A generalized arrhenius law in dilute KTaO3Li versus the Vogel-Fulcher approach

Abstract

The temperature-frequency dependencies (5 K-300 K, 100 Hz-1 MHz) of the dielectric permittivity ε′ and ε″ in dilute (x < 0.01) K_1-xLi_xTaO₃ were studied and analyzed in detail. From the positions of the permittivity temperature maxima at various frequencies it was obtained that the temperature dependence of the mean relaxation time of Li⁺ off-centre related 90° dipole reorientations doesn't obey an Arrhenius law, but follows the empirical Vogel-Fulcher law. Such behaviour is usually believed to be an evidence of freezing phenomenon and polar glass formation at low temperatures. Here we suggest an alternative explanation and show that taking into consideration the coupling of the Li⁺ dipole impurities to the soft mode allows to obtain an analytical expression for a “Generalized Arrhenius law”, which describes quantitatively the deviation from the Arrhenius law and agrees well with the experiment. The approach developed describes the dependence of the ′'(T) maxima too due to the hardening of the soft mode caused by random fields. This hardening suppresses the divergent dielectric permittivity at the ferroelectric-type phase transition and can possibly lead to the appearance of polar regions.