in the $lim_{q \rightarrow 0}$ originates from the differing energy and lengthscales of the two measurements. Owing to temporal resolution, neutron scattering measure fluctuations on the THz timescale while ultrasound measures the dynamic response for long wavelengths typically on the MHz timescale. Similar differences between neutron scattering and ultrasound have previously been reported for spinels in Ref. . The neutron scattering results do not reflect an observable softening of the TA2 phonon on the THz timescale, rather an anomaly over a range of intermediate wavevectors of $\Delta v \approx \left(12 \pm 5\right) \,\%$.

It is interesting to compare our results with theoretical predictions of soft acoustic phonons near a Jahn-Teller distortion. Considering the Jahn-Teller effect and coupling to acoustic phonons, a theoretical model for the phase transition from the tetragonal to the cubic phase is given in papers by Pytte [@Pytte71; @Pytte73]. In the first paper, Pytte presents a theory which models the temperature dependence of the elastic constants as a result of the coupling between the elastic strain tensor and the twofold degenerate $d$ orbitals. Including higher-order anharmonic coupling, the $T$-dependence of the transverse acoustic phonon mode propagating along $[110]$ with polarisation along $[1\overline{1}0]$ – the tetragonal shear elastic 