Magnetostatic modes in Fibonacci magnetic and nonmagnetic multilayers.

Abstract

We study the magnetostatic modes in a Fibonacci multilayer consisting of alternating magnetic and nonmagnetic layers. The constant of motion, depending on both the in-plane wave vector and the frequency of the mode, is explicitly obtained and used to describe general features of the frequency spectra. Furthermore, spin wave spectra and precession amplitudes of magnetization for a finite Fibonacci multilayer are numerically calculated by the transfer matrix method. For a given in-plane wave vector, the distribution of frequency exhibits a triadic Cantor structure with large gaps in the low-frequency region, small gaps in the high-frquency region, and many ``isolated'' modes in the gaps. The gaps strongly depend on the in-plane wave vector and the thicknesses of the magnetic and nonmagnetic layers. We find three types of states in the quasiperiodic direction: extended states in the high-frequency region near the upper band edge, critical states in the triadic subbands, and surface states in gaps. Besides the conventional Damon-Eshbach surface mode localized at two opposite surfaces of the multilayer for positive and negative wave vectors, respectively, another kind of surface modes are discovered. When the wave vector is reversed, these modes are still localized at the same sides of the multilayer.