Magnetization Process in Thin Laminations up to 1 GHz

Amorphous and nanocrystalline ribbons with transverse anisotropy have been characterized by magneto-optical, fluxmetric, and transmission line techniques from DC to 1 GHz. The contributions of domain wall displacements and magnetization rotations to the magnetization process, singled out by direct domain observations, consistently fit with the observed dependence of complex permeability and energy losses on frequency. With the domain wall motion suffering progressive hindering with increasing frequency and falling into full relaxation on reaching the MHz range, the magnetization process becomes amenable to a classical description, the concept of loss decomposition being secured. For this description, the conventional rate-independent constitutive relation for the magnetic material proves, however, inadequate. The diffusion equation for the electromagnetic field is therefore coupled with the Landau-Lifshitz-Gilbert equation, taken as a dynamic constitutive magnetic equation, and a solution is worked out by a numerical procedure. Magnetization and eddy-current field are thus obtained versus time at any point of the lamination, account being taken of the exchange field and its restraining action on the skin effect. The so calculated magnetic loss behavior turns out to correctly describe the high-frequency results, while coalescing with the classical eddy-current loss prediction at low frequencies