Dipolar interaction induced band gaps and flat modes in surface-modulated magnonic crystals

Theoretical results for the magnetization dynamics of surface-modulated magnonic crystals (SMMCs) are presented. For such systems, the role of the periodic dipolar field induced by the geometrical modulation is addressed by using the plane-wave method. The results unveil that under the increasing of the etched depth, zones with magnetizing and demagnetizing fields act on the system, in such a way that magnonic band gaps are observed in both Damon-Eshbach (DE) and backward volume (BV) geometries. Particularly, in BV configuration, high frequency band gaps and low frequency nearly at modes are obtained. By controlling the geometry of the etched zones, the frequency modes, spatial profiles and forbidden frequency gaps of spin waves (SWs) can be manipulated. To test the validity of the model, the theoretical results of this work are confirmed by micromagnetic simulations, where a good agreement between both methods is achieved. It is demonstrated that the spin-wave dynamics of a surface modulated magnonic crystal contrasts to bi-component magnonic crystals or periodic arrays of wires, for instance, since the SMMCs allow enhancing the magnetizing character in some regions of the film, promoting thus the confinement of the SWs. The theoretical model allows for a detailed understanding of the physics underlying these kind of systems, thereby providing an outlook to potential applications on magnonic devices.