Standing spin waves in magnonic crystals

Abstract

The features of standing spin waves (SWs) excited during ferromagnetic resonance in three different one-dimensional magnonic crystals (MC) are intensively studied. The investigated magnonic crystals were: an array of air-spaced cobalt stripes, an array of air-spaced permalloy (Py) stripes, and a bi-component MC composed of alternating Co and Py stripes. All MC structures were made by etching technique from Co and Py thin films deposited onto Si substrates. Two configurations are considered with the in-plane external magnetic field applied parallel or perpendicular to the stripes. The supporting calculations are performed by the finite element method in the frequency domain. A number of intensive SW modes occurred in periodic structures under ferromagnetic resonance conditions as a consequence of standing spin waves excitation. These modes were analyzed theoretically in order to explain the origins of SW excitations. With the support of numerical calculations, we analyze also the possible scenarios for the occurrence of standing SWs in the investigated structures. It is demonstrated that the SW propagation length is an important factor conditioning the standing SW formation in MCs.

Nonreciprocal dispersion of spin waves in ferromagnetic thin films covered with a finite-conductivity metal

“…The bound-ary conditions for dynamic components of the magnetization vector are imposed only via LL and Maxwell equations, these provide zero of the first derivative of the dynamical magnetization with respect to the normal to the surface. [34][35][36] After applying the Bloch theorem in linearized LL equation and in Maxwell equations the following set of equations is formed:…”

“…The FEM has already been used successfully for calculating the dispersion of SWs in thin films. 4,32,34 The paper is organized as follows. In Section II we present the FEM and a semi-analytical method for the solution of the LL and Maxwell equations in the magnetostatic approximation for a magnetic film covered with a metal layer.…”

Control of spin-wave excitations in deterministic fractals

“…An adequate tuning of the modulation enables one to tailor band gaps in the material and to control the generation and propagation of spin waves that are limited to certain permitted frequency ranges [19]. The concept of magnonic crystals is not limited only to propagating spin-wave modes but also standing spin waves are in the focus of research [20,21].…”

Role of boundaries in micromagnetic calculations of magnonic spectra of arrays of magnetic nanoelements

“…[1][2][3][4][5][6] In particular, investigations of propagating and standing spin waves in such structures are in the focus of one of the youngest areas of magnetism-magnonics. 7,8 From the point of view of technological applications, the study of spin waves in periodic magnetic structures has attracted a great deal of attention for two main reasons.…”