Domain wall width

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... 

Note than typical domain-wall widths are much smaller than the domains themselves. When the size of a magnetic particle is smaller than the domain-wall width Sa, as encountered for example in small soft-magnetic nanodots, then the distinction between domains and domain walls blurrs, and the determination of the micromagnetic spin structure requires additional considerations [102], One example is curling-type flux-closure or vortex states. 

When the anisotropy energy within the hard layer cannot be considered as infinite as compared to the Zeeman energy, the nucleation field depends on the hard layer magnetic properties [122], However, as long as <7hard > 34ard ( hard and 4ard are the hard layer thickness and domain wall width respectively), Hn does not depend much on dhard. For 10 nm, the room temperature nucleation field jU()Hn is typically 1 T. 

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. 

The results can be used as a guide for the future experimental work. In order to determine the twin domain wall width W in the bulk, one only needs to determine the characteristic width IFs of the surface structure of the domain wall. Previously, these features of the twinning materials were investigated using mainly X-ray techniques. In fact, the theoretical work leads to the conclusion that the only necessary information for the determination of the twin domain wall width W are the real space positions of the particles in the surface layer. 

Chrosch J, Salje EKH (1999) The temperatrrre dependence of the domain wall width in LaAlOs. J Appl Phys 85 722-727. 

Domain-wall surface energy y, domain-wall width W, single-domain particle diameter Dc, average width of the domain Z) and grain diameter Da in various permanent magnet materials. 

Magnetic nanostructures possess promising features due to their characteristic sizes that are comparable to the spin-flip diffusion length and magnetic domain-wall width. In practice, their fabrication and characterization become increasingly difficult with feature sizes decreasing beyond the standard photolithography limit [1,2]. 

This means that to consider the spontaneous flexoelectric effect influence on the substance physical properties one has to rewrite all earlier analytical expressions for long nanorods and nanowires without flexoelectric effect [8, 78] by the substitution g 2 and X for g and Xs in the expressions for the corresponding property. Note that for polydomain (if any) wires the predicted effect of R decrease with /44 increase should lead to the decrease of the intrinsic domain-wall width defined as 2 R. Below we demonstrate the spontaneous flexo-effect influence on the critical parameters (temperature and radius) of size-induced phase transition and correlation radius using the results [8,78] obtained without flexoeffect. 

It is clear from the Fig. 4.28a, b that in ferroelectric phase (i.e. at R>Rcr) the correlation radius monotonically decreases with the increase of the flexoelectric coefficient/44. At the same time, in paraelectric phase correlation radius increases with the increase of the flexoelectric coefficient, since the critical temperature (see Eq. (4.22)) increases with the increase of the flexoelectric coefficient. This opens the possibility to control the phase diagram and polar properties (e.g. via influence on domain wall width) by the choice of the material with necessary flexoelectric coefficient at given temperature or nanoparticle radius. 

Lower Curie temperatures and greater atomic spacing (greater domain wall width) reduces the domain wall energy. 

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