Phonon-Magnon Interaction in Magnetic Crystals. II. Antiferromagnetic Systems

A theoretical study of phonon-magnon interaction in antiferromagnets is made on the basis of a microscopic mechanism developed earlier. The mechanism, which in essence takes into account the mixing of excited orbital states with the ground orbital states of the magnetic ions owing to crystal field oscillations, is applied to a crystal which can be subdivided into two interpenetrating identical sublattices coupled antiferromagnetically.The interaction terms for one-phonon direct processes are first derived following the methods of the previous paper. The expressions for phonon-magnon relaxation times are then obtained for these processes in the low-temperature limit. It is found that the relaxation time τₛₚ is inversely proportional to fifth power of temperature (T⁵) in this region. Numerical estimate for MnF₂ at 10^∘{}K gives the tentative value of τₛₚ~10^-8 sec.