  Artificial spin ices are periodic arrangements of interacting nanomagnets
successfully used to investigate emergent phenomena in the presence of
geometric frustration. Recently, it has been shown that artificial spin ices
can be used as building blocks for creating functional materials, such as
magnonic crystals, and support a large number of programmable magnetic states.
We investigate the magnetization dynamics in a system exhibiting anisotropic
magnetostatic interactions owing to locally broken structural inversion
symmetry. We find a rich spin-wave spectrum and investigate its evolution in an
external magnetic field. We determine the evolution of individual modes, from
building blocks up to larger arrays, highlighting the role of symmetry breaking
in defining the mode profiles. Moreover, we demonstrate that the mode spectra
exhibit signatures of long-range interactions in the system. These results
contribute to the understanding of magnetization dynamics in spin ices beyond
the kagome and square ice geometries and are relevant for the realization of
reconfigurable magnonic crystals based on spin ices.
