Microscopic Theory of Far-Infrared Two-Magnon Absorption in Antiferromagnets. I. Perturbation-Theory Search and Application of Fourth-Order Process to FeF2

Abstract

A microscopic description of the mechanism responsible for an absorption line observed in antiferromagnetic Fe${\mathrm{F}}_2$ at 154 ${\mathrm{cm}}^{-1\mathrm{}}$ is proposed. The mechanism appears to account for the properties of the observed line which are described in the preceding paper. In isolating the proposed mechanism, we set up a model which includes magnon, phonon, exciton, and photon fields and their interactions. The mechanism involves an indirect coupling between odd-parity excitons and magnons which we have previously called the odd-exciton-magnon interaction. This coupling is a consequence of the combined action of the spin-orbit interaction and the quadrupole-dipole part of the spin-orbit interaction. A search through fourth order in perturbation theory in this model yields several other possible processes. Our estimates indicate that the process we propose is the largest contributor in Fe${\mathrm{F}}_2$ and that a third process, involving a phonon, may be contributing to the absorption intensity. The proposed process is used to derive the spin Hamiltonian used in the preceding paper and to estimate the intensity and polarization ratio.