Domain wall relaxation

The analysis in the last paragraph has shown that the incommensurate Xe layer on Pt(lll) at misfits of about 6% is a striped phase with fully relaxed domain walls, i.e. a uniaxially compressed layer. For only partially relaxed domain walls and depending on the extent of the wall relaxation and on the nature of the walls (light, heavy or superheavy) additional statellites in the (n, n) diffraction patterns should appear. Indeed, closer to the beginning of the C-I transition, i.e. in the case of a weakly incommensurate layer (misfits below 4%) we observe an additional on-axis peak at Qcimm + e/2 in the (2,2) diffraction pattern. In order to determine the nature of the domain walls we have calculated the structure factor for the different domain wall types as a function of the domain wall relaxation following the analysis of Stephens et al. The observed additional on-axis satellite is consistent with the occurrence of superheavy striped domain wails the observed peak intensities indicate a domain wall width of A=i3-5Xe inter-row distances. With... 

Srivastava, C. M., Shringi, S. N., Srivastava, R. G. Nanadikar, N. G. (1976). Magnetic ordering and domain wall relaxation in zinc-ferrous ferrites. 

The requirements of high permeability and high working frequency lead to a compromise, since for a given composition, an increase in grain size leads simultaneously to an increase in permeability and a decrease in domain wall relaxation frequency. The choice of the basic composition... 

Freitas, P.P. Domain wall relaxation, creep, sliding, and switching in superferromagnetic discontinuous CosoFe2o/Al203 multilayers. Phys. Rev. Lett. 89, 137203(4) (2002)... 

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...

Ultrathin films of hexagonal symmetry under compressive strains (e.g. Ag/Pt(lll) with a misfit of +4.3%) relax the strain in a similar way by forming striped-phases. The domain walls are now regions of locally lower atomic density and are imaged dark in STM [73]. The stable configuration, however, consists of a trigonal network of crossed domain walls. 

Figures 8 and 9, plate 3, are lattice images of two compounds (n = 2 and n = 5 respectively) showing evidence of 180° domain walls. The c axes, normal to the dark Bi202 sheets in the plane of the image, are nearly, but not exactly, parallel in the two domains the two component c axes, C and C, are inclined at about 3°. These observations suggest that the domain walls are of 180° type and that the polar axes of both the n = 2 and n = 5 compounds deviate slightly from the Ct or c0 axes. As in Bi4Ti3012, there may be some small monoclinic distortion. Selected area diifraction patterns, nominally taken from both sides of the domain boundary, were identical, but the small size of the domain, about 50 nm across, makes the evidence from selected area diffraction inconclusive. As expected for 180° domains, the domain walls are quite thin since only a small adjustment or relaxation of the [B08] octahedra would be necessary, the structure of the wall is undoubtedly simple. As a consequence, the lines of contrast due to the A site cations are clearly visible in the neighbourhood of the wall (figure 9), with only minor distortions around the boundary (dashed line).

Fig. 1 Domains of the projected atomic structure of the a-Al203-(v/3l x >/3T)R 9° reconstruction, where the unit cells as well as domain walls are drawn. The two constituting A1 planes are shown separately, with evidence of one being much better ordered than the other. Numerical relaxation has shown that the ordered layer could be associated to the outermost layer and the more disordered one to the layer adjacent to the substrate (from Ref. 43).

The relation between W and Ws, the domain wall widths in the bulk and at the surface, can be seen in Figure 8. The effect of the surface relaxation is clearly visible as the order parameter at the surface Qs never reaches the bulk value Qo- The distribution of the square of the order parameter at the surface shows the structure that some of the related experimental works have been reported (Tsunekawa et al. 1995, Tung Hsu and Cowley 1994), namely a groove centred at the twin domain wall with two ridges, one on each side. 

In addition, the square of the surface order parameter is proportional to the chemical reactivity profile of the twin domain wall interface at the surface (Locherer et al. 1996, Houchmanzadeh et al.(1992). Intuitively, one would expect the chemical reactivity of the surface to be largest at the centre of the twin domain wall, falling off as the distance from the centre of the wall increases. Contrary to the expected behaviour, a more complex behaviour is found. The reactivity, a monotonic function of Q, is expected to fall off as the distance from the centre of the wall increases, but only after if has reached a maximum of a distance of - 3 IF from the centre of the domain wall. If such a structure is expected to show particle adsorption (e.g. in the MBE growth of thin films on twinned substrates) we expect the sticking coefficient to vary spatially. In one scenario, adsorption may be enhanced on either side of the wall while being reduced at the centre. The real space topography of the surface is determined by both sources of relaxation-twin domain wall and the surface. These are distinct and, when considered separately, the wall... 

Overlayer relaxed with antiphase domain walls and off-center atoms ... 

These internal modes can be individual movements which are easily detectable (for example, in the case of magnetic materials at high frequency there is a magnetic spin resonance called gyromagnetic resonance ). Many others (collective modes) should be noted, whether by physical intuition or by response calculation of heavily coupled systems (relaxation of magnetic domains at low frequencies wall relaxation ). Such collective modes are also observed in the case of heterogeneous materials based on conductive inclusions. They are due to capacitive effects and induced currents. 

At very high frequencies, domain walls are unable to follow the field and the only remaining magnetisation mechanism is spin rotation within domains. This mechanism eventually also shows a dispersion, which always takes the form of a resonance. Spins are subjected to the anisotropy field, representing spin-lattice coupling as an external field is applied (out of the spins easy direction), spins experience a torque. However, the response of spins is not instantaneous spins precess around the field direction for a certain time (the relaxation time, r) before adopting the new orientation. Fig. 4.62. The frequency of this precession is given by the Larmor frequency ... 

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