Magnetization distribution

It should be noted that the decomposition shown in Eq. 3.7.2 is not necessarily a subdivision of separate sets of spins, as all spins in general are subject to both relaxation and diffusion. Rather, it is a classification of different components of the overall decay according to their time constant. In particular cases, the spectrum of amplitudes an represents the populations of a set of pore types, each encoded with a modulation determined by its internal gradient. However, in the case of stronger encoding, the initial magnetization distribution within a single pore type may contain multiple modes (j)n. In this case the interpretation could become more complex [49]. 

In order to elucidate the details of the magnetization distribution in the bulk of the sample, several pick-up coils were used. They were inductively coupled with different parts of the crystal (Fig. 6). 

Figure 6. Remanence enhancement in a two-phase Nd2Fe 4B/Fe3B magnet containing 343 grains. Left Finite element model of the grain structure. Right Magnetization distribution in a slice plane for zero applied field. The arrows denote the magnetization direction projected on a slice plane.

A further structure effect, the proton polarizability, is only estimated to be < 4 ppm [28], of the same order than the value above. The agreement between theory and experiment is therefore only valid on a level of 4 ppm. Thus, we can say that the uncertainty in the hyperfine structure reflects dominantly the electric and magnetic distribution of the proton, which is related to the origin of the proton anomalous moment, being a current topics of particle-nuclear physics. 

Let us assume that we have observed some magnetic potential Ur C) on the surface of the Earth. The problem is to determine the function /( ) of complex magnetization distribution. We introduce a complex Hilbert space D of data (magnetic potential) with the metric given by formula (7.2), and a complex Hilbert space M of models (functions /(C)) with the metric... 

Fig. 21. The vacuum-polarization-like Feynman diagrams for the hyperfine-structure splitting, (a) and (b) are the wave-function corrections and (c) is the magnetic-loop modification. The cross x signifies the interaction with the nuclear magnetization distribution.

Just as in the case of isotope shifts discussed in Sec. IID, we expect the effect to scale essentially as R, but also higher moments of the magnetization distribution continue, and the integrals can be approximated by... 

From these considerations, we conclude that the differences in the magnetization distribution must give relatively large positive contribution to corresponding to a magnetization distribution closer to the nucleus for Cs, than for Cs. 

We only briefly mention that a similar modification, i.e., a change from a Dirac delta distribution to an extended distribution, would be required for the spin-dependent electron-nucleus contact term, known as Fermi contact term, if the usual point-like nuclear magnetization distribution (the pointlike nuclear magnetic dipole approximation) is replaced by an extended nuclear magnetization distribution. 

Figure 7.5. Domain structure observation by means of the Cotton-Mouton effect In the Iron-garnet film with crystallographic orientation (100). (a) Magnetization distribution In the sample (b, c) images obtained at different polarizer and analyzer orientations [28],...

The fact that susceptibility x( ) depends only on the Z-spatial coordinate means that we examine here a medium with a stratified structure. The polarization vector Pi(r,t) is determined by the kind of inhomogeneities. If it is related to the magnetization distribution, then in Unear magnetoopfics we have... 

Figure 7.17. Magnetization distribution in magnetic nanocontact (a) and simulated near-field images obtained in crossed polarizers (s-polarization is incident, p-polarization is detected) for the case of light incidence parallel to the XZ plane with (b) and without (c) taking into account the crystalline part of %,j in equation (21). Height of scanning is lOnm. Spatial resolution is about 15nm.

The magnetic system is based on magnets distributed along the track. An on-board sensor detects the magnetic fields generated by each magnet in order to follow the track. 

Fig. 4.29 (a) Sketch of one-dimensional polarization and magnetization distributions (solid curves) inside the nanotube and are corresponding extrapolation lengths, which geometrical sense is the distance on x-axes cut by the tangent line to the points x = (b) Spontaneous... 

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