Predicting Energy Loss and Permeability of Field-Annealed Amorphous and Nanocrystalline Alloys up to 1 GHz

Crucial limitations on the permissible energy dissipation are one main factor hindering the use of soft magnetic cores at high frequencies. However, applications find limited support in present-day empirical magnetic loss models, which can hardly afford seamless high-frequency extrapolation of the predicting tools available at low frequencies. This is the case, for example, of very thin soft magnetic plates and ribbons, where the rise of eddy currents and their shielding effects at high frequencies must be attuned to the rate-dependent magnetic constitutive equation of the material. We provide in this work a comprehensive broadband (DC-1 GHz) magnetic characterization and the associated physical modeling of the energy loss and permeability properties of different types of amorphous and nanocrystalline ribbons,
$6~\mu $
m to
$25~\mu $
m thick, endowed with transverse induced anisotropy (7 – 251 J/m3) and well-defined transverse domain structure. The achieved condition of quasi-linear response and excellent broadband soft magnetic properties is shown to conform to an analytical treatment of the dynamics of the magnetization process, which is mostly accomplished by moment rotations and increasingly so under increasing frequencies. By virtue of their spatially homogeneous character, rotations provide a loss contribution matching the classical loss framework. Its broadband calculation by Maxwell’s diffusion equation is carried out by introducing a rate-dependent magnetic constitutive equation of the material, worked out in terms of complex susceptibility using the Landau-Lifshitz equation. The separation between domain wall (low frequencies) and rotational (high frequencies, including spin damping and eddy currents) loss contributions is eventually obtained across a many-decade-wide frequency range.