New characteristic parameter of energy loss in permalloy

Abstract

Characteristic parameters of energy storage and loss in soft magnetic materials (SMMs), product S of initial susceptibility $ \chi_\mathrm{i} $ and resonance frequency $ \omega_\mathrm{r} $ and product L of maximum $ \chi_\mathrm{m}^{^{\prime\prime}} $ and half width $ \Delta\omega $ of imaginary part, were introduced in permalloy films. Expressions of characteristic parameters were derived from Landau–Lifshits–Gilbert equation with a general anisotropic free energy model. It was found S = L equals to intrinsic quantity of SMMs $ {Q} \equiv \gamma M_\mathrm{s} \sqrt{1+H_\perp/H_\parallel} $ , where γ is the gyromagnetic ratio, $ M_\mathrm{s} $ is the saturation magnetization, and $ H_\perp $ and $ H_\parallel $ are mutually orthogonal effective magnetic fields. In the presence of eddy current, it was found S remains equal to Q while L < Q results from inhomogeneity of microwave magnetic field caused by eddy current. Moreover, a linear scale of $ {L}/{S} $ versus Gilbert damping factor α was found in permalloy films with different thicknesses. Hence, our findings provide a new perspective on energy storage and loss of SMMs.

Keywords

• energy loss
• characteristic parameter
• susceptibility
• permalloy