Domain wall structure

Of course, the above discussion apphes only to systems exhibiting domain wall structure, i.e., to weakly inhomogeneous phases formed on surfaces with low corrugation of the gas-solid potential and characterized by the presence of more then one type of equivalent sublattices. When this is not the case, i.e., when the dense incommensurate phase can be considered to be... 

As this expression only rehes on the temperature dependence of the magnetic correlations, Eq. 44 is valid for any Ising-Hke chain independently of the domain wall structure. More specifically, in the case of narrow domain walls and for single-ion anisotropy this expression becomes (using the notations of Eqs. 7a and 23) ... 

Domain wall structures in thin films and small particles can be different from those in massive samples, because some energy contributions may become significant when sample dimensions are decreased. In thin films, the magnetisation vector tends to remain parallel to the film plane to avoid any contribution to the magnetostatic energy. The spins within a domain wall also rotate within the film plane, which leads to Neel walls. Fig. 4.31. Neel walls appear in thin films below a critical thickness limit. 

Fig. 9a - c. Possible domain wall structures for strain relief on hexagonally close packed surfaces (a) unidirectional compression or expansion along the close packed atomic rows. For isotropic strain relief on a mesoscopic scale often two of the three possible rotational domains alternate leading to a herringbone pattern, (b) and (c) trigonal networks with wall crossings [97Bru]. 

The ferroelectric domain structure in the crystal is a reason of the non-linear behavior of the polarization as a function of an electric field. Dielectric hysteresis appears in the alternating electric fields. The dielectric hysteresis loop is one of the most important features of ferroelectric materials (Fig. 5.6). Hysteresis loop or domain structure observation could serve as a proof of ferroelectricity in the material. Due to the presence of domain wall structure, the remanent polarization Pr is always smaller than the spontaneous polarization Ps. 

It turns out that, in the CML, the local temporal period-doubling yields spatial domain structures consisting of phase coherent sites. By domains, we mean physical regions of the lattice in which the sites are correlated both spatially and temporally. This correlation may consist either of an exact translation symmetry in which the values of all sites are equal or possibly some combined period-2 space and time symmetry. These coherent domains are separated by domain walls, or kinks, that are produced at sites whose initial amplitudes are close to unstable fixed points of = a, for some period-rr. Generally speaking, as the period of the local map... 

Figure 21. A low-energy portion of the energy level structure of a tunneling center is shown. Here e < 0, which means that the reference, liquid, state structure is higher in energy than the alternative configuration available to this local region. A transition to the latter configuration may be accompanied by a distortion of the domain wall, as reflected by the band of higher energy states, denoted as ripplon states.

At the same time, the main conclusions of the original semiclassical argument remain valid each structural transition may be thought of as a rearrangement of about 200 molecules accompanied by distortion of the domain wall that separates the two alternative local atomic arragements. 

Fig. 46. An STM image of the ( /3 x /3)A30° Se structure on Au(l 11) in the early stages of its growth. A network of domain walls separating rhombic domains. Adapted from ref. [237],...

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. 

Figure 3.30 Magnetic domains in a ferromagnetic crystal (schematic). The magnetic dipoles, represented by arrows, are aligned parallel in each domain. The domain walls constitute (approximately) planar defects in the structure.

Ferromagnetic and ferroelectric materials are only two examples of a wider group that contains domains built up from switchable units. Such solids, which are called ferroic materials, exhibit domain boundaries in the normal state. These include ferroelastic crystals whose domain structure can be switched by the application of mechanical stress. In all such materials, domain walls act as planar defects running throughout the solid. 

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