  We study the transversal motion of paramagnetic particles on a uniaxial
garnet film, exhibiting a longitudinal ratchet effect in the presence of an
oscillating magnetic field. Without the field, the thermal diffusion
coefficient obtained by video microscopy is $D_{0}\approx 3\times 10^{-4}$ $\mu
m^2/s$. With the field, the transversal diffusion exhibits a giant enhancement
by almost four decades and a pronounced maximum as a function of the driving
frequency. We explain the experimental findings with a theoretical
interpretation in terms of random disorder effects within the magnetic film.
