Transverse acoustic phonon anomalies at intermediate wavevectors in MgV$_{2}$O$_{4}$

Magnetic spinels (with chemical formula $AX_{2}$O$_{4}$, with $X$ a 3$d$ transition metal ion) that also have an orbital degeneracy are Jahn-Teller active and hence possess a coupling between spin and lattice degrees of freedom. At high temperatures, MgV$_{2}$O$_{4}$ is a cubic spinel based on V$^{3+}$ ions with a spin $S$=1 and a triply degenerate orbital ground state. A structural transition occurs at T$_{OO}$=63 K to an orbitally ordered phase with a tetragonal unit cell followed by an antiferromagnetic transition of T$_{N}$=42 K on cooling. We apply neutron spectroscopy in single crystals of MgV$_{2}$O$_{4}$ to show an anomaly for intermediate wavevectors at T$_{OO}$ associated with the acoustic phonon sensitive to the shear elastic modulus $\left(C_{11}-C_{12}\right)/2$. On warming, the shear mode softens for momentum transfers near close to half the Brillouin zone boundary, but recovers near the zone centre. High resolution spin-echo measurements further illustrate a temporal broadening with increased temperature over this intermediate range of wavevectors, indicative of a reduction in phonon lifetime. A subtle shift in phonon frequencies over the same range of momentum transfers is observed with magnetic fields. We discuss this acoustic anomaly in context of coupling to orbital and charge fluctuations.