Finite driving rates in interface models of Barkhausen noise

We consider a single-interface model for the description of Barkhausen noise in soft ferromagnetic materials. Previously, the model was used only in the adiabatic regime of infinitely slow field ramping. We introduce finite driving rates and analyze the scaling of event sizes and durations for different regimes of the driving rate. Coexistence of intermittency, with nontrivial scaling laws, and finite-velocity interface motion is observed for high enough driving rates. Power spectra show a decay approximately omega(-t), with t<2 for finite driving rates, revealing the influence of the internal structure of avalanches.