Scattering of Light by One- and Two-Magnon Excitations

TLDR

The study develops and experimentally tests a theory of light scattering by one‑ and two‑magnon excitations in MnF₂ and FeF₂, including a second‑order scattering model based on excited‑state exchange between sublattices. First‑order scattering arises from either direct magnetic‑dipole coupling or indirect electric‑dipole coupling via spin‑orbit interaction, while second‑order scattering is described by an excited‑state exchange mechanism constrained by D₂h¹² symmetry that predicts intensity, polarization, and magnetic‑field dependence. Measurements confirm that the spin‑orbit mechanism dominates first‑order scattering, that second‑order scattering is stronger and not a higher‑order spin‑orbit effect, and that the second‑order spectra quantitatively map magnons at specific Brillouin‑zone points, allowing full determination of the FeF₂ magnon dispersion.

Abstract

We present details of the theory of light scattering by one- and two-magnon excitations, and compare predictions of the theory with our experimental results in the tetragonal antiferromagnets Mn${\mathrm{F}}_{2}$ and Fe${\mathrm{F}}_{2}$. Two mechanisms are considered for first-order (one-magnon) light scattering: one involving a direct magnetic-dipole coupling and the other involving an indirect electric-dipole coupling which proceeds through a spin-orbit interaction. Experimental results on the intensity and polarization selection rules of the first-order scattering show that the spin-orbit mechanism is the important one. On the other hand, second-order (two-magnon) scattering is observed to be even stronger than first-order scattering in these antiferromagnets, implying that the process is not due to the spin-orbit mechanism taken to a higher order in perturbation theory. A theory of second-order scattering based on an excited-state exchange interaction between opposite sublattices is given. When coupled with group-theoretical requirements for the ${{D}_{2h}}^{12}$ crystals, the mechanism predicts the intensity, the polarization selection rules, and the magnetic field dependence of the second-order spectrum. Features of the second-order spectra are related quantitatively to magnons at specific points in the Brillouin zone. Analysis of both first- and second-order magnon scattering has thus enabled determination of the complete magnon dispersion relation for Fe${\mathrm{F}}_{2}$.