  We present a combined Brillouin light scattering and micromagnetic simulation
investigation of the magnetic-field dependent spin-wave spectra in a hybrid
structure made of permalloy (NiFe) artificial spin-ice (ASI) systems, composed
of stadium-shaped nanoislands, deposited on the top of an unpatterned permalloy
film with a nonmagnetic spacer layer. The thermal spin-wave spectra were
recorded by Brillouin light scattering (BLS) as a function of the magnetic
field applied along the symmetry direction of the ASI sample. Magneto-optic
Kerr effect magnetometry was used to measure the hysteresis loops in the same
orientation as the BLS measurements. The frequency and intensity of several
spin-wave modes detected by BLS were measured as a function of the applied
magnetic field. Micromagnetic simulations enabled us to identify the modes in
terms of their frequency and spatial symmetry and to extract information about
the existence and strength of the dynamic coupling, relevant only to a few
modes of a given hybrid system. Using this approach, we suggest a way to
understand if dynamic coupling between ASI and film modes is present or not,
with interesting implications for the development of future three-dimensional
magnonic applications and devices.
