Theory of far-infrared reflectivity and surface magnetic polaritons of rare-earth magnets

Abstract

We derive expressions for oblique-incidence reflectivity of bulk and thin-film rare-earth magnets with helical magnetic orderings (spiral and cone states) in the far-infrared frequency region. The main question that is addressed is whether the high metallic reflectivity precludes detection of magnetic features. Significant dips are found at the magnetic resonance frequencies and nonreciprocal reflection can be seen in the spectra. The magnitudes of the dips depend on the magnon damping, which is unknown, but for likely values the dips are about at the limit of experimental detectability. Dispersion curves of surface magnetic polaritons on a semi-infinite rare earth in the Voigt geometry are presented for both spiral and cone states. In the spiral state, the surface polaritons are reciprocal and exhibit backbending near the magnetostatic frequency limit. In the cone state, we find new surface modes with no magnetostatic analogs and the propagation of the surface polaritons is nonreciprocal. The curves in this state also bend back toward the light line near the magnetostatic frequency limit. In addition, the surface wave in both states is strongly localized to the surface and highly attenuated during its propagation. We conclude with numerical calculations for the attenuated-total-reflection (ATR) spectra of these materials. The ATR dips are much stronger than those predicted for ordinary reflectivity and should be observable with existing experimental techniques. We speculate that this result is general, so that ATR essentially overcomes the problem of metallic reflectivity.