  A model for domain wall motion in ferromagnets is analyzed. Long-range
magnetic dipolar interactions are shown to give rise to self-similar dynamics
when the external magnetic field is increased adiabatically. The power spectrum
of the resultant Barkhausen noise is of the form $1/\omega^\alpha$, where
$\alpha\approx 1.5$ can be estimated from the critical exponents for interface
depinning in random media.
