Additional mode of PbZr$_{x}$Ti$_{1-x}$O$_{3}$ films

In addition to the phonon modes predicted by the selection rule, a phonon mode at 45 cm$^{-1}$ (lower than soft mode frequency) was observed in the first order Raman spectrum of ferroelectric PbZr$_{x}$Ti$_{1-x}$O$_{3}$ films with $x$ = 0 - 1. Thus, this additional mode is not a zone-center mode. Its existence in the first order spectrum is due to the zone folding in structures with strain, defect and disorder. This additional mode, like soft mode, also significantly downshifts as approaching the phase boundaries, e.g. at $x$ = 0.5 and 0.95, or with the grain size change. The similar change of the additional mode and the soft mode implies a strong interaction between the soft mode and the additional mode.