Flat Bands, Indirect Gaps, and Unconventional Spin-Wave Behavior Induced by a Periodic Dzyaloshinskii-Moriya Interaction

Periodically patterned metamaterials are known for exhibiting wave properties similar to the ones observed in electronic band structures in crystal lattices. In particular, periodic ferromagnetic (FM) materials, also known as magnonic crystals (MCs), are characterized by the presence of bands and bandgaps (BGs) at tunable frequencies in their spin-wave (SW) spectrum. While those frequencies typically cover the GHz-range, no fundamental reason prevents one from extending this range towards THz-frequencies, a regime of high importance in communication technologies. Recently, the fabrication of magnets hosting Dzyaloshinskii-Moriya interactions (DMIs) has been pursued with high interest since properties such as the stabilization of chiral spin textures and nonreciprocal SW propagation originate from this antisymmetric exchange interaction. In this context, to further engineer the band structure of MCs, we propose the implementation of MCs with periodic DMIs, which can be obtained, for instance, patterning periodic arrays of heavy metals (HMs) on top of an ultrathin FM film. We demonstrate through theoretical calculations and micromagnetic simulations that such systems exhibit a unique evolution of the standing SWs around the BGs in areas of the FM film that are in contact with the HM wires. We also predict the emergence of at SW bands and indirect magnonic gaps, and we show that these effects depend on the strength of the DMI. This study opens further pathways towards engineered metamaterials for SW-based devices.