Influence of next nearest neighbor interaction on the spin wave resonance frequency in ferromagnetic heterogeneous bilayer films

The next nearest neighbor (NNN) interaction is sometimes non-negligible for the application of spintronic devices in magnetic materials. Thus, understanding the contribution of the NNN interaction has been a significant research target. Although numerous approaches have been explored to control the NNN interaction, few reports of the competition of the NNN interaction of heterogeneous bilayer films have been presented. In this work, the spin wave resonance frequency of ferromagnetic heterogeneous bilayer films with the NNN interaction has been investigated using the linear spin wave approximation and Green's function methods. To clarify the contribution of the NNN interaction, the effects of the characteristic parameters of the system, such as interface coupling, surface anisotropy, external magnetic field, film thicknesses and symmetry, on the spin wave resonance frequency have also been studied in detail. It is found that the spin wave resonance frequencies of three lower-frequency modes depend strongly on the thickness of film. The frequency gap between the two neighbor modes is broadened when the thickness of the film is decreased. Besides, the NNN interaction and the symmetry play an important role in increasing the spin wave resonance frequency. Moreover, it is worth noting that the spin wave resonance frequency of the lowest-frequency mode depends weakly on the NNN interaction, the interface coupling, and the symmetry. Considering these effects in an opportune way, the spin wave resonance frequency of ferromagnetic thin film system can be controlled.