Investigation of Magnetic Properties of Multilayer Thin Films with Spin-Wave Resonance

A theory has been developed to simulate spin-wave resonance (SWR) modes in the multilayer systems consisting of alternate magnetic and nonmagnetic layers. An equation of motion of magnetization with Gilbert-type damping parameter for simulating SWR modes was used. It has been realized that the theory developed for the magnetic multilayer films is suitable to study the spin dynamics and extract various magnetic parameters. It has been shown that SWR modes strongly depend on an effective magnetic anisotropy constant (Keff), interlayer exchange coupling constant (A12) and effective magnetization (Meff). The nature of the effective magnetic anisotropy and interlayer exchange coupling constants has been investigated by using the developed SWR theory in detail. The separation between optic and acoustic modes strongly depends on the magnitude of the interlayer exchange coupling constant, whereas the relative position of the acoustic and optic modes depends on the sign of A12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A_{12}$\end{document}. With increasing the interlayer exchange coupling constant, the resonance field of the optic mode decreases (increases) for ferromagnetic (antiferromagnetic) coupling. When the effective magnetic anisotropy constant increases, the resonance field of the acoustic and optic modes increases for both the ferromagnetic and antiferromagnetic couplings. The increasing of the effective magnetization results in decreasing of the resonance field of SWR mode at parallel geometry, whereas that of SWR mode increases at the perpendicular geometry. The results are compatible to the other theories and experimental results.