Soft Acoustic Mode at the Cooperative Jahn-Teller Phase Transition in Dy VO4

The temperature dependence of the elastic constant $\frac{1}{2}(c_{11}-c_{12})$ shows that the $B_{1g}$ acoustic phonon branch is the soft mode at the cooperative Jahn-Teller phase transition in DyV${\mathrm{O}}_4$. For $T>\mathrm{}2\mathrm{}{T}_{ D}$ ($T_{ D}$ is the transition temperature) the data can be described by mean field theory and show that the dominant driving mechanism for the transition is the coupling of the Jahn-Teller ions to the static elastic strain. However, for $T_D<T<\mathrm{}2\mathrm{}{T}_D$ we find significant deviations from mean field theory due to critical fluctuations.