Domain Wall Depinning in Random Media by ac Fields

The viscous motion of an interface driven by an ac external field of frequency ${\omega }_0$ in a random medium is considered here in the nonadiabatic regime. The velocity exhibits a smeared depinning transition showing a double hysteresis which is absent in the adiabatic case ${\omega }_0\to 0$. Using scaling arguments and an approximate renormalization group calculation we explain the main characteristics of the hysteresis loop. In the low frequency limit these can be expressed in terms of the depinning threshold and the critical exponents of the adiabatic case.

Figure 1

Numerical solution of Eq. (1) for a 1D interface in the dc (solid line) and ac case (dotted line) for $\omega ={\omega }_0/{\omega }_P=0.3$ and $h_0>h_P\approx 0.27$. $x$ is discretized in $N=1000$ sites and $g$ random in $[-0.5,0.5]$. The solution is averaged over typically 100 disorder ($g$) configurations. The arrows show the direction of the hysteresis: for $|h(t)|<h_P$ it is clockwise and anticlockwise for $|h(t)|>h_P$. The dashed line shows the hysteresis in the case $h_0\approx h_P$.

Figure 2

Schematic frequency-field diagram for the depinning in an ac external field (with $h_0>h_P$): For $0<{\omega }_0\ll {\omega }_P$ the depinning transition is smeared but traces of the ${\omega }_0=0$ transition are seen in the frequency dependency of the velocity at $h=h_P$. This feature disappears for ${\omega }_0\gg {\omega }_P$.

Figure 3

Numerical results for $v(h_P)$, using Eq. (1), as a function of $\omega ={\omega }_0/{\omega }_P$ in $D=1$. The dashed line shows the prediction of Eq. (4) with $\beta /\nu z=0.17$, in good agreement with the value 0.19 found in 12.