Domain structure and energy losses up to 10 kHz in grain-oriented Fe-Si sheets

We investigate in theory and experiment the frequency dependence of magnetic losses in Grain-Oriented 0.29 mm thick high-permeability steel sheets up to 10 kHz. Such unusually broad frequency range, while responding to increasing trends towards high-frequency regimes in applications, is conducive to a complex evolution of the magnetization process, as imposed by increasing frequencies to a non-linear high-permeability saturable material. We show that the concept of loss decomposition, supported by observations of the domain wall dynamics through Kerr experiments, is effective in the assessment of the broadband frequency dependence of the energy loss. By calculating, in particular, the instantaneous and time averaged macroscopic induction profiles across the sheet thickness through the Maxwell's diffusion equation, the classical loss component Wclass, versus frequency f and peak polarization Jp is obtained. Instrumental to a simplified theoretical approach is the assumption of the normal magnetization curve as the magnetic constitutive equation of the material. While the hysteresis loss Whyst invariably increases with frequency, the excess loss Wexc, the quantity directly associated with the eddy currents circulating around the moving domain walls, tends to vanish upon increasing both frequency and induction values. The Kerr experiments actually show that, while the oscillating 180° domain walls can adjust to the depth of the induction profile by bowing at low Jp values, the magnetization reversal at high inductions and frequencies occurs by inwardly motion of symmetric fronts originating at the sheet surface, according to a classical framework.