Nuclear Quadrupole Spin-Lattice Relaxation and Critical Dynamics of Ferroelectric Crystals

Abstract

The effect on the nuclear spin-lattice relaxation of the anomalous temperature dependence of generalized unstable lattice modes near the ferroelectric transition is investigated both theoretically and experimentally. Expressions for the relaxation rate near $T_c$ are derived for typical cases of critical dynamics of ferroelectric crystals. For the case of undamped soft-phonon modes it is shown that, on the basis of a Raman two-phonon relaxation mechanism, the relaxation rate should behave near the transition temperature as ${(T-T_0)}^{-n}$, where $n$ depends on the shape of the dispersion curve of the soft branch. On the other hand, for the case of dampedoscillatory modes or diffusive modes, the relaxation rate, derived by using the classical approach for the direct relaxation process, should behave as ${(T-T_0)}^{\frac{-1\mathrm{}}{2}}$ or as $\ln (T-T_0)$ if the anisotropic character of the dipolar interaction is taken into account. An experimental investigation of the nuclear spin-lattice relaxation rate in NaN${\mathrm{O}}_2$ single crystal is presented. The resonance spectrum and the recovery law under different conditions are discussed. The results of the relaxation rate as a function of temperature, angular orientation, and resonance frequency indicate the existence of a damped generalized soft mode or critical diffusive mode. The available data on the shape of the relaxation-rate peak tends to favor the logarithmic singularity, in agreement with the prediction of an anisotropic interaction. From the analysis of the data, it is inferred that the soft mode can be identified as the flipping motion along the ferroelectric $c$ axis of the electric dipoles associated with the N$\mathrm{O}_2^{}{}_{}{}^{-}$ group, which seem to be mainly correlated along the $a$ axis. The relaxation measurements support the recent suggestion for a new low-temperature phase transition.