Eddy-current losses in Mn-Zn ferrites

We predict the contribution of eddy currents to power losses in polycrystalline Mn-Zn ferrites and apply it to experimental results obtained on a broad frequency range in different commercial materials and differently sized ring samples. It is verified by theory and experiment that the eddy currents can, in sufficiently large specimens, measurably contribute to the energy dissipation, in conjunction with spin damping mechanisms. In this context, the direct role of the domain wall processes is shown to be negligible, with the so-called classical losses, chiefly associated with the rotations, accounting for all of the eddy-current losses. To predict the frequency dependent classical loss Weddy (cl)(f) in the actual heterogeneous material, the electromagnetic field equations are formulated under a variational multiscale approach, with fine and coarse scales identified with the thickness of grain boundary layers and grain size, respectively. The eddy-current patterns are correspondingly observed to evolve, on increasing the magnetizing frequency, from mostly grain-confined to circulating on the scale of the sample cross-section. Based on the measurement of the electrical resistivity versus frequency and knowledge of the average grain size, an overall frequency dependence of the classical loss Weddy (cl)(f) is formulated. With the energy loss W(f) measured from dc to 10 MHz in different types of commercial Mn-Zn ferrites having different cross-sectional areas, it is found that the W(f) behaviors in a given material all tend to fall onto a single W(f) curve once purged of the calculated Weddy (cl)(f). The residual size-independent loss is the one associated with the damping of the precessional spin motion, which can separately be accounted for.