Parallel-pumping studies of magnon damping in MnF2

The relaxation rate of electronic magnons with wave vectors $\overrightarrow{\mathrm{k}}$ smaller than $0.03k_{\mathrm{ZB}}$ has been measured as a function of temperature and $\overrightarrow{\mathrm{k}}$, using the technique of parallel pumping. The experiments utilized high magnetic fields to probe the region just below the antiferromagnetic spin-flop transition, which then involves magnons with microwave frequencies. The measured relaxation rates in the temperature range 1.4 to 10 K span the range ${10}^5$-${10}^6$ ${\sec }^{-1\mathrm{}}$, and show two distinct temperature dependences. At lower temperatures a nearly linear $T$ dependence, and at higher ones a $T^4$ dependence, are observed. Magnon-relaxation calculations reveal that at lower temperatures the three-magnon dipole-dipole interaction is probably responsible for the damping, whereas four-magnon exchange and anisotropy interactions prevail at the higher ones, in satisfactory agreement with experiment. The latter result is in agreement with antiferromagnetic resonance measurements in Mn${\mathrm{F}}_2$, which showed the linewidth to be accurately described by the four-magnon process for $T>\mathrm{}5\mathrm{}$ K.