Magnon pairs and interactions in a disordered two-dimensional antiferromagnet

Magnon-pair modes and their temperature dependence have been studied by inelastic light scattering in the disordered two-dimensional antiferromagnet ${\mathrm{Rb}}_2$ ${\mathrm{Mn}}_{0.5}$ ${\mathrm{Ni}}_{0.5}$ ${\mathrm{F}}_4$. At 10 K pair modes arising from one-Mn- plus one-Ni-branch magnons, and from two-Ni-branch magnons were observed at 248 and 372 ${\mathrm{cm}}^{-1\mathrm{}}$, respectively. Surprisingly, the former exhibits a scattering efficiency only ∼20% less than the latter, even though the two-Mn-branch magnon pair could not be detected at all. The observed low-temperature pair-mode frequencies and line shapes can be reasonably estimated from the Ising cluster model, using exchange values for $J_{\mathrm{NiNi}}$ and $J_{\mathrm{NiMn}}$ of 58 and 5.8 ${\mathrm{cm}}^{-1\mathrm{}}$, respectively. This model accounts well for the dominant effects of disorder. Upon increasing temperature, both pair modes broaden and renormalize in frequency in essentially the same manner as that previously observed in the ordered two-dimensional isomorphs such as ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$.