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We consider a single-interface model for the description of Barkhausen noisein soft ferromagnetic materials. Previously, the model had been used only inthe adiabatic regime of infinitely slow field ramping. We introduce finitedriving rates and analyze the scaling of event sizes and durations fordifferent regimes of the driving rate. Coexistence of intermittency, withnon-trivial scaling laws, and finite-velocity interface motion is observed forhigh enough driving rates. Power spectra show a decay $\sim \omega^{-t}$, with$t<2$ for finite driving rates, revealing the influence of the internalstructure of avalanches.Comment: 7 pages, 6 figures, RevTeX, final version to be published in Phys.  Rev.

Finite driving rates in interface models of Barkhausen noise