Emergence of flat bands and localized spin-wave modes in coupled bilayer magnonic crystals with different periodicities

Abstract

Magnonic crystals, characterized by their periodic magnetic modulation, are promising metamaterials for nanoscale high-frequency signal processing due to their control over spin-wave properties. This work investigates spin-wave dynamics in bilayer bi-component systems with distinct one-dimensional periodicities, focusing on two configurations: one with a noticeable difference in periodicities and another with a slight mismatch. Both configurations are examined under parallel and antiparallel equilibrium magnetization states. In a system with significantly different periodicities, the parallel configuration exhibits multiple flat bands, which are associated with defect-like behavior, similar to that observed in magnonic crystals with structural defects. In contrast, the antiparallel configuration is characterized by the presence of low-frequency flat bands and the emergence of small band gaps. These dispersionless bands are tunable via the external field. For the bilayer with slightly mismatched periodicities, flat modes appear in both parallel and antiparallel magnetic states. These modes are sensitive to local material arrangement, forming a superlattice of direct and indirect interlayer coupling regions where localization occurs. The findings are supported by micromagnetic simulations, which show good agreement between the two methods. This study demonstrates how interlayer periodicity mismatch, spatial configuration, magnetic coupling, and external fields could control the emergence of localized, flat spin-wave modes, offering routes for reconfigurable magnonic device design.