Origin of excess core loss in amorphous and nanocrystalline soft magnetic materials

Core losses of amorphous and nanocrystalline soft magnetic ribbons with a range of saturation magnetostriction constants (${\ensuremath{\lambda}}_{\mathrm{s}}$) from near zero to $+38\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ have been investigated experimentally with complementary micromagnetic simulations in order to clarify the effect of magnetostriction on the excess loss, i.e., the core loss component unaccounted for by the hysteresis and classical eddy-current losses. The excess loss at 400 Hz and a peak polarization of 1.0 T (${P}_{\mathrm{ev}}$) has been found to increase linearly with ${\ensuremath{\lambda}}_{\mathrm{s}}$, and ${P}_{\mathrm{ev}}$ varies considerably between $0.27\phantom{\rule{0.28em}{0ex}}\mathrm{k}\mathrm{W}/{\mathrm{m}}^{3}$ for near zero-magnetostrictive nc-$\mathrm{F}{\mathrm{e}}_{85}\mathrm{N}{\mathrm{b}}_{6}{\mathrm{B}}_{9}$ and $11.0\phantom{\rule{0.16em}{0ex}}\mathrm{k}\mathrm{W}/{\mathrm{m}}^{3}$ for amorphous $\mathrm{F}{\mathrm{e}}_{80}\mathrm{S}{\mathrm{i}}_{11}{\mathrm{B}}_{9}$ with ${\ensuremath{\lambda}}_{\mathrm{s}}=+38\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. By substituting the domain wall damping coefficient (${\ensuremath{\beta}}_{\mathrm{dw}}$) for the eddy current one in Bertotti's statistical model of core losses, the excess loss is predicted to be proportional to $\sqrt{{\ensuremath{\beta}}_{\mathrm{dw}}}$, indicating that the observed linear increase of ${P}_{\mathrm{ev}}$ is caused by mechanisms where ${\ensuremath{\beta}}_{\mathrm{dw}}$ increases with ${\ensuremath{\lambda}}_{\mathrm{s}}^{2}$. Such a quadratic relationship is confirmed by modeling a free wall damping process with lattice anelasticity, suggesting that the anelastic lattice relaxation mediated by magnetostriction could be a potential mechanism. However, the absolute value of ${\ensuremath{\beta}}_{\mathrm{dw}}$ remains open because of the uncertainty of the viscosity, and further investigation is needed to validate the mechanism of the excess loss induced by magnetostriction. Our results show that magnetostriction plays a significant role in determining the excess loss in the exchange-softened magnetic materials, and lowering the saturation magnetostriction is crucial for reducing the wall damping effect and the core loss at high frequencies.