Scattering of Light by One- and Two-Magnon Excitations

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${\mathrm{F}}_{2}$.