Wave-Vector Dependence of the Jahn-Teller Interactions in TmVO4

The resonant Jahn-Teller coupling of the $B_{2\mathrm{g}}$ acoustic phonon and the Zeeman-split ground doublet in TmV${\mathrm{O}}_4$ has been studied by inelastic neutron scattering. Tuning of the magnetic field provides a means for investigating the wave-vector dependence of the interactions. We find that the coupling is constant in the region where the phonon dispersion is linear, up to 0.4 of the distance to the zone boundary. This agrees with the predictions of a Debye model.