Microscopic Theory of Far-Infrared 2-Magnon Absorption in Antiferromagnets. II. Second-Order Process and Application to MnF2

A theory of a second-order mechanism giving two-magnon electric dipole absorption in rutile structure antiferromagnets is developed. In the mechanism, the absorption arises from indirect coupling of the spins to the field through the infrared-active optical phonons via the exchange-strictive part of the spin-phonon interaction. Detailed expressions are derived for the constants in the phenomenological Hamiltonian used by Allen et al. in interpreting experiments on a two-magnon electric dipole absorption recently observed in Mn${\mathrm{F}}_2$ at 110 ${\mathrm{cm}}^{-1\mathrm{}}$. Thus, the frequency, temperature dependence, and electric dipole character of the observed line are predicted. To further compare the theory with the Mn${\mathrm{F}}_2$ experiments, a model for the exchange interactions is postulated which gives an expected line shape and magnetic field dependence which are consistent with observations. A very imprecise intensity estimate is also consistent with experiment. The question of the choice between this mechanism and another proposed for the Mn${\mathrm{F}}_2$ line and involving the interaction of the field with the exchange via the perturbation of the electronic orbitals is discussed.