Dispersion and Damping of Soft Zone-Boundary Phonons in KMnF3

Neutron inelastic-scattering experiments have been performed upon the cubic perovskite phase of KMn${\mathrm{F}}_3$. The anisotropy in the dispersion of the lowest-energy phonon branch around the $R$ point [${\overrightarrow{\mathrm{q}}}_R=(\frac{1}{2},\frac{1}{2},\frac{1}{2}) a^{*}$] has been determined. The phonon energies remain very low for ($\overrightarrow{\mathrm{q}}-{\overrightarrow{\mathrm{q}}}_R$) along [100], which accounts for the anisotropic x-ray diffuse scattering seen in this material. The energy profiles of the soft modes at (½½½) (${\Gamma }_{25}$) and (½½ 0) ($M_3$) are analyzed on the basis of a damped-harmonic-oscillator model taking into account the effect of the instrumental resolution. For the ${\Gamma }_{25}$ mode, the temperature dependence of the characteristic frequency ${\omega }_0$ is represented by a Curie-Weiss law ${\left(\hslash {\omega }_0\right)}^2=C(T-T_0)$ with $C=0.\mathrm{}11\pm 0.02$ me${\mathrm{V}}^2$ °${\mathrm{K}}^{-1\mathrm{}}$ and $T_0=(186\mathrm{}\pm 2)$ °K. The damping parameter $\Gamma$ increases as the temperature approaches $T_0$.