Equation of motion of domain walls and equivalent circuits in soft ferromagnetic materials

Abstract

The equation of motion for ferromagnetic domain walls is compared with initial permeability measurements of Co-based soft ferromagnetic amorphous ribbons at frequencies in the range 100 Hz–13 MHz. The analysis of these results by complex permeability methods leads to an equivalent circuit formed by a parallel RL arrangement in series with a small resistance RW due to resistance of the measurement coil. This equivalent circuit, however, cannot model the irreversible magnetization behavior for fields higher than the pinning (or propagation) field. It is shown that the equation of motion is also consistent only with the reversible magnetization mechanism, if the displacement term, x, represents instead the bulging of the pinned wall. The correlations between the terms in the equation of motion and the elements of the equivalent circuit are established.