# Modulation of Standing Spin Waves in Confined Rectangular Elements

## TL;DR

This paper explores how to control spin waves in magnetic nanostructures by adjusting material properties and shape.

## Contribution

A new method to modulate standing spin waves in confined rectangular elements using micromagnetic simulations and FMR experiments.

## Key findings

- Bulk and edge modes hybridize in magnetic elements, affecting spin wave behavior.
- Reducing MS increases frequencies of Kittel and standing spin waves.
- Changing the aspect ratio splits spin wave modes, revealing new magnetic spectra.

## Abstract

Magnonics is an emerging field within spintronics that focuses on developing novel magnetic devices capable of manipulating information through the modification of spin waves in nanostructures with submicron size. Here, we provide a confined magnetic rectangular element to modulate the standing spin waves, by changing the saturation magnetisation (MS), exchange constant (A), and the aspect ratio of rectangular magnetic elements via micromagnetic simulation. It is found that the bulk mode and the edge mode of the magnetic element form a hybrid with each other. With the decrease in MS, both the Kittel mode and the standing spin waves undergo a shift towards higher frequencies. On the contrary, as A decreases, the frequencies of standing spin waves become smaller, while the Kittel mode is almost unaffected. Moreover, when the length-to-width aspect ratio of the element is increased, standing spin waves along the width and length become split, leading to the observation of additional modes in the magnetic spectra. For each mode, the vibration style is discussed. These spin dynamic modes were further confirmed via FMR experiments, which agree well with the simulation results.