Long-Wavelength Polarization Fluctuations in Antiferroelectric N${\mathrm{H}}_4$${\mathrm{H}}_2$P${\mathrm{O}}_4$

The low-frequency Raman spectra of crystalline N${\mathrm{H}}_4$ ${\mathrm{H}}_2$P${\mathrm{O}}_4$ are reported for temperatures above the Curie point. Both $B_2$ and $E$ species are fitted to the model of two coupled harmonic oscillators, which accounts for the strong proton-phonon coupling existing in this type of crystal. The temperature dependence of the equivalent relaxation time is determined for both modes and the results are compared with those of Ryan et al., who have neglected the proton-phonon coupling for the $E$ mode. In addition, the square of the uncoupled overdamped frequency ${\omega }^2\left(B_2\right)$ and the inverse static susceptibility $\frac{1}{\chi \left(B_2\right)}$ of the $B_2$ mode are found to depend on temperature linearly. The temperature dependence of $\frac{1}{\chi \left(B_2\right)}$, which compared well with the microwave data of Kaminow, is shown to relate directly to the corresponding long-wave-length polarization fluctuations discussed in this paper.