Domain wall dynamics

Many of the specific applications of ferrites depend on their behaviour at high frequencies. When subjected to an ac field, ferrite permeability shows several dispersions as the field frequency increases, the various magnetisation mechanisms become unable to follow the field. The dispersion frequency for each mechanism is different, since they have different time constants. Fig. 4.59. The low-frequency dispersions are associated with domain wall dynamics and the high-frequency dispersion, with spin resonance the latter, usually in the GHz range, is discussed in Section 4.6.2. 

The two main magnetisation mechanisms are wall bowing and wall displacement (see Section 4.3.2) in fact, any field results in a bowing of pinned walls, and if this field has a higher value than the corresponding critical field, walls are unpinned and displaced. Otherwise, bowed walls remain pinned to material defects. Measurements at low fields therefore show only one wall dispersion. Fig. 4.60 at high fields, several, complex dispersions are observed, such as those in Fig. 4.59. Wall displacement 

Domain wall dynamics are usually represented by an equation of 

The techniques of impedance spectroscopy, widely used in dielectrics (Jonscher, 1983 MacDonald, 1987) have been applied to magnetic materials. In this method, impedance measurements as a function of frequency are modelled by means of an equivalent circuit and its elements are associated with the physical parameters of the material. The complex permeability, p, is determined from the complex impedance, Z, by  

A different type of experiment can be performed on single crystals to measure the domain wall propagation at constant velocity, by applying a constant field. The acceleration term is eliminated and Eq. (4.62) can be written  

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The switching or memory phenomena induced by electric field application or photo irradiation have been studied on Mott insulators, charge ordered insulators, and N-I transition systems and were found to be fast phase transitions in general. For the former two systems, the phase transitions caused a pronounced change in reflectance and conductivity from insulating to metallic features. The third system also exhibited a change in conductivity and dielectric response connected with the transports of solitons and/or domain walls, dynamic dimerization, and... 

D. Gomila, P. Colet, M. San Miguel, and Oppo G.-L. Domain wall dynamics Growth laws, localized structures and stable droplets. Eur. Phys. J. - Special Topics, 146 71-86, 2007. 

Valenzuela, R. Irvine, J. T. S. (1993). Domain wall dynamics and short range order in ferromagnetic amorphous ribbons. Journal of Noncrystalline Solids, 156-158, 315-18. 

Domain wall behavior during this switching process has attracted interest because most device applications in some way involve domain wall movement to modulate electromagnetic or acoustic energy. Domain wall dynamics will be discussed in section 3.6. 

Dynamic domain imaging or Kerr microscopy of low coercivity thin films at MHz domain-switching frequencies allows one to examine domain wall motion in detail. ... 

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],... 

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... 

Remaut, G., Gevers, R., Lagasse, A., Amelinckx, S. (1965). Dynamical theory of the images of microtwins as observed in the electron microscope. 11 overlapping domain wall boundaries, phys. stat. sol., 10, 121-39. 

Stamp PCE (1991) Quantum dynamics and tuimeling of domain walls in ferromagnetic insulators. Phys Rev Lett 66 2802-2805... 

The change in the sign of the order parameter at the surface has been observed (for ferroelectricty) by using a model of imaging developed for the detection of static surface charge (Saurenbach and Terris 1990). For ferroelastics, this corresponds to the profile of the lateral reactive force. The SFM non-contract dynamic mode images (Lithi et al 1993) would correspond to the distribution of the normal reactive force. The divergence of the lateral force distribution away from the centre of the wall can be attributed to the simulated infinite extension of the lattice. In the simulated array, the lateral component of the force reached a finite value between two adjacent domain walls. 

Abstract Pattern formation is a widespread phenomenon observed in different physical, chemical and biological systems on varions spatial scales, including the nanometer scale. In this chapter discussed are the universal features of pattern formation pattern selection, modulational instabilities, structure and dynamics of domain walls, fronts and defects, as well as non-potential effects and wavy patterns. Principal mathematical models used for the description of patterns (Swift-Hohenberg equation, Newell-Whitehead-Segel equation, Cross-Newell equation, complex Ginzburg-Landau equation) are introduced and some asymptotic methods of their analysis are presented. 

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