Surface mode enhancement of the Goos-Hänchen shift in direct reflection off antiferromagnets

We examine how, in the presence of an external magnetic field, the Goos-H\"anchen shift for terahertz radiation reflected, at oblique incidence, off an antiferromagnet can show significantly enhanced values under the right circumstances. Such enhanced shifts, which have associated absorptions in the presence of damping, occur in one of the magnon reststrahl regions and are related to the excitation of surface resonances, which can be considered as extensions of surface polariton modes into the reflectivity regime. Although the enhancement of the Goos-H\"anchen shift due to surface modes is well known in the attenuated total reflection configuration using a three-layer prism geometry, such effects have not previously been reported in direct reflection and only occur here due to the presence of the externally applied field. We confirm the effect using simulations for reflection off ${\mathrm{MnF}}_{2}$ at low temperature and show that only a small applied field is necessary to induce a significant enhancement along with an associated sharp absorption. For a larger field, the effects are less distinct.