  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. Here, we numerically explore the
ferromagnetic resonance of square ASIs as each nanomagnet is rotated out of
plane into 3D ASIs, in which the vertex gap can be either kept constant or
varying. We study both remanent and vortex configurations using a
semi-analytical dynamic approach and micromagnetic simulations. We find that
both methods show qualitative agreement of the main spectral features. However,
there are important limitations. On one hand, the semi-analytical approach
relies on a minimal model of the demag field, preventing exact predictions. On
the other hand, micromagnetic simulations suffer from sufficient resolution,
making the results grid-dependent and extremely slow. Regardless, both methods
display tunability as a function of the tilt angle. These results showcase
advantages and limitations of both methods and are promising to further our
understanding of 3D ASI dynamics.
