Ferromagnetic resonance in three-dimensional tilted-square artificial spin ices

Artificial spin ices (ASIs) arranged in square formations have been explored from the perspective of reconfigurable magnonics. A new frontier in ASIs is their three-dimensional (3D) extension. The analytical and numerical study of such geometries is difficult due to the additional degrees of freedom. Here, we numerically explore the ferromagnetic resonance of the simplest 3D modification of a square ASI: an out-of-plane rotation of the nanomagnets. We consider cases in which the vertex gap can be either kept constant or varying with the tilt angle. We study both remanent and vortex configurations using a semianalytical dynamic approach and micromagnetic simulations. We find that both methods capture the expected qualitative frequency dependence on tilt angle based on the static stray field coupling. However, we also find important limitations for both approaches that depend on the particularities of the shape-dependent demagnetization field. These results showcase advantages and limitations of both methods in their use of predicting and understanding the resonant magnetization dynamics of 3D ASI. © 2024 American Physical Society.