Curvature-driven ac-assisted creep dynamics of magnetic domain walls

The dynamics of micrometer-sized magnetic domains in ultrathin ferromagnetic films is so dramatically slowed down by quenched disorder that the spontaneous elastic tension collapse becomes unobservable at ambient temperature. By magneto-optical imaging we show that a weak zero-bias ac magnetic field can assist such curvature-driven collapse, making the area of a bubble to reduce at a measurable rate, in spite of the negligible effect that the same curvature has on the average creep motion driven by a comparable dc field. An analytical model explains this phenomenon quantitatively.

Figure 1

Schematics of the magnetic field protocol. Pulses applied to grow the domain (red) are followed by the ac-driving pulses (green) with amplitudes $H_{\uparrow }$ and $-H_{\downarrow }$. The sequence of PMOKE images in the bottom corresponds to the case $H_{\uparrow }=H_{\downarrow }$ for an increasing number $N$ of pulses. (Inset) Diagram of the contour ${\mathrm{\Gamma }}_t$ of a typical domain at an arbitrary time $t$, where $u_t\left(\theta \right)$ indicates the domain profile measured from the average radius ${\rho }_t\left(\theta \right)$. ${\mathbf{F}}_e$ and ${\mathbf{F}}_H$ are the elastic and field normal forces per unit length, respectively.

Figure 2

Field pulse asymmetry $\mathrm{\Delta }H$ used to compensate the curvature collapse of domains with different initial radii $R$. (Inset) Evolution of the domain area $A$ with the pulse number, for symmetric pulses $\mathrm{\Delta }H=0$ and for nearly compensating asymmetric pulses $\mathrm{\Delta }H=0.5\text{Oe}$.

Figure 3

Open symbols and dashed regions show the evolution of the mean value and statistical variance of $\mathrm{\Lambda }\left(N\right)$ (see text) (a) and of the relative domain area change $\mathrm{\Delta }A/A_0$ (b), for different amplitudes of symmetric pulses in sample S2. The black line in (a) is a linear fit of the initial evolution of $\mathrm{\Lambda }\left(N\right)$ with $H$ ranging from 160 to 180 Oe, yielding the micromagnetic constant $C$. In (b) numerical simulation results are shown with full symbols. Inset (c) shows DW mean squared displacements for $H=160$ Oe pulses.