domain wall dynamics under spin-polarized currents

We present a theoretical study of the influence of magnetic viscosity on current-driven domain wall dynamics. In particular we examine how domain wall depinning transitions, driven by thermal activation, are influenced by the adiabatic and nonadiabatic spin torques. We find the Arrhenius law that describes the transition rate for activation over a single energy barrier remains applicable under currents but with a current-dependent barrier height. We show that the effective energy barrier is dominated by a linear current dependence under usual experimental conditions, with a variation that depends only on the nonadiabatic spin-torque coefficient $\beta$.

Figure 1

(Color online) Escape of a particle over an energy barrier by thermal activation. The barrier height is ${ϵ}_b=U\left(x_b\right)-U\left(x_a\right)>0$ and the characteristic potential well width is $\Delta x=x_b-x_a>0$.

Figure 2

(Color online) (a) Domain wall potential energy $U$ for three different applied fields with $H_p/M_s=1$. (b) Field dependence of the energy barrier ${ϵ}_{b,0}$, where squares correspond to the numerically calculated values and the solid line represents a fit of the form ${ϵ}_{b,0}=C{\left(1-h^{\mu }\right)}^{\nu }$.

Figure 3

(Color online) Field dependence of (a) barrier width $\Delta x$ and (b) characteristic frequencies ${\omega }_{a,b}$. The latter are proportional to the curvature of the potential well and energy barrier, respectively. Solid lines represent the anisotropy defect, dashed lines represent the field defect.

Figure 4

(Color online) Energy barrier ${ϵ}_b$ (in reduced units) as a function of (a) and (b) applied field $h$, with (a) $\overline{u}=0.1$ and (b) $\overline{u}=-0.1$, and (c) and (d) applied current $\overline{u}$, with (c) $h=0.1$ and (d) $h=0.5$, for three values of the nonadiabatic torque coefficient $\beta$.