Domain wall polarization

Domain wall polarization plays a decisive role in ferroelectric materials and contributes to the overall dielectric response. The motion of a domain wall that separates regions of different oriented polarization takes place by the fact that favored oriented domains with respect to the applied field tends to grow. 

Ferroelectric domains have been visualized in the ferroelectric phase in sbn with high resolution piezo-response force microscopy (see Figure 15.8) [23], The domains are found to be needlelike with lengths in the range of 10 to 500 nm and are oriented along the polar c-axis. The dynamics of the domain walls under externally applied electric fields or heating are expected to influence the polarization especially at low frequencies (see domain wall polarization, Chapter 1) [24],... 

In dielectric materials there can be both permanent and induced polarization domains. The walls between these domains may also act as barriers to dislocation motion. They tend to have larger energies than magnetic domain walls so they may have more effect on hardness (McColm, 1990). 

The starting system is achiral (plates at 90° with isotropic fluid between), but leads to the formation of a chiral TN structure when the fluid becomes nematic. In this case, enantiomeric domains must be formed with equal likelihood and this is precisely what happens. The size of these domains is determined by the geometry and physics of the system, but they are macroscopic. Though the output polarization is identical for a pair of heterochiral domains, domain walls between them can be easily observed by polarized light microscopy. This system represents a type of spontaneous reflection symmetry breaking, leading to formation of a conglomerate of chiral domains. 

Fig. 12 Temperature dependence of the FC spin-spin relaxation time T2 in PMN. The minimum at 200 K corresponds to the freezing of polar clusters. The shallow minimum at 140 K, which is absent in the ZFC data, is related to the motion of FE domain walls...

Fig. 3. Temperature dependent Raman spectra for zz polarization of single crystal LasflSr1/3Ni04. Inset shows an idealized structure of the stripe-ordered phase in the plane perpendicular to the charge domain walls for 1/3 doping. The open circles indicate correlated in the Ni02 layers spins at Ni2+ sites. The filled circles show o 200 400 6oo 8oo iooo 1200 locations of doped holes on...

When a ferroelectric single crystal is cooled below the phase transition temperature the electrical stray field energy caused by the non-compensated polarization charges is reduced by the formation of ferroelectric domains, see Figure 1.19. The configuration of the domains follows a head-to-tail condition in order to avoid discontinuities in the polarization at the domain boundary, VP = a. The built-up of domain walls, elastical stress fields as well as free charge carriers counteract the process of domain formation. In addition, an influence of vacancies, dislocations and dopants exists. 

The ferroelectric hysteresis originates from the existence of irreversible polarization processes by polarization reversals of a single ferroelectric lattice cell (see Section 1.4.1). However, the exact interplay between this fundamental process, domain walls, defects and the overall appearance of the ferroelectric hysteresis is still not precisely known. The separation of the total polarization into reversible and irreversible contributions might facilitate the understanding of ferroelectric polarization mechanisms. Especially, the irreversible processes would be important for ferroelectric memory devices, since the reversible processes cannot be used to store information. 

For ferroelectrics, mainly two possible mechanisms for irreversible processes exist. First, lattice defects which interact with a domain wall and hinder it from returning into its initial position after removing the electric field that initiated the domain wall motion ( pinning ) [16]. Second, the nucleation and growth of new domains which do not disappear after the field is removed again. In ferroelectric materials the matter is further complicated by defect dipoles and free charges that also contribute to the measured polarization and can also interact with domain walls [17]. Reversible contributions in ferroelectrics are due to ionic and electronic... 

The domain energy W consists of the depolarization field energy W,i, the energy of the domain walls Ws, and the energy, Wt, of the interaction between the electric field of the tip and the spontaneous polarization of the domain. Following Landauer [63] hereafter we assume that the domain has a shape of an elongated half-ellipsoid in the polar direction. 

More generally, the dynamic behavior of domain walls in random media under the influence of a periodic external field gives rise to hysteresis cycles of different shape depending on various external parameters. According to a recent theory of Nattermann et al. [54] on disordered ferroic (ferromagnetic or fe) materials, the polarization, P, is expected to display a number of different features as a function of T, frequency, / = iv/2tt, and probing ac field amplitude, E0. They are described by a series of dynamical phase transitions, whose order parameter Q = uj/2h) Pdt reflects the shape of the P vs. E loop. When increasing the ac... 

Several studies have examined the thickness of the domain wall in ferroelectric materials [17]. The 90° a-c domain wall thickness has been measured using a transmission electron microscope (tem), [14] but distinguishing the positive and negative domains in 180° opposite polarization areas is difficult because these methods are used to observe the strain of arrangements of molecules. Direct clarification of the domain wall thickness is important with respect to both scientific and engineering aspects. 

Keywords Magnetic multilayers, interlayer exchange coupling, exchange bias, magnetization reversal, X-ray reflectivity, polarized neutron reflectivity, domain walls, magnetic roughness. 

Alternating fields cause domain walls to oscillate. At low fields the excursions of 90°, 71° or 109° walls result in stress-strain cycles that lead to the conversion of some electrical energy into heat and therefore contribute to the dielectric loss. When peak fields are sufficient to reverse the spontaneous polarization the loss becomes very high, as shown by a marked expansion of the hysteresis loop (Fig. 6.9). 

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