  We show that Barkhausen noise in two-dimensional disordered ferromagnets with
extended domain walls is characterized by the avalanche size exponent $\tau_s
=1.54$ at low disorder. With increasing disorder the characteristic domain size
is reduced relative to the system size due to nucleation of new domains and a
dynamic phase transition occurs to the scaling behavior with $\tau_s=1.30$. The
exponents decrease at finite driving rate. The results agree with recently
observed behavior in amorphous Metglas and Fe-Co-B ribbons when the applied
anisotropic stress is varied.
