  Magnetic field driven domain wall velocities in [Co/Ni] based multilayers
thin films have been measured using polar magneto-optic Kerr effect microscopy.
The low field results are shown to be consistent with the universal creep
regime of domain wall motion, characterized by a stretched exponential growth
of the velocity with the inverse of the applied field. Approaching the
depinning field from below results in an unexpected excess velocity with
respect to the creep law. We analyze these results using scaling theory to show
that this speeding up of domain wall motion can be interpreted as due to the
increase of the size of the deterministic relaxation close to the depinning
transition. We propose a phenomenological model which allows to accurately fit
the observed excess velocity and to obtain characteristic values for the
depinning field $H_d$, the depinning temperature $T_d$, and the characteristic
velocity scale $v_0$ for each sample.
