Stokes to anti-Stokes intensity ratio in Raman spectra of the soft mode in KH2PO4 near the phase transition temperature

We investigate the Stokes to anti-Stokes intensity ratio for the Raman spectrum of a central peak in a potassium dihydrogen phosphate (KDP) crystal. The ratio deviates from the Boltzmann factor as the temperature approaches the phase transition temperature. The response functions evaluated by three ways assuming the fluctuation–dissipation theorem do not agree in a frequency region below ～30 cm^?1. This means that the usual relation based on the fluctuation–dissipation theorem are not directly applicable to the spectral analysis of the soft mode. Further, we compare the result of KDP with that of the cooperative rotational dynamics in liquid carbon disulfide.