The relaxor enigma — charge disorder and random fields in ferroelectrics

ABSTRACTQuenched random fields (RFs) are well-known to be a basic driving force of the peculiar behavior of relaxor ferroelectrics such as PbMg1/3Nb2/3O3 (PMN), SrxBa1-xNb2O6 (SBN), and BaTi1-xZrxO3 (BTZ), hence, giving rise to strong frequency dispersion of the dielectric response, an apparent lack of macroscopic symmetry breaking at low temperatures, and the formation of polar nanoregions (PNRs) thus creating random ‘domain states’. A fundamental completion of relaxor physics toward a superdipolar cluster glass ground state of the randomly interacting PNRs appears necessary as evidenced by dynamic criticality and non-ergodic aging and rejuvenation processes.

It is with great pleasure that we present this special issue focused on topological structures in ferroic materials. It is composed of invited contributions from the International Workshop on Topological Structures in Ferroic Materials held at the University of South Wales, Sydney, Australia from 19-21 st May 2015. The aim of the workshop was to capture current research interests regarding interfaces, domains, domain walls, vortices and skyrmions in ferroics as an emerging and highly active fi eld in solid state physics and materials science. Signifi cant emphasis was placed on understanding the fundamental commonalities that bridge topological defects across various types of ferroic materials, and therefore lessons learned on how new and groundbreaking functionalities afforded by the aforementioned concepts could be translated into emerging technologies.

Quenched random fields (RFs) are well‐known to be a basic driving force of the relaxor behavior in disordered ferroelectrics containing either random charges as in PbMg1/3Nb2/3O3 or random cation vacancies as in SrxBa1−xNb2O6. They give rise to the formation of polar nanoregions in the paraelectric regime, which freeze into a nanodomain state at low temperatures thus precluding the ferroelectric phase transition. On the other hand, isovalent relaxors like bond‐disordered BaTi1−xZrxO3 prevalently experience random bonds (RBs), which are responsible for glassy features such as polydispersivity and non‐ergodic aging and rejuvenation processes. Inspection shows, however, that all of the above characteristics apply generally to relaxor systems albeit with different weight. Subsequent formation of ferroic nanoregions via RFs followed by mesoscopic cluster glassy freezing via RBs upon cooling are universal signatures.

Phase transitions in PbZn 1/3 Nb 2/3 O 3 -7%PbTiO 3 (PZN-7%PT) relaxor ferroelectric crystals have been investigated by the acoustic emission (AE) method. Two types of transitions have been detected: (i) associated with the thermally induced (on cooling) formation of intrinsic polar nanoregions (PNRs) and (ii) related to the electric-field-induced macroscopic phase transitions. An AE signal found near 740 K corresponds to the Burns temperature, below which the PNRs begin to form. Further cooling reveals an AE signal at 500 K, which is ascribed to the shift of PNRs along their polar direction relative to the surrounding non-polar matrix in the framework of the “phase-shifted condensed soft mode” model. Monitoring of the AE response of PZN-7%PT crystals under an increasing [001] dc electric field has allowed a unique in situ observation of a sequence of phase transitions, from the zero-field rhombohedral via M A monoclinic (∼ 3 kV/cm) and M C monoclinic (∼ 16 kV/cm) to the tetragonal (∼ 19 kV/cm) phase, respectively. It is shown that AE is a very sensitive method for detecting both the PNRs kinetics and low distortion phase transitions in relaxor ferroelectrics.

Relaxor ferroelectric 0.83Pb(Mg1/3Nb2/3)O3–0.17PbTiO3 (PMN–17PT) single crystals were studied by Brillouin scattering to investigate the role of polar nanoregions (PNRs) with intermediate random fields (RFs). Upon cooling, the central peak began to appear at the Burns temperature (TB) of ∼600 K, indicating the existence of polarization relaxations induced by PNRs. The fitting performed using the equation of stretched slowing down at the inverse relaxation time revealed that the slowing down of PNRs was suppressed in PMN–17PT compared with that in PMN–56PT owing to the increase in the strength of RFs. At room temperature, the splitting of the longitudinal acoustic mode at 1.6 kV/cm was observed owing to the coexistence of the macrodomain formed by the external electric field along the [100] axis and the nanodomains formed by RFs. The appearance of the transverse acoustic mode at 3.2 kV/cm indicates the field-induced rhombohedral-to-tetragonal phase.

Combined theoretical and nanoscale experimental study of Pb(Ca,Ba)TiO3, Pb(Sr,Ba)TiO3, and Pb(Sr,Ca)TiO3 complex perovskite structures: An investigation of the ferroelectric and electronic properties

The relaxor-like dynamics of the cubic-tetragonal ferroelectric phase transition was studied by Brillouin and Raman scattering in K(Ta1−xNbx)O3 (KTN) crystals with x = 0.40 (KTN40). The local symmetry breaking by the polar nanoregions (PNRs) was observed in a paraelectric phase by Raman scattering on the A1(z) mode of the PNRs with R3m symmetry. Upon cooling from a high temperature, the remarkable increase in the LA phonon damping starts at 45 K above the cubic-tetragonal phase transition temperature of TC-T = 308 K, which is defined as the intermediate temperature, T* ∼ 353 K, indicating the start of the rapid growth of the PNRs. The coupling between the LA mode and fluctuation of the PNRs caused a remarkable elastic anomaly in the vicinity of TC-T. The analysis of the temperature dependent central peak shows a critical slowing down towards TC-T, which is the evidence for the order-disorder nature of a ferroelectric phase transition. The evolution of the dynamic PNRs is discussed by the estimation of their length scale, and it is found that it starts to increase near T* and gradually grows towards TC-T.

We develop a method by which certain classical equations of state may be modified to produce nonclassical critical scaling behavior. We then apply this method to the classical free energy describing a tricritical point that was originally introduced by Griffiths. The phase behavior of the resulting nonclassical free energy is characterized by the competition between critical scaling and tricritical scaling already envisioned by previous authors.

Phase transitions and relaxor properties of doped quantum paraelectrics

The high-frequency dielectric behavior of uniaxial tungsten-bronze strontium barium niobate crystals with various Sr/Ba ratios, including both ferroelectric and relaxor compositions, have been studied in a broad frequency range (${10}^{4}$ to ${10}^{13}\phantom{\rule{0.16em}{0ex}}\mathrm{Hz}$) and temperature interval 100--500 K in order to thoroughly understand the evolution of the relaxation dynamics across the ferroelectric phase transition. The dielectric response along the polar axis consists of three relaxations corresponding to polarization mechanisms related to several correlation lengths of mesoscopic order. All of them show dissimilar behaviors with temperature, pointing out to their distinct nature. A temperature-dependent central mode at THz frequencies and a relaxation above 10 GHz are accompanied by the slowing down of a relaxation in the MHz range. This response reveals the complex mechanism of the phase transition and supports the coexistence of displacive and order-disorder scenarios. Relaxor and ferroelectric compositions surprisingly reveal similar qualitative behavior within the frequency window used. However, relaxor crystals display relaxations at higher frequency because of the smaller extent of the polar fluctuations and ferroelectric regions, which coexist in almost all the compositions. The presence of two different ferroelectric subsystems in the structure agrees with the existence of several polarization mechanisms involved in the complex dielectric and ferroelectric response.

Evolution of domain structure and ferroelectric polarization in praseodymium doped BiFeO3 ceramics

Barium titanate-based energy-storage dielectric ceramics have attracted great attention due to their environmental friendliness and outstanding ferroelectric properties. Here, we demonstrate that a recoverable energy density of 2.51 J cm-3 and a giant energy efficiency of 86.89% can be simultaneously achieved in 0.92BaTiO3-0.08K0.73Bi0.09NbO3 ceramics. In addition, excellent thermal stability (25-100 °C) and superior frequency stability (1-100 Hz) have been obtained under 180 kV cm-1. The first-order reversal curve method and transmission electron microscopy measurement show that the introduction of K0.73Bi0.09NbO3 makes ferroelectric domains to transform into highly dynamic polar nanoregions (PNRs), leading to the concurrently enhanced energy-storage properties by the transition from ferroelectric to relaxor ferroelectric (RFE). Furthermore, it is confirmed by piezoresponse force microscopy that the appearance of PNRs breaks the long-range order to some extent and reduces the stability of the microstructure, which explains the excellent energy-storage performance of RFE ceramics. Therefore, this work has promoted the practical application ability of BaTiO3-based energy-storage dielectric ceramics.

Heteroepitaxial PbTiO3 film on an Nb-doped (001) cubic SrTiO3 substrate was fabricated by hydrothermal epitaxy at 200°C. Piezoresponse force microscopy and x-ray Θ rocking curves confirmed that the film showed a c∕a∕c∕a multi-domain structure even though it did not undergo a cubic paraelectric (PE) to tetragonal ferroelectric (FE) phase transition. After heat treatment of this film at 600°C, we observed the [110] surface band within the a-domain, which was formed through the PE to FE phase transition. We also found that a [110] surface band existed along the (11¯1) plane within the a-domain. We predicted that the [110] surface band would be monoclinic phase due to the interaction of two different variants of a-domains in the presence of a c-domain in the heteroepitaxial PbTiO3 film.

Peculiarities in the nonlinear dielectric response of the relaxor lead magnoniobate (PMN) are explained within the classic Landau-Ginzburg-Devonshire theory. It turns out that a correction term proportional to the square of the polarization, P 0 2 , of polar nanoregions (PNRs) becomes relevant in relaxor ferroelectrics. These PNRs are stabilized by fluctuations of quenched random electric fields. In contrast to regular ferroelectrics with continuous phase transitions, where the third harmonic susceptibility, χ 3 , is negative at T > T c , the contribution due to PNRs drives χ 3 positive in PMN. The lack of an anomaly in χ 3 at the freezing temperature, T f , does not favor a glassy scenario of relaxors.

Mixed ferroelectrics exhibit unusual precursor effects. In ${\mathrm{KTa}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$ ${\mathrm{Nb}}_{\mathrm{x}}$ ${\mathrm{O}}_{3}$ , polar nanoregions have been shown to condense approximately 20 K above the transition for all Nb concentrations, 1.2%50%, as a result of medium-range collective interactions between Nb off-center ions. These interactions are also responsible for the observation of hysteresis loops in the polarization and dielectric nonlinearities far above the transition. In the present study we have identified three distinct polarization regimes: (1) dynamic and (2) quasistatic, both above the transition, and (3) static, below the transition. The first two regimes can be distinguished by the shape of the hysteresis loops, changing from oval to s shape, and by their frequency dependence. We have analyzed the harmonic content of the polarization response and show that the condensation of polar nanoregions coincide with the appearance of odd harmonics which are indicative of a nonlinear response. This is further supported by the observation of a nonlinear dielectric response that becomes progressively stronger with decreasing temperature below the condensation. We also show that there exists a direct relationship between dielectric and polarization response and that one can be calculated from the other. Finally, the low-frequency dynamics exhibited in the quasistatic range can be qualitatively explained by the strong interaction between neighboring off-center Nb ions within polar nanoregions and random interactions between these regions.