Ultrasonic Attenuation near the Soft-Mode Transition in KMnF3

The frequency and temperature dependence of the longitudinal ultrasonic attenuation along the [123] direction of KMn${\mathrm{F}}_3$ has been measured above the structural phase transition near $T_A=186\mathrm{}$ K. The attenuation of 30, 90, and 270-MHz sound was measured and was found to have a critical contribution which diverges as $\Delta \alpha =A{\omega }^x{\epsilon }^{-\eta }$ (with $x=1.18\mathrm{}\pm 0.03$ and $\eta =1.30\mathrm{}\pm 0.04$) in the region $0.001<\mathrm{}\epsilon <0.10\mathrm{}$, where $\epsilon =\frac{(T-T_A)}{T_A}$. Additional data taken at 150 MHz support this conclusion. The best fits over the whole range of $\epsilon$ were found by allowing the background attenuation to be a varying parameter of the fit. We do not observe any evidence of the crossover behavior predicted by Schwabl and reported by Fossheim et al., nor do we see the ${\omega }^2$ dependence predicted by Pytte and by Schwabl.