The ferroelectric transitions of several SrTiO3-based ferroelectrics are investigated experimentally and theoretically, with special attention to the critical scaling exponents associated with the phase transitions, in order to understand the competition among quantum fluctuations (QFs), quenched disorder, and ferroelectric ordering. Two representative systems with sufficiently strong QFs and quenched disorders in competition with the ferroelectric ordering are investigated. We start from non-stoichiometric SrTiO3 (STO) with the Sr/Ti ratio deviating slightly from one, which is believed to maintain strong QFs. Then, we address Ba/Ca co-doped Sr1−x(Ca0.6389Ba0.3611)xTiO3 (SCBT) with the averaged Sr-site ionic radius identical to the Sr2+ ionic radius, which is believed to offer remarkable quenched disorder associated with the Sr-site ionic mismatch. The critical exponents associated with polarization P and dielectric susceptibility , respectively, as functions of temperature T close to the critical point Tc, are evaluated. It is revealed that both non-stoichiometric SrTiO3 and SCBT exhibit much bigger critical exponents than the Landau mean-field theory predictions. These critical exponents then decrease gradually with increasing doping level or deviation of Sr/Ti ratio from one. A transverse Ising model applicable to the Sr-site doped STO (e.g., Sr1−xCaxTiO3) at low level is used to explain the observed experimental data. It is suggested that the serious deviation of these critical exponents from the Landau theory predictions in these STO-based systems is ascribed to the significant QFs and quenched disorder by partially suppressing the long-range spatial correlation of electric dipoles around the transitions. The present work thus sheds light on our understanding of the critical behaviors of ferroelectric transitions in STO in the presence of quantum fluctuations and quenched disorder, whose effects have been demonstrated to be remarkable.

http://iopscience.iop.org/article/10.1088/1674-1056/22/7/077701/pdf

Critical exponents of ferroelectric transitions in modulated SrTiO3: Consequences of quantum fluctuations and quenched disorder

Strontium Calcium titanate (SCT) Sr1−xCaxTiO3 nanopowders have been successfully synthesized by sol–gel method. The effect of Ca2+ ion content from 0 to 1 on their crystal structure, microstructure, transmission and dielectric properties in terahertz range was systematically investigated. The results revealed that single SCT phases with well crystallinity were formed at 900 °C for 2 h. The grain size of the SCT powders was decreased by increasing the Ca2+ ion molar ratios. X-ray diffraction (XRD) and Raman spectra measurement results demonstrated that obvious reduction of symmetry and Raman modes related to structural information varied with the Ca2+ ion composition x. The sequence of SCT phase transitions with increasing Ca content is from cubic through tetragonal I4/mcm to orthorhombic Pbnm. The THz transmission of SCT revealed by terahertz time-domain spectroscopy was changed by varying the Ca2+ ion composition. Meanwhile, the time lag between reference and the SCT could be adjusted between around 20 ps and 30 ps, which increased with increased Ca content. The permittivity of stressed Sr1−xCaxTiO3 powders was obtained by terahertz time-domain spectroscopy. These results revealed that the Ca2+ ion in SCT led to tuning of dielectric response in terahertz range. Sr0.9Ca0.1TiO3 exhibited a smeared-out maximum; for x ≥ 0.3, the real and imaginary components of dielectric permittivity (e′) and (e″) decreased with increasing x. These results may offer considerable insights into the application of Sr1−xCaxTiO3 in smart THz device.

High-frequency response in Sr1−xCaxTiO3 powders studied by terahertz time-domain spectroscopy

The transverse Ising model (TIM), with pseudospins representing the lattice polarization, is often used as a simple description of ferroelectric materials. However, we demonstrate that the TIM, as it is usually formulated, provides an incorrect description of SrTiO3 films and interfaces because of its inadequate treatment of spatial inhomogeneity. We correct this deficiency by adding a pseudospin anisotropy to the model. We demonstrate the physical need for this term by comparison of the TIM to a typical Landau-Ginzburg-Devonshire model. We then demonstrate the physical consequences of the modification for two model systems: a ferroelectric thin film, and a metallic LaAlO3/SrTiO3 interface. We show that, in both cases, the modified TIM has a substantially different polarization profile than the conventional TIM. In particular, at low temperatures the formation of quantized states at LaAlO3/SrTiO3 interfaces only occurs in the modified TIM.

https://robots.iopscience.iop.org/article/10.1088/1361-648X/ab4fa7/pdf

Modified transverse Ising model for the dielectric properties of SrTiO3 films and interfaces

We investigate the effect of Zn doping on the dielectricity and ferroelectricity of a series of polycrystalline Sr0.9−xZnxBa0.1TiO3 (0.0% ≤ x ≤ 5.0%) ceramics. It is surprisingly observed that the Zn doping will produce the multifold polar states, i.e., the Zn-doped ceramic will convert a reduced polar state into an enhanced polar state, and eventually into a stabilized polar state with increasing the doping level x. It is revealed that in the background of quantum fluctuations, the competition between the Zn-doping-induced lattice contraction and the Ba-doping-induced lattice expansion is responsible for both the reduced polar state and the enhanced polar state coming into being. Also, the addition of the antiferrodistortive effect, which is the antipolar interaction originating from the opposite tilted-TiO6 octahedra rotation, represents the core physics behind the stabilized polar state.

https://iopscience.iop.org/article/10.1088/1674-1056/24/12/127701/pdf

Multifold polar states in Zn-doped Sr0.9Ba0.1TiO3 ceramics*

The transverse Ising model (TIM), with pseudospins representing the lattice polarization, is often used as a simple description of ferroelectric materials. However, we demonstrate that the TIM, as it is usually formulated, provides an incorrect description of SrTiO$_{3}$ films and interfaces because of its inadequate treatment of spatial inhomogeneity. We correct this deficiency by adding a pseudospin anisotropy to the model. We demonstrate the physical need for this term by comparison of the TIM to a typical Landau-Ginzburg-Devonshire model. We then demonstrate the physical consequences of the modification for two model systems: a ferroelectric thin film, and a metallic LaAlO$_{3}$/SrTiO$_{3}$ interface. We show that, in both cases, the modified TIM has a substantially different polarization profile than the conventional TIM. In particular, at low temperatures the formation of quantized states at LaAlO$_{3}$/SrTiO$_{3}$ interfaces only occurs in the modified TIM.

Modified transverse Ising model for the dielectric properties of SrTiO$_3$ films and interfaces

Mean-field theory of ferroelectricity in Sr 1-x Ca x TiO 3 (0⩽x⩽0.4)

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Mean-field theory of ferroelectricity in Sr 1-x Ca x TiO 3 (0⩽x⩽0.4)