Observation of nonequilibrium behavior near the Lifshitz point in ferroelectrics with incommensurate phase

Abstract

We have investigated non-equilibrium properties of proper uniaxial Sn2P2(SexS1−x)6 ferroelectrics with the Type II incommensurate phase above Lifshitz point xLP ∼ 0.28. We measured dielectric susceptibility with cooling and heating rate ranging 0.002-0.1 K/min, and high-resolution ultrasound experiments and hypersound Brillouin scattering. For samples with x 0.28 clear anomalies were observed at incommensurate second order transition (Ti) and at first order lock-in transition (Tc) in the regime of very slow cooling rate, whereas the intermediate IC phase is not observed when the rate is faster then 0.1 K/min. In general, increasing the cooling rate leads to smearing the anomaly at Tc. We explain this effect in terms of Kibble-Zurek model for non-equilibrium second order phase transitions. In the ferroelectrics with strongly nonlinear local potential cooling rate defines concentration of domain walls and their size: domain width decreases when cooling rate increases. At certain conditions the size of domain is comparable to the incommensurate phase modulation period, which lies in micrometer scale in the vicinity of Lifshitz point and leads to pinning of the modulation period by domain wall.

Valence fluctuations in Sn(Pb)2P2S6 ferroelectrics

“…This behavior can be determined by some polar fluctuations, like in quadrupole phase according to MC simulations [31], and some growth of dielectric susceptibility at cooling can be expected. Let's try to found some explanation for quantum paraelectric behavior in Pb 2 P 2 S 6 crystal.…”

“…Here we use a transformation of the local three-well potential V (x i ) (Fig. 9) as function of pressure according to the results of [31]. In present calculations the mass of oscillator was equal to tin atomic mass.…”

“…In present calculations the mass of oscillator was equal to tin atomic mass. Moreover, it is possible to calculate a dielectric response of such the system of oscillators using following relation [39]: The shape of local potential for Sn 2 P 2 S 6 crystal at different pressures [31].…”

Description of lattice anharmonicity observed in ferroelectrics with unusual three-well local potential

“…Moreover, the spectra of pseudospin fluctuations were calculated and compared with the Raman scattering data [11]. Here, we present temperature and baric dependencies of the pseudospin fluctuations spectra taking into account the pressure transformation of the local three-well potential [see figure 2(a)] [1,10]. Based on this transformation, the baric behavior of a spin fluctuation spectrum for Sn 2 P 2 S 6 crystal at room temperature, for example, was calculated and presented in figure 3(b).…”

Temperature controller for immersion type cryostat

“…При проведенні досліджень в околі фазових переходів особливий інтерес представляє вузький температурний діапазон (~0.1-0.5К), в якому спостерігаються релаксаційні явища та критична поведінка параметрів, які обумовлені нерівноважністю системи [1,6]. У зв'язку з обмеженим температурним діапазоном спостережуваних явищ виникають підвищені вимоги до алгоритму та системи зміни і стабілізації температури, яка повинна забезпечувати точність близько 0,01÷0.001К без «перерегулювання».…”