This study presents a general theoretical framework for investigating surface magnon-polaritons in a trilayer system composed of a gyromagnetic slab sandwiched between graphene layers and surrounded by a non-magnetic medium, specifically under the application of a perpendicular static magnetic field. By employing a model based on Maxwell's equations and boundary conditions that incorporate the conductivity tensor of graphene and the permeability tensor of the magnetic medium, we analyze the dispersion relations for both ferromagnetic (using YIG) and antiferromagnetic (using MnF₂) cases. A key finding of this work is that, unlike the non-reciprocal behavior typically observed when magnetic fields are applied parallel to the surface, the surface and bulk modes in this perpendicular configuration exhibit reciprocal propagation. The results demonstrate that the dispersion of these modes is highly tunable through the adjustment of the graphene Fermi level and the magnetic slab thickness. Additionally, we report material-specific phenomena, such as the emergence of ``wing'' and ``ghost'' modes in the ferromagnetic case and a strong dependence on the applied magnetic field magnitude in the antiferromagnetic case. These predictions highlight the potential of graphene-gyromagnetic heterostructures for the development of tunable opto-magnetic and spintronic devices.
Dantas et al. (2026) studied this question.