Electron coherent phonon coupling in Pr$_{0.5}$Ca$_{1.5}$MnO$_4$ measured with ultrafast broadband spectroscopy

Photoexcitation of single-layered La$_{0.5}$Mn$_{1.5}$MnO$_4$ has played a key role in understanding orbital ordering and non-thermal states in the manganites. However, while orbital ordering in La$_{0.5}$Sr$_{1.5}$MnO$_4$ breaks the in-plane C$_4$ symmetry, many layered manganites show much more complex phase diagrams in which orbital ordering emerges from an already symmetry-broken high-temperature phase and also exhibit additional low-temperature phases. In this work, we examine the role of these phases in relation to orbital ordering in the single-layered manganite Pr$_{0.5}$Ca$_{1.5}$MnO$_4$ with a combination of optical reflection anisotropy and ultrafast broadband pump-probe spectroscopy. We find that the reflection anisotropy, measured in equilibrium, is strongly sensitive to charge and orbital-ordering transition only. However, the ultrafast response, measuring the non-equilibrium state is sensitive to all phases. In particular, we deduce that coherent phonons modulate unoccupied electronic states that are sensitive to the different phases of the material. This gives rise to a non-linear scaling of the phonon signal with pump fluence at specific probe wavelengths.