Nuclear Magnetic Resonance and Nonexponential Spin-Lattice Relaxation in Ferroelectric Ammonium Fluoroberyllate

Abstract

Nuclear spin-lattice relaxation times ${T}_{1}$ and relaxation times along the rf field (${T}_{1\ensuremath{\rho}}$) have been measured for ${\mathrm{H}}^{1}$ and ${\mathrm{F}}^{19}$ in ${(\mathrm{N}{\mathrm{H}}_{4})}_{2}$Be${\mathrm{F}}_{4}$. Below 250\ifmmode^\circ\else\textdegree\fi{}K the relaxation is due to reorientation of N${\mathrm{H}}_{4}^{+}$ ions; proton ${T}_{1}$ versus $T$ has two minima due to two inequivalent N${\mathrm{H}}_{4}^{+}$ ions in the unit cell. Above the transition temperature ${T}_{c}$ (176\ifmmode^\circ\else\textdegree\fi{}K) and below 130\ifmmode^\circ\else\textdegree\fi{}K, the logarithm of the correlation time ${\ensuremath{\tau}}_{c}$ is a linear function of ${T}^{\ensuremath{-}1}$ with normal values of pre-exponential factors. Immediately below ${T}_{c}$, the time ${\ensuremath{\tau}}_{c}$ is anomalously short, as found previously in ${(\mathrm{N}{\mathrm{H}}_{4})}_{2}$S${\mathrm{O}}_{4}$. Above 250\ifmmode^\circ\else\textdegree\fi{}K, both proton and ${\mathrm{F}}^{19}$ relaxation become nonexponential and may be characterized by the same pair of relaxation times ${{T}_{1}}^{\ensuremath{'}}$ and ${{T}_{1}}^{\ensuremath{'}\ensuremath{'}}$. The shorter component (${{T}_{1}}^{\ensuremath{'}}$) is ascribed to H-F dipolar interactions, and the longer component (${{T}_{1}}^{\ensuremath{'}\ensuremath{'}}$) to H-F, H-H, and Be-F dipolar interactions. On deuteration, only the longer component remains; also, ${{T}_{1}}^{\ensuremath{'}}$ and ${{T}_{1}}^{\ensuremath{'}\ensuremath{'}}$ depend only on the rate of reorientation of Be${\mathrm{F}}_{4}$ tetrahedra. Deuteron-resonance results indicate that the dipole moment per N${\mathrm{H}}_{4}^{+}$ ion in ${(\mathrm{N}{\mathrm{H}}_{4})}_{2}$Be${\mathrm{F}}_{4}$ is about half that in ${(\mathrm{N}{\mathrm{H}}_{4})}_{2}$S${\mathrm{O}}_{4}$, in agreement with spontaneous-polarization measurements. The phase transition in ${(\mathrm{N}{\mathrm{H}}_{4})}_{2}$Be${\mathrm{F}}_{4}$ is not as abrupt as in ${(\mathrm{N}{\mathrm{H}}_{4})}_{2}$S${\mathrm{O}}_{4}$, and may be described by a weaker dependence of the interaction parameter on the spontaneous polarization.