Phonon-magnon relaxation effects in ferrimagnetic resonance (Europium Iron Garnet)

Phonon-magnon interaction mechanisms arising from a microscopic formulation of the exchange modulation by crystal field oscillations are discussed. The processes considered involve two magnons, one of acoustical mode and the other of exchange (optical) mode and one phonon of the longitudinal optical mode. These three-boson processes are found to be important for the resonance relaxation effects in ionic ferrimagnets such as Europium Iron Garnet (EuIG). The linewidth contribution from the decay of a uniform mode magnon in conjunction with exchange mode magnon with the simultaneous creation of an optical phonon is calculated. In the low temperature region it is found to be proportional to ω H exp [-θ E/T]T-1, where ωH is the operating frequency, θ E the Einstein temperature and T the temperature. This is in very good agreement with the empirical relation which fits the experimental data of LeCraw et al. on EuIG. The high temperature data are explicable in terms of the exact relation which involves ω HJM2(T)eθE/T [eθ E/T-1]-2T-1/geff(T), the coupling parameter JM(T) and geff(T) being temperature dependent in this region