Frequency response of the low-temperature ionic conductivity of single crystals $R_{1-y}M_y$F$_{3-y}$ ($R$ = La–Er; $M$ = Ca, Sr, Ba, Cd)

The frequency response (10$^{-1}$–10$^7$ Hz) of the ionic conductivity $\sigma$ of $R_{1-y}M_y$F$_{3-y}$ single crystals ($R$ is a rare-earth element, and $M$ stands for an alkaline-earth element and Cd) with a tysonite structure is studied over a wide temperature range (114–410 K), which includes (for the first time for these phases) the interval below room temperature. The dependences $\sigma(\nu)$ obtained are discussed within the hopping relaxation model. The characteristics of the relaxation and migration processes and the carrier concentration and mobility are determined.