Effect of Proton-Phonon Coupling on the Ferroelectric Mode in KH2PO4

Abstract

The low-frequency Raman spectra of crystal K${\mathrm{H}}_2$P${\mathrm{O}}_4$ are reexamined experimentally. For temperatures above the Curie point, the $B_2$ spectra below 270 ${\mathrm{cm}}^{-1\mathrm{}}$ are fitted to the model of two coupled harmonic oscillators. When the proton-phonon-coupling effect is accounted for in this manner, the square of the uncoupled-ferroelectric-mode frequency ${\omega }_a^2$ and the temperature-weighted inverse equivalent relaxation time $\frac{T}{\tau }$ are found to depend on the temperature linearly, contrary to previous interpretation. The extrapolated transition temperature of the uncoupled soft mode (30 °K) is much lower than 116°K as determined from the $\frac{1}{\chi \mathrm{}\left(0\right)\mathrm{}}$ plot. This discrepancy is attributable to the level repulsion of the proton-phonon coupling which forces the coupled mode to become soft at a higher temperature (116°K). The evidence presented suggests that the validity of the collective pseudospin model of K${\mathrm{H}}_2$P${\mathrm{O}}_4$ is questionable.