Strophoidal Argand diagram and the distribution of relaxation times inK1−xLi

Abstract

We have studied the relaxation of off-center Li + ions in KTaC>3 by dielectric measurements on 1% and 1.5% crystals, from 20 Hz to 2 MHz and from 4 to 200 K. The shape of the e" vs e Argand diagrams demonstrates the existence of a distribution of relaxation times. In analogy with spin glasses, a new expression is proposed for the analysis of these diagrams, a strophoidal function, which leads to a distribution function D(0) decreasing for large 6 as #~( 1+a) with 0 < a < 1. The most probable relaxation time 0 m p of the distribution follows an Arrhenius law with a barrier height close to 950 K.PACS numbers: 77.22.Gm, 64.60.-i When Li + ions are substituted for larger K + ions in KTaC>3 crystals they occupy off-center positions, therefore inducing an electric dipole moment as well as a nonspherical elastic quadrupole moment. Owing to the randomness of substitution, the interaction between dipoles is also random. This includes the usual dipolar interaction and the indirect coupling due to the soft ferroelectric mode in this highly polarizable crystal. The combination of these two types of interaction is expected to lead to unusual dipole dynamics and, upon cooling, to a phase transition, the nature of which is still not well understood [1,2]. In this Letter, we propose a new description of the dipole dynamics which is believed to play a crucial role in the transition.In order to investigate the relaxation of the Li dipoles, we have performed a systematic study of the complex dielectric constant s = e-ie" and the resulting Argand diagrams (AD), also called Cole-Cole diagrams, e" vs e. The shape of these diagrams clearly reveals the unusual character of the relaxation which we intend, in contrast to previous studies [3][4][5][6][7][8], to explain more precisely. To this end, we propose a new dielectric susceptibility function, the form of which was inspired by an analogy with the magnetic susceptibility of spin glasses. In both cases, the susceptibility is the response to an external field of an assembly of identically relaxing dipoles (magnetic or electric) when the interactions between dipoles are random. The eigenmodes of the system may be determined by diagonalization of the interaction matrix. The corresponding transformation leads to a distribution of relaxation times for the eigenmodes which, in turn, determines the form of the dynamic susceptibility [9,10].The dielectric measurements have been carried out on two crystals of Ki-x Li x Ta03 (KLT) with concentrations JC = 1% and 1.5% as a function of the temperature (4 K < T < 200 K) and over a broad range of frequency (20 Hz</<2 MHz) with Hewlett-Packard 4192A impedance analyzer. All the experiments were performed without any applied static electric field. The 1.5% crystal has already been studied using Raman scattering [11] and acoustic propagation [12] (sample I of Ref. [12]).To keep a consistent labeling scheme in all our publications we refer to the 1% crystal as sample IV.The variations of e and e" are shown in Fig. 1 as functions of temperature T at the f...

Critical behaviors of photoinduced giant permittivity in potassium tantalate

“…This temperature dependence of the dielectric relaxation time is contradictory to the conventional Ahrenius-type relaxation ( Ϫ1 ϰe ϪE/kT ) in the permanent dipole systems such as KLT (K 1Ϫx Li x TaO 3 ) crystals. 12 In KLT, the relaxation rate increases when the temperature increases. We should emphasize that the difference in the temperature dependence between the photoinduced dipoles in KTaO 3 and the permanent dipoles in KLT shows clearly an exotic aspect of photoinduced giant permittivity.…”

Influence of lattice polarizability on interacting Li-induced dipoles distributed in incipient ferroelectricKTaO3

“…3,4,16 On the basis of rich experimental results regarding the dielectric properties, a number of theories on the diffused phase transition in KLT have been proposed. [17][18][19][20][21][22] Much attention has also been directed to determining the correlation length of the Li-induced dipoles through various experiments, such as Raman scattering, 23 dielectric measurement, 24 second-harmonic generation, 25,26 x-ray diffuse scattering, 27 and neutron diffuse scattering. 28 The reported correlation lengths are summarized in Table II in the study by Yong et al 28 Azzini et al have also proposed the presence of two kinds of correlation: dipolar and quadrupolar.…”