# Spin-Wave Modes in Transition from a Thin Film to a Full Magnonic Crystal

## TL;DR

This study investigates the evolution of spin-wave modes during the transition from a thin ferromagnetic film to a full magnonic crystal, revealing complex mode transformations and establishing transition rules through experiments and simulations.

## Contribution

It provides new insights into spin-wave mode evolution and formulates transition rules for modes in hybrid magnonic structures, combining experimental and theoretical approaches.

## Key findings

- Gradual mode transition from film to magnonic crystal observed.
- Complex spin-wave mode structures characterized in different geometries.
- Transition rules for mode transformation derived and validated.

## Abstract

Spin-wave modes are studied under the gradual transition from a flat thin film to a 'full' (one-dimensional) magnonic crystal. For this purpose, the surface of a pre-patterned 36.8 nm thin permalloy film was sequentially ion milled resulting in magnonic hybrid structures, referred to as surface-modulated magnonic crystals, with increasing modulation depth. After each etching step, ferromagnetic resonance measurements were performed yielding the spin-wave resonance modes in backward-volume and Damon-Eshbach geometry. The spin-wave spectra of these hybrid systems reveal an even larger variety of spin-wave states compared to the 'full' magnonic crystal. The measurements are corroborated by quasi-analytical theory and micromagnetic simulations in order to study the changing spin-wave mode character employing spin-wave mode profiles. In backward-volume geometry, a gradual transition from the uniform mode in the film limit to a fundamental mode in the thin part of the magnonic crystal was observed. Equivalently, the first and the second film modes are transform into a center and an edge mode of the thick part of the magnonic crystal. Simple transition rules from the $n^{\mathrm{th}}$ film mode to the $m^{\mathrm{th}}$ mode in the 'full' magnonic crystal are formulated unraveling the complex mode structure particularly in the backward-volume geometry. An analogous analysis was performed in the Damon-Eshbach geometry.