Dynamic negative permeability in a lossless ferromagnetic medium

It is shown according to analytical and numerical calculations that in a lossless and in-plane saturated ferromagnetic film the dynamic permeability calculated in the magnetostatic limit is negative for frequencies corresponding to those of the so called backward volume spin waves. These spin excitations have frequencies in the lowest part of the spectrum lying between the ferromagnetic resonance and the Larmor resonance. The negative sign of the dynamic permeability (real part) is connected to the peculiar dynamical properties of the backward spin waves. At the Larmor resonance frequency and just above it the electromagnetic radiation can be coupled to backward spin waves allowing the ferromagnetic film to behave as a magnetic metamaterial with negative permeability.