  We demonstrate theoretically a strong local enhancement of the intensity of
the in-plane microwave magnetic field in multilayered structures made from a
magneto-insulating yttrium iron garnet (YIG) layer sandwiched between two
non-magnetic layers with a high dielectric constant matching that of YIG. The
enhancement is predicted for the excitation regime when the microwave magnetic
field is induced inside the multilayer by the transducer of a stripline
Broadband Ferromagnetic Resonance (BFMR) setup. By means of a rigorous
numerical solution of the Landau-Lifshitz-Gilbert equation consistently with
the Maxwell's equations, we investigate the magnetisation dynamics in the
multilayer. We reveal a strong photon-magnon coupling, which manifests itself
as anti-crossing of the ferromagnetic resonance (FMR) magnon mode supported by
the YIG layer and the electromagnetic resonance mode supported by the whole
multilayered structure. The frequency of the magnon mode depends on the
external static magnetic field, which in our case is applied tangentially to
the multilayer in the direction perpendicular to the microwave magnetic field
induced by the stripline of the BFMR setup. The frequency of the
electromagnetic mode is independent of the static magnetic field. Consequently,
the predicted photon-magnon coupling is sensitive to the applied magnetic field
and thus can be used in magnetically tuneable metamaterials based on
simultaneously negative permittivity and permeability achievable thanks to the
YIG layer. We also suggest that the predicted photon-magnon coupling may find
applications in microwave quantum information systems.
