Phonon-associated relaxation of local magnons in FeF2:Mn

The ${\mathrm{Mn}}^{2+}$ impurity-associated mode that lies just below the host spin-wave band in Fe${\mathrm{F}}_2$ has a residual linewidth (in the limit of very small impurity concentrations, sample dimension, and temperature) in excess of 1 kOe. This value is surprisingly large, since the $k=0\mathrm{}$ magnon has a linewidth less than 30 Oe and since the down-going impurity mode is energetically the lowest-lying magnetic excitation in the system. In this paper we analyze several phonon-associated processes that would contribute to the decay of local magnon modes in antiferromagnets in the limit of vanishing impurity concentration and zero temperature. We show that the linewidth of the down-going impurity mode ($\nu <1.507\mathrm{}$ THz) can be quantitatively accounted for by the decay into a single acoustic phonon, whereas that of the up-going mode above 1.93 THz is due mainly to decay into a phonon-magnon pair.