# Mode localization in chiral periodic approximants of Fibonacci magnonic superlattices

## TL;DR

This paper explores how Fibonacci-based magnonic structures can control spin-wave behavior with tunable flat bands and spatial localization.

## Contribution

The study introduces aperiodic Fibonacci approximants in chiral nanomagnets to achieve dispersionless flat bands and tunable mode localization.

## Key findings

- Dispersionless flat bands emerge at low frequencies with spatial localization patterns.
- Aperiodic modulation enables modal selectivity through material contrasts in anisotropy and DMI.
- Flat-band excitation frequency window is tunable via external magnetic fields.

## Abstract

Deterministic magnonic systems based on Fibonacci superlattices provide unique opportunities for manipulating spin-wave dynamics beyond the capabilities of simple periodic metamaterials. In this work, one-dimensional periodic approximants of Fibonacci superlattices are studied in both chiral and nonchiral nanomagnets, where a deterministic aperiodic ordering derived from a Fibonacci sequence is implemented through spatial modulations of the saturation magnetization, perpendicular anisotropy, and the interfacial Dzyaloshinskii–Moriya interaction (DMI). A combination of plane-wave calculations and micromagnetic simulations consistently predicts the emergence of dispersionless flat bands at low frequencies, along with their associated spatial localization patterns. The results show that aperiodic modulation encodes modal selectivity, enabling spin-wave modes to localize in regions defined by material contrasts in anisotropy, DMI, and saturation magnetization. Furthermore, it is shown that the frequency window in which the flat bands are excited is determined by the dispersion of the corresponding continuous films and can be tuned by an external magnetic field. This tunability provides a direct means of externally controlling and enhancing the flat-band regime, thereby broadening the operational bandwidth of dispersionless modes. These findings establish periodic approximants of Fibonacci superlattices as promising platforms for reconfigurable, compact magnonic devices, such as filters, multiplexers, and logic elements, in which deterministic spatial-mode control and external-field tunability are essential.