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Using DFT-based molecular dynamics simulation of Cu$^+$ cations flipping and In$^{3+}$ cations displacive dynamics, we clarify the dipole ordering of CuInP$_2$S$_6$ ferrielectrics through the second order Jahn-Teller effect which determines the double-well potential for copper cations as well as three-well potential for indium cations inside the structural layers. The temperature dependence of the spatial distribution of Cu$^+$ and In$^{3+}$ cations is also described within the quantum anharmonic oscillators model. In$^{3+}$ cations play a decisive role in the character of the polar ordering: at ambient or for positive pressures, the first order transition occurs; with the rise of negative compression, the ferrielectric transition evolves to the second order. The peculiarities of spontaneous polarization switching are related to the contributions of copper and indium cationic sublattices.

It is well known that disordered relaxor ferroelectrics exhibit local polar correlations. The origin of localized fields that disrupt long range polar order for different substitution types, however, is unclear. Currently, it is known that substituents of the same valence as Ti4+ at the B-site of barium titanate lattice produce random disruption of Ti-O-Ti chains that induces relaxor behavior. On the other hand, investigating lattice disruption and relaxor behavior resulting from substituents of different valence at the B-site is more complex due to the simultaneous occurrence of charge imbalances and displacements of the substituent cation. The existence of an effective charge mediated mechanism for relaxor behavior appearing at low (< 10%) substituent contents in heterovalent modified barium titanate ceramics is presented in this work. These results will add credits to the current understanding of relaxor behavior in chemically modified ferroelectric materials and also acknowledge the critical role of defects (such as cation vacancies) in lattice disruption, paving the way for chemistry-based materials design in the field of dielectric and energy storage applications.

The dipole ordering in Sn(Pb)$_2$P$_2$S(Se)$_6$ materials may be tuned by chemical substitution realizing a ferroelectric quantum phase transition and quantum glassy or relaxor type phenomena on different parts of the phase diagram. The introduction of Ge impurity increases the temperature of the phase transitions and initiates a more pronounced Ising type critical anomaly in Sn$_2$P$_2$S$_6$ crystal, does not shift the coordinate of the Lifshitz point $x_{\textrm {LP}}$ in Sn$_2$P$_2$(Se$_x$S$_{1-x}$)$_6$ mixed crystals, induces the appearance of a ferroelectric phase transition in quantum paraelectrics Pb$_2$P$_2$S$_6$ and inhomogeneous polar ordering in (Pb$_{0.7}$Sn$_{0.3}$)$_2$P$_2$S(Se)$_6$ crystals. For Pb$_2$P$_2$S$_6$ crystal, the real part of the dielectric susceptibility in the quantum critical regime varies as $1/T^2$ instead of the expected $1/T^3$ behavior for uniaxial materials. This can be partially explained by a screening phenomenon in the semiconductor materials of the Sn(Pb)$_2$P$_2$S(Se)$_6$ system, which weakens the long range electric dipole interactions, and also provides, at high temperatures, a critical behavior near the Lifshitz point (studied by thermal diffusivity) similar to the one predicted in the case of systems with short range interactions. At low temperatures, a quantum critical behavior in Pb$_2$P$_2$S$_6$ crystal can be established by the nonlinear coupling between polar and antipolar fluctuations. An increase in thermal conductivity is induced by Ge impurity in Pb$_2$P$_2$S$_6$ crystal, which is explained through the weakening of the acoustic phonons resonance scattering by soft optic phonons because of the appearance of ferroelectric phase polar clusters.

For the first time in a bulk proper uniaxial ferroelectrics, double antiferroelectric-like hysteresis loops have been observed in the case of Sn$_2$P$_2$S$_6$ crystal. The quantum anharmonic oscillator model was proposed for description of such polarization switching process. This phenomenon is related to three-well local potential of spontaneous polarization fluctuations at peculiar negative ratio of coupling constants which correspond to inter-site interaction in given sublattice and interaction between two sublattices of Sn$_2$P$_2$S$_6$ modeled crystal structure. Obtained data can be used for development of triple-level cell type memory technology.

The valence fluctuations which are related to the charge disproportionation of phosphorous ions $P^{4+} + P^{4+}\rightarrow P^{3+} + P^{5+}$ are the origin of ferroelectric and quantum paraelectric states in Sn(Pb)$_2$P$_2$S$_6$ semiconductors. They involve recharging of SnPS$_3$ or PbPS$_3$ structural groups which could be represented as half-filled sites in the crystal lattice. Temperature-pressure phase diagram for Sn$_2$P$_2$S$_6$ compound and temperature-composition phase diagram for (Pb$_y$Sn$_{1-y}$)$_2$P$_2$S$_6$ mixed crystals, which include tricritical points and where a temperature of phase transitions decrease to 0 K, together with the data about some softening of low energy optic phonons and rise of dielectric susceptibility at cooling in quantum paraelectric state of Pb$_2$P$_2$S$_6$, are analyzed by GGA electron and phonon calculations and compared with electronic correlations models. The anharmonic quantum oscillators model is developed for description of phase diagrams and temperature dependence of dielectric susceptibility.

For Sn$_2$P$_2$S$_6$ ferroelectrics the second order phase transitions line is observed until reaching the tricritical point at transition temperature lowering to 250 K by compression. Observed temperature-pressure phase diagram agrees with simulated diagram by MC calculations based on early founded by DFT study local potential for Sn$_2$P$_2$S$_6$ crystals. In addition to the tricritical point, the possibility of disordered and quadrupolar phases occurrence was shown. For mixed crystals with tin by lead substitution, the investigated ultrasound, hypersound and low frequency dielectric properties also reveal appearance of heterophase peculiarities at decreasing of ferroelectric transition temperature below so named "temperature waterline" near 250~K. The tricriticality at similar temperature level also appears in mixed crystals at sulfur by selenium substitution. Such behavior agree with Blume-Emery-Griffiths (BEG) model, that is appropriated for investigated ferroelectric system with three-well local potential for the order parameter (spontaneous polarization) fluctuations.

We have investigated non-equilibrium properties of proper uniaxial Sn$_2$P$_2$(Se$_x$S$_{1-x}$)$_6$ ferroelectrics with the Type II incommensurate phase above Lifshitz point $x_{\rm LP} \sim 0.28$. 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 $x \geqslant 0.28$ clear anomalies were observed at incommensurate second order transition ($T_i$) and at first order lock-in transition ($T_c$) 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 $T_c$. 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., Comment: 13 pages, 12 figures

Dynamics of the main dielectric anomaly in Na1/2Bi1/2TiO3 (NBT) was studied by time-domain THz and microwave spectroscopy, using also previously published data and their new overall fits. Above the dielectric maximum temperature Tm ~ 600 K, the response consists of coupled sub-THz oscillator and a relaxation mode, assigned to strongly anharmonic Bi-ion vibrations and hopping, whose slowing down explains the paraelectric-like permittivity increase to Tm. Below Tm, the main relaxation continues slowing down and additional relaxation, assigned to quasi-Debye losses, appears in the 10^11 Hz range. The oscillator hardens on cooling and takes over the whole oscillator strength. The permittivity decrease below Tm is caused by the reduced strength of the relaxations due to dominance of the rhombohedral phase within the coexistence region with the tetragonal phase. The anharmonic dynamics of Bi is supported by previous structural studies. NBT represents a hybrid between standard and relaxor ferroelectric behaviour.

The interaction between soft optic and acoustic phonons was investigated for Sn2P2(Se0.28S0.72)6 proper uniaxial ferroelectrics by Brillouin scattering and ultrasonic pulse-echo techniques. The elastic softening of hypersound velocity of transverse acoustic phonons and for both longitudinal and transverse ultrasound waves which propagate near direction of the modulation wave vector (in the incommensurate phase at x>xLP) was found at cooling to the Lifshitz point in the paraelectric phase. The strong increase of the ultrasound attenuation have also been observed. Such phenomena are related to the linear interaction of the soft optic and acoustic branches in the region of relatively short-range hypersound waves and to the strongly developed long-range order parameter fluctuations in the ultrasound frequency range. The hypersound velocity temperature dependence was described within the Landau-Khalatnikov approximation for the ferroelectric phase., Comment: 11 pages, 12 figures; minor text changes

In this article mixed CuInP$_2$(S$_x$Se$_{1-x}$)$_6$ crystals were investigated by broadband dielectric spectroscopy (20 Hz - 3 GHz). The complete phase diagram has been obtained from these results. The phase diagram of investigated crystals is strongly asymmetric - the decreasing of ferroelectric phase transition temperatures in CuInP$_2$(S$_x$Se$_{1-x}$)$_6$ is much more flat with small admixture of sulphur then with small admixture of selenium. In the middle part of the phase diagram (x=0.4-0.9) the dipolar glass phase has been observed. In boundary region between ferroelectric order and dipolar glass disorder with small amount of sulphur (x=0.2-0.25) at low temperatures the nonergodic relaxor phase appears. The phase diagram was discussed in terms of random bonds and random fields., Comment: 11 pages 14 figures

Relaxor ferroelectric PbMg_1/3Ta_2/3O_3 ceramics and thin films were investigated by means of broad-band dielectric, time-domain terahertz (THz) and Fourier-transform infrared (IR) spectroscopy in the frequency range 100 Hz - 90 THz at temperatures 100 - 490 K, the THz and IR spectra were studied from 20 to 900K. Diffused and strongly temperature dependent peak in the complex permittivity is caused by a dielectric relaxation due to the dynamics of polar clusters. The relaxation appears below Burns temperature T_d in the THz range, slows down on cooling through the microwave and MHz range and anomalously broadens. The shortest and longest relaxation times of the distribution of relaxation times follow Arrhenius and Vogel-Fulcher law, respectively. The degree of B-site order has only a small influence on the parameters of the dielectric relaxation and almost no influence on the phonon parameters. Below T_m ~ 180K, the distribution of relaxation frequencies becomes broader than our experimental spectral range and frequency independent dielectric losses develop below 100 GHz in the spectra. Although the macroscopic crystal structure is cubic, IR spectra give evidence about the lower local symmetry which can be assigned to the presence of polar clusters below T_d. Infrared spectra above T_d still reveal more modes than predicted by selection rules in the paraelectric phase of the Fm-3m space group so that we suggest selection rules which take into account chemical inhomogeneity in the beta''-perovskite sublattice., Comment: subm. to J. Appl. Phys