Polar nanoregions

While many researchers believe that the above mentioned three ingredients for rl behavior to appear are more or less independent, we have argued since long [6] that the primary cause of RL behavior is the lattice disorder, which is at the origin of the occurrence of polar nanodomains and their fluctuations within the highly polarizable lattice. In order to describe disordered systems and to explore their basic thermodynamic behavior simple spin models are frequently used. The model Hamiltonian 

The manifestation of the presence of polar nanodomains in strong rls in terms of the electro-optic effect was first demonstrated by Burns and Dacol [3] in measurements of the T dependence of the refractive index, n. For a normal ABO3 fe crystal, starting in the high-temperature PE phase, n decreases linearly with decreasing T down to Tc at which point n deviates from linearity. The deviation is proportional to the square of the polarization and 

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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]. 

Recent neutron scattering measurements [25] have revealed a well-defined fe (TO) soft mode in pmn at high temperatures that becomes overdamped by the polar nanoregions below the Burns temperature, Td. Thus, while the soft mode below Td is not a well-defined excitation in the spectrum, the large value of e and its strong temperature and pressure dependences between Td and Tm clearly implicate low-lying optic mode excitations. 

Tenne DA, Soukiassian A, Zhu MH, Clark AM, Xi XX, Choosuwan H, He Q, Guo R, Bhalla AS (2003) Raman study of BaxSrj.xTiOa films evidence for the existence of polar nanoregions. Phys Rev B 67 012302... 

Figure 9-5. A fragment of a centrosymmetric crystal structure with the molecules (represented as arrows parallel to their molecular dipoles) NH+—N hydrogen-bonded into antiparallel chains along [y] (the anions are neglected for clarity). The ideal crystal structure with antiparallel molecules in neighbouring chains is marked in green (full arrowheads). Due to defects in the fourth and seventh chains, in which 5 and 6 molecules have reversed orientation, respectively, two polar nanoregions are formed. The red and blue colours and open arrowheads mark these nanoregions, the polarisation of which is indicated with large grey arrows...

Another exanple of this type of microstructure is provided by the relaxor ferroelectrics related to PbMgj Nb Oj. These have a structure described as consisting of polar nanoregions, coherently intergrown within the crystal matrix and sensitive to temperature (Section 6.7). Similarly, the oxide Sm, 8,5Ba3 is nominally... 

The actual nature of the polar nanoregions remains an important question. At high temperatures, well above T, the cations are mobile and PNRs, in this case, are... 

At the Bums temperature, T, nucleation and growth of stable polar nanoregions occurs. This state is called the ER state, which implies that the PNRs, although still forming and reforming, form a quasi-equilibrium situation, so that over the course... 

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