$^{1}$H NMR Measurements on the Phase Transition of (NH$_{4}$)$_{3}$H(SO$_{4}$)$_{2}$ Single Crystal

$^{1}$H nuclear magnetic resonance (NMR) experiments have been performed in the temperature range of 30 - 300 K at 7 T to investigate~the phase-dependent nature of the dynamic network of hydrogen bonds~in a (NH$_{4})_{3}$H(SO$_{4})_{2}$ single crystal. The crystal has six phases, which are ferroelectric, antiferroelectric, incommensurate, antiferroelectric, ferroelastic, and superionic conductor with the respective transition temperatures of 63, 133, 139, 256, and 413 K. The spin-lattice relaxation time T$_{1}$ of $^{1}$H NMR is similar for the ammonium protons and the hydrogen-bond protons in all range of experimental temperature. T$_{1}$ of $^{1}$H NMR gradually decreases down to 120 K and then starts to steeply increase below 100 K. Then T$_{1}$ shows an abrupt decrease below 68 K with a sharp minimum at 63 K, where the ferroelectric transition occurs. The $^{1}$H NMR spectrum shifts to the high frequency side below 63 K due to the ferroelectric phase transition. This temperature dependence of T$_{1}$ and spectrum confirms a dramatic change in the dynamics of hydrogen bonds~associated with~the ferroelectric phase transition at 63 K.