Quantum paraelectric state and critical behavior in Sn(Pb)2P2S(Se)6 ferroelectrics

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 the Sn 2 P 2 S 6 crystal, does not shift the coordinate of the Lifshitz point x LP in Sn 2 P 2 ( Se x S 1 − x ) 6 mixed crystals, and 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 the Pb 2 P 2 S 6 crystal, the real part of the dielectric permittivity in the quantum critical regime varies as 1 / T 2 instead of the expected 1 / T 3 behavior for uniaxial materials. Such an observation 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 the Pb 2 P 2 S 6 crystal can be established by a small amplitude of electric dipoles together with the nonlinear coupling between polar and antipolar fluctuations. An increase in thermal conductivity is induced by Ge impurity in the Pb 2 P 2 S 6 crystal, which is explained by the weakening of the acoustic phonons resonance scattering by soft optic phonons because of the appearance of ferroelectric phase polar clusters.