Extended domain wall

The mechanism for coercivity in the Cr—Co—Fe alloys appears to be pinning of domain walls. The magnetic domains extend through particles of both phases. The evidence from transmission electron microscopy studies and measurement of JT, and anisotropy vs T is that the walls are trapped locally by fluctuations in saturation magnetization. 

The wall-width parameter 80 varies from about 1 nm in extremely hard materials to several 100 nm in very soft materials. It determines the thickness Sb = nSa and energy yw = AK S0 of Bloch domain walls [13, 14, 97, 98], and describes the spatial response of the magnetization to local perturbations [95], Essentially, the thickness of the walls is determined by the competition between exchange, which favors extended walls, and anisotropy, which favors narrow transition regions. 

Typical domain walls are smooth and extend over many interatomic distances. However, deviations from this continuum picture occur in very hard materials (narrow walls), at grain boundaries and in the case of geometrical constraints. Narrow-wall phenomena, which have been studied for example in rare-earth cobalt permanent magnets [189] and at grain boundaries [95, 96], involve individual atoms and atomic planes and lead to comparatively small corrections to the extrinsic behavior. 

The original magnetic properties of hard nanostructures, described in the above sections, are direct consequences of the crystallite particle size reduction, when this size approaches the domain wall thickness, S. In this section, we apply and extend the findings of Chapters 3 and 4 to hard-magnetic nanostructures. We discuss (i) systems of exchange decoupled particles, and (ii) systems of exchange-coupled particles, themselves divided into single-phase systems and nanocomposites. 

Figure 11.16 Domains due to the differing alignment of dipoles in adjacent regions of a crystal. The regions are separated by a domain wall, which extends over several tens of nanometres in practice...

Here, Nj (r) is the number of spins in block A, and the summation extends over all spins in that block. In contrast to what happens at the atomic domain, we expect the magnetization to vary fairly smoothly in proceeding from one block to the next. To ensure smoothness we must insert an extra term into the Landau formalism that penalizes extreme variations or discontinuities in 2Vt(r) domain walls are energetically very expensive. The simplest analytic variation that achieves this aim is expected to be of the form... 

Besides the (7x7) structure, the DAS model can easily be extended to (2n+1) X (2 +1) reconstructions with n= 1,2,3,4,... The corresponding unit cells possess n(n +1) adatoms and (n — 1) rest atoms. The domain walls separating the (2x2) adatom islands exhibit 3x dimers. Vanderbilt [56] suggested a relatively simple model for the energetics of the Si(lll) and Ge(lll) surfaces. For Si, he estimated the formation energy for the various stractural elements ... 

If the direction of the spins is not uniform in space, we are dealing with noncollinear magnetism. Noncollinear spin structures appear, e.g., as canted or helical spin configurations in rare-earth compounds, as helical spin-density waves, or as domain walls in fer-romagnets. To describe these, one requires a formulation of SDFT in which the spin magnetization is not a scalar, as above, but a three-component vector m(r). Different proposals for extending SDFT to this situation are available. 

There is also rapid development in the domain of standard silica-based zeolites. Their versatility can be extended by imprinting. For instance, Davis and Katz [15] recently successfully carried out imprinting and obtained a silica framework with pore walls anchoring three aminopropyl groups in cavities. Another achievement was reported by Ramamurthy, Schefer and coworkers [16]. The latter authors were able to obtain 90% diastereomeric excess of a product of the photochemical reaction in a commercially available zeolite containing chiral tropolone ether 433 in its pores. 

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