Dynamics of ions of the two-dimensional superionic conductor AgCrS2

AgCr${\mathrm{S}}_2$ is a quasi-two-dimensional superionic conductor for silver ions which shows a second-order phase transition at $T_c=673\mathrm{}$ K. Well below $T_c$, AgCr${\mathrm{S}}_2$ is ordered and pyroelectric; above $T_c$ the silver ions are disordered and the phase is nonpyroelectric. The ion dynamics below $T_c$ has been studied by means of far-infrared and inelastic neutron scattering experiments. The most interesting feature of the phonon structure is the existence of very-low-frequency acoustic and flat optic modes. The low-frequency TO mode at $q=0\mathrm{}$ shows a strong and anomalous temperature dependence down to 10 K. We show that this temperature dependence can be explained by a highly anharmonic motion of a particle in an effective potential. The patterns of ionic displacements of the low-frequency modes have been obtained from a calculation based on a rigid-ion model. This calculation shows that in the low-frequency modes the silver ions are strongly involved and vibrate parallel to the layers. These modes therefore contribute strongly to the mean-square displacements of the silver ions and to the reaction coordinates for ionic jumps. The jumps of silver ions reduce the spontaneous polarization of the pyroelectric phase and finally lead to the order-disorder pyroelectric phase transition at $T_c$.