Dynamical critical phenomena in ND4Br

The dynamical critical phenomena associated with the structural phase transition of N${\mathrm{D}}_4$ Br ($T_c=215\mathrm{}$ °K) have been studied by neutron-scattering techniques. The measurements of the low-energy part of neutron spectra of N${\mathrm{D}}_4$Br single crystals have been carried out along the principal symmetry directions of cubic reciprocal space. The spectra observed along the [110] direction show a "triple-peak" structure. The central (quasielastic) component is clearly due to the coupled relaxational motion of displacement of ${\mathrm{Br}}^{-}$ ions and the flipping of N$\mathrm{D}_4^{}{}_{}{}^{+}$ ions. The width $\Gamma$ (full width at half-maximum) of the central component is less than the instrumental resolution (${\Gamma }_{\mathrm{cent}}\le 0.28$ meV). In addition to the central component, there exists a well-defined T${\mathrm{A}}_2$ phonon mode at the [110] zone boundary whose eigenvector exactly corresponds to the spontaneous displacement of ${\mathrm{Br}}^{-}$ ions in the low-temperature phase. However, this phonon mode does not show any appreciable softening nor broadening throughout the temperature region of $220<T<\mathrm{}295\mathrm{}$ °K. Rather the intensity of the central component at the $M$ point critically increases. These experimental results are analyzed by looking upon the system as a pseudospin-phonon coupled system. It is shown that the observed neutron spectra $S(\mathrm{K},\omega )$ are satisfactorily explained with such a formalism by taking the relaxation time of the flipping of an independent ammonium ion longer than 1.3 × ${10}^{-12\mathrm{}}$ sec. The distribution of intensity of the central peak shows two maxima in the reciprocal space, one at the $\Gamma$ point (zone center) and another at the $M$ point ([110] zone boundary). This gives direct evidence for the existence of the two competitive interactions: direct interaction between ammonium ions and indirect interaction via phonon modes. This competition is postulated to explain the two successive phase transitions which occur in N${\mathrm{D}}_4$Br.