Dynamic permeability in a dissipative ferromagnetic medium

It is shown that the dynamic relative permeability in a thin ferromagnetic film with in-plane magnetization in the presence of intrinsic dissipation exhibits negative values for the range of microwave frequencies belonging to those of backward volume spin-wave modes. This is accomplished according to the linearization of the equation of motion in the magnetostatic limit. By studying the coupling of backward volume spin waves with electromagnetic waves in the range of negative permeability the ferromagnetic film can be considered as a magnetic metamaterial.