Hysteresis and noise in ferromagnetic materials with parallel domain walls

We investigate dynamic hysteresis and Barkhausen noise in ferromagnetic materials with a huge number of parallel and rigid Bloch domain walls. Considering a disordered ferromagnetic system with strong in-plane uniaxial anisotropy and in-plane magnetization driven by an external magnetic field, we calculate the equations of motion for a set of coupled domain walls, considering the effects of the long-range dipolar interactions and disorder. We derive analytically an expression for the magnetic susceptivity related to the effective demagnetizing factor and show that it has a logarithmic dependence on the number of domains. Next, we simulate the equations of motion and study the effect of the external field frequency and the disorder on the hysteresis and noise properties. The dynamic hysteresis is very well explained by means of the loss separation theory.