Phonon-Magnon Interaction in Magnetic Crystals

A microscopic theory of phonon-magnon interaction in magnetic crystals is developed from first principles. The crystal field oscillations are treated as perturbations which superpose some excited orbital states on the ground orbital state of the magnetic ions. When use is made of these perturbed states as the starting one-electron functions in the second quantization representation, the formulation of the Heisenberg-type exchange interaction furnishes the relevant phonon-magnon interaction terms. Following the above interactions, the phonon-magnon relaxation times are calculated for the processes involving one-phonon direct and two-phonon Raman processes. Estimates made for iron, where the excited orbitals are taken to be the $4p$ and the ground $3d\gamma$ orbitals, yield values for the relaxation time for the one-phonon processes (${\tau }_{\mathrm{sp}}\approx {10}^{-6\mathrm{}}$ sec at 10°K) in agreement with the suggested results. Two-phonon Raman processes do not seem to be important at low temperatures.