  Cavity photons and ferromagnetic spins excitations can exchange information
coherently in hybrid architectures, at speeds set by their mutual coupling
strength. Speed enhancement is usually achieved by optimizing the geometry of
the electromagnetic cavity. Here we show that the geometry of the ferromagnet
plays also an important role, by setting the fundamental frequency of the
magnonic resonator. Using focused ion beam patterning, we vary the aspect ratio
of different Permalloy samples reaching operation frequencies above 10 GHz
while working at low external magnetic fields. Additionally, we perform broad
band ferromagnetic resonance measurements and cavity experiments that
demonstrate that the magnon-photon coupling strength can be estimated using
either open transmission lines or resonant cavities, yielding very good
agreement. Finally, we describe a simple theoretical framework based on
electromagnetic and micromagnetic simulations that successfully accounts for
the experimental results. This approach can be used to design hybrid quantum
systems exploiting whatsoever magnetostatic mode excited in ferromagnets of
arbitrary size and shape and to tune their operation conditions.
