Soft modes, ferroelectrics

The problem of the structural multidomaining below Ta makes it difficult to reach a definite conclusion, as shown in Figs. 5 and 13. Measurements for defect-free and stress-free STO samples are indispensable for a definite conclusion about the symmetry of the ferroelectric phase of STO 18. Finally, we can conclude that STO 18 may be a typical soft mode ferroelectric. 

Weyrich KH, Siems R (1984) Molecular dynamics calculations for systems with a localized soft-mode. Ferroelectrics 55 333-336... 

G. Andetsson, 1. Dahl, L Kornilov. S T. Lagerwall. K. Sharp, and B. Stabler, AppHcatinns of the soft-mode ferroelectric effect, Proc. 18. FnAarger Arbeitsiuipmg, Freiwi Gcnnany, 1989. 

The experimental setup for realizing the soft-mode ferroelectric effect is depicted in Figure 6.11. For this geometry, the ftee-eneigy density is given by ... 

Blinc, R. and Zeks, B. (1974). Soft Modes in Ferroelectrics and Antiferroelectrics . 

Blinc R, Zeks B (1974) Soft modes in ferroelectrics and antiferroelectrics. Elsevier,... 

Ferroelectric liquid crystals where a continuous symmetry group is broken at Tc and the doubly degenerate relaxational soft mode of the high-temperature phase splits below Tc into an amphtudon -type soft mode and a symmetry restoring Goldstone (i.e., phason ) mode [e.g., p-decyloxybenzylidene p -amino-2-methylbutylcinnamate (DOBAMBC)]. 

Whereas the first microscopic theory of BaTiOs [1,2] was based on order-disorder behavior, later on BaTiOs was considered as a classical example of displacive soft-mode transitions [3,4] which can be described by anharmonic lattice dynamics [5] (Fig. 1). BaTiOs shows three transitions at around 408 K it undergoes a paraelectric to ferroelectric transition from the cubic Pm3m to the tetragonal P4mm structure at 278 K it becomes orthorhombic, C2mm and at 183 K a transition into the rhombohedral low-temperature Rm3 phase occurs. 

The concept of quantum ferroelectricity was first proposed by Schneider and coworkers [1,2] and Opperman and Thomas [3]. Shortly thereafter, quantum paraelectricity was confirmed by researchers in Switzerland [4], The real part of the dielectric susceptibihty of KTO and STO, which are known as incipient ferroelectric compounds, increases when temperature decreases and becomes saturated at low temperature. Both of these materials are known to have ferroelectric soft modes. However, the ferroelectric phase transition is impeded due to the lattice s zero point vibration. These materials are therefore called quantum paraelectrics, or quantum ferroelectrics if quantum paraelectrics are turned into ferroelectrics by an external field or elemental substitution. It is well known that commercially available single crystal contains many defects, which can include a dipolar center in the crystal. These dipolar entities can play a certain role in STO. The polar nanoregion (PNR originally called the polar microregion) may originate from the coupling of the dipolar entities with the lattice [5-7]. When STO is uniaxially pressed, it turns into ferroelectrics [7]. 

Figure 6 shows the influence of the pressure of e T) on both ST018-92(a) and SCT(0.007) [21]. We first note the large shift in the transition to lower temperature for STO 18. The initial slope is dTcdP = - 20 K/kbar, a large effect. Second, there is a large decrease in the ampHtude of the peak with pressure. At 0.70 kbar, the transition is completely suppressed, and the e (T) response closely resembles that of STO 16 at 1 bar. These pressure effects are characteristic of displacive ferroelectrics in the quantum regime and can be understood in terms of the soft-mode theory. The situation is similar for SCT(0.007), as shown in Fig. 6b. In the case of SCT(0.007), ferroelectricity completely disappears at 0.5 kbar.

It has been widely recognized that the Ught scattering technique yields essential information on a dynamic mechanism of ferroelectric phase transition because it clearly resolves the dynamics of the ferroelectric soft mode that drives the phase transition. Quantum paraelectricity is caused by the non-freezing of the soft mode. Therefore, the isotope-exchange effect on the soft mode is the key to elucidating the scenario of isotopically induced ferroelectricity. 

Figure 14 shows the result of a Brillouin scattering experiment in the vicinity of Tc [11]. Closed circles and open circles below Tc indicate the modes split from the doubly degenerated ferroelectric soft mode. The closed circles above Tc denote the frequency of the doubly degenerated soft u mode in the paraelectric phase. The results clearly show a softening of the soft mode toward zero frequency at Tc following the Curie-Weiss law. The soft mode remains underdamped even at Tc. Generally, a soft mode is heavily damped in the vicinity of Tc, e.g., as for PbTiOs, which are typical displacive-type... 

However, the incomplete softening of the soft mode still raises fundamental questions about the mechanism underlying the occurrence of a ferroelectric region in ST018-32. The most plausible interpretation for this phenomenon is the inhomogeneity of the soft mode dynamics. 

Measurements of NMR for Ti, Ti [33], and Sr [34,35] were carried out for STO 16 and STO 18-96. Ti and Sr nuclear magnetic resonance spectra provide direct evidence for Ti disorder even in the cubic phase and show that the ferroelectric transition at Tc = 25 K occurs in two steps. Below 70 K, rhomb ohedral polar clusters are formed in the tetragonal matrix. These clusters subsequently grow in concentration, freeze out, and percolate, leading to an inhomogeneous ferroelectric state below Tc. This shows that the elusive ferroelectric transition in STO 18 is indeed connected with local symmetry lowering and impHes the existence of an order-disorder component in addition to the displacive soft mode [33-35]. Rhombohedral clusters, Ti disorder, and a two-component state are found in the so-called quantum paraelectric... 

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