Evidence of an Improper Displacive Phase Transition in Cd_{2}Re_{2}O_{7} via Time-Resolved Coherent Phonon Spectroscopy.

We have used a combination of ultrafast coherent phonon spectroscopy, ultrafast thermometry, and time-dependent Landau theory to study the inversion symmetry breaking phase transition at T_{c}=200  K in the strongly spin-orbit coupled correlated metal Cd_{2}Re_{2}O_{7}. We establish that the structural distortion at T_{c} is a secondary effect through the absence of any softening of its associated phonon mode, which supports a purely electronically driven mechanism. However, the phonon lifetime exhibits an anomalously strong temperature dependence that decreases linearly to zero near T_{c}. We show that this behavior naturally explains the spurious appearance of phonon softening in previous Raman spectroscopy experiments and should be a prevalent feature of correlated electron systems with linearly coupled order parameters.