Cross-Relaxation Determination of Short Quadrupolar Spin-Lattice Relaxation Rates in Solids: Proton-Iodine Cross Relaxation in Antiferroelectric ${\mathrm{Ag}}_2$${\mathrm{H}}_3$I${\mathrm{O}}_6$ and ${\left(\mathrm{N}{\mathrm{H}}_4\right)}_2$${\mathrm{H}}_3$I${\mathrm{O}}_6$

The application of rotating- and dipolar-frame proton-relaxation measurements for the determination of fast quadrupolar relaxation rates of nonresonant spins $S$, the signals of which are too weak to be measured by the conventional NMR technique, is discussed. Both the case where the proton-$S$ cross-relaxation rate is fast as compared to the $S$-spin-lattice relaxation rate and the case where it is slow are treated. The method is applied to ${\mathrm{Ag}}_2$ ${\mathrm{H}}_3$I${\mathrm{O}}_6$ and ${\left(\mathrm{N}{\mathrm{H}}_4\right)}_2$ ${\mathrm{H}}_3$I${\mathrm{O}}_6$. The $T$ dependence of the ${}_{}{}^{127}{}_{}{}^{}\mathrm{I}$ quadrupolar spin-lattice relaxation rates is extracted from the $T$ dependence of the proton dipolar- and rotating-frame spin-lattice relaxation times. The iodine-spin-lattice relaxation times are found to be very short and seem to be controlled by electric-field-gradient (EFG) fluctuations due to the motion of protons between the two equilibrium sites in the O-H—O bonds. Using the known values of the static ${}_{}{}^{127}{}_{}{}^{}\mathrm{I}$ EFG tensor, the O-H—O proton intrabond jump time $\tau$ was found to be of the order of ${10}^{-10\mathrm{}}$ sec at room temperature, i.e., of the same order as in K${\mathrm{H}}_2$P${\mathrm{O}}_4$-type ferroelectrics.