  The dynamics of a domain wall in magnetostrictive materials is investigated.
The domain wall is modeled by a d-dimensional interface moving in a
d+1-dimensional environment. Long-range demagnetization effects and quenched
disorder are considered, while the external magnetic field is increased at
constant rate. Exact expressions for the average interface velocity and
susceptibility are obtained, resulting that the system is critical when the
demagnetization constant and the average interface velocity vanishes. The
critical exponents are computed to O(4-d). Our predictions are compared with
numerical simulations and Barkhausen noise measurements reported in the
literature.
