Negative permeability due to exchange spin-wave resonances in thin magnetic films with surface pinning

TL;DR: In this paper, a theory of the effective permeability of multilayered metamaterials containing thin ferromagnetic layers with magnetization pinned on either one or both surfaces is presented.

Abstract: We report a theory of the effective permeability of multilayered metamaterials containing thin ferromagnetic layers with magnetization pinned on either one or both surfaces. Because of the pinning and small film thickness, the lowest frequency magnetic resonances are due to nonuniform exchange spin waves with frequencies far above those expected for uniform ferromagnetic resonance in known magnetic materials. Yet, the coupling of the nonuniform spin-wave modes to the electromagnetic field is shown to be strong enough to lead, for magnetic parameters characteristic for conventional transition metal alloys, to negative values of the effective permeability at frequencies of several hundred gigahertzs. The permittivity of metals is already negative in this frequency range. Hence, this system represents a negative refractive index metamaterial at subterahertz frequencies. The ways by which to maximize the frequency and the strength of the negative magnetic response are analyzed.