Microwave study of the soft ferroelectric mode in Sn₂P₂S₆crystals

Abstract

This paper presents the results of the investigation of dielectric dispersion in semiconductive ferroelectric Sn,P,S, crystals over the frequency range 1 kHz to 78.5 GHz. The main dielectric dispersion in Sn,P,S, is caused by the soft ferroelectric B, mode and in the vicinity of the Curie point it occurs in the millimeter region. The frequency of the soft mode in the paraelectric phase varies according to v, = 35 ( T -r)1/2 GHz on approaching the Curie point. The soft mode is strongly overdamped. Close to T, the relative damping is y/v, = 14. The dielectric contribution of the soft mode is equal to the static dielectric permittivity and it explains its whole temperature-dependence.

Acoustic attenuation in ferroelectric Sn2P2S6 crystals

“…A full set of available data about critical dynamics related to PT in Sn 2 P 2 S 6 crystals, including results of both back-wave and microwave dielectric spectroscopy [13,14], is presented in Fig. 3.…”

“…The temperature dependencies for the reciprocal of the order parameter relaxation time in the paraelectric and ferroelectric phases of Sn 2 P 2 S 6 crystals that were determined on the data of microwave dielectric spectroscopy (dark squares) [13], back-wave dielectric spectroscopy (open circles) [14], neutron scattering (open triangles) [12] and Raman scattering (open inverted triangles) [11]. The dependence τ at T 0 , respectively [11,12], and the relaxational mode is actrually fully softened at T → T 0 , as was observed by dielectric microwave spectroscopy [13]. In the ferroelectric phase with P space group, both B and A modes find A symmetry and already linearly interact.…”

“…From these measurements, the optic soft mode temperature instability and its interaction with the set of low energy nearest optic modes were observed. The critical dynamics were also investigated by dielectric spectroscopy [13,14]. The thermal diffusivity and thermal expansion were studied, and the crystal anharmonicity was characterized [15][16][17].…”

The second order phase transition in Sn_2P_2S_6 crystals: anharmonic oscillator model

“…The latter occurred in Sn 2 P 2 S 6 crystals (ω(T C ) ≈ 10 cm −1 ) [19]. Using all these facts we numerically calculate the equation (17) and find that it is satisfied at β /α ≈ 2.38 and (β ) 1/2 /δ ≈ 1.92 (point in figure 3). Let us return to figure 3.…”

“…The dielectric properties of Sn 2 P 2 S 6 crystals were investigated in a series of works [17,18]. Using a representation of dielectric constant by means of damping oscillators, one can find its frequency dependence as follows:…”