Anisotropy magnetic

The magnetic hysteresis curves discussed in Section 20.7 have different shapes depending on various factors (1) whether the specimen is a single crystal or polycrystalline (2) if it is polycrystalhne, whether there is any preferred orientation of the grains (3) the presence of pores or second-phase particles and (4) other factors such as temperature and, if a mechanical stress is applied, the stress state. 

Tohoku Univ., 15,721 (1926) and from S. Kaya, On the Magnetisation of Single Crystals of Nickel, Sci. Rep. Tohoku Univ., 17,639 (1928).) 

Rggure 20.19 Schematic magnetization curves for soft and hard magnetic materials. (From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright 1976 by John Wiley Sons, New York. Reprinted by permission of John Wiley Sons, Inc.) 

By definition, a magnetic moment of substance per unit volume is magnetization M = xH. For an anisotropic material, the magnetization vector components are Ma = and the contribution to the fi-ee energy density of the mesophase from the magnetic field is given by [1]  

All groups in a molecule that have it electrons generate secondary anisotropic fields. In acetylene, the magnetic field generated by induced circulation of the n electrons has a geomehy such that the acetylenic hydrogens are shielded (Fig. 3.22). Hence, acetylenic hydrogens have 

130 Nuclear Magnetic Resonance Spectroscopy Part One Basic Concepts 

FIGURE 3.23 Anisotropy caused by the presence of TT electrons in some common multiple-bond systems. 

FIGURE 3.24 The effects of anisotropy in some actual molecules. 

The close agreement of these numbers is no accident. Styrene was the model compound used to generate the A8 values for a phenyl substituent Now, let us try a more challenging example.  

There is another type of hydrogen that, at first glance, appears quite similar to a vinyl hydrogen. It is called a formyl (or aldehydic) hydrogen and is directly bonded to a carbonyl (i.e., C=0) carbon  

Notice also that in the regions outside the cones (i.e., perpendicular to the triple-bond axis) the induced field is 

TYPICAL RANGES FOR PROTONS WITH VARIABLE CHEMICAL SHIFT 

Hydrogens which can exchange either with the solvent medium or with one another also tend to be variable in their absorption positions. The following equations illustrate possible situations. 

R—O—Hh- SOLV H SOLV-I-R—0 Chapter 6 will discuss all of these situations in more detail. 

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Pastor G M, Dorantes-Davila J, Pick S and Dreysse H 1995 Magnetic anisotropy of 3d transition-metal clusters Phys. Rev. Lett. 75 326... 

From the write and read process sketched so far, some requirements for MO media can be derived (/) a high perpendicular, uniaxial magnetic anisotropy K in order to enable readout with the polar Kerr effect (2) a magnetoopticady active layer with a sufficient figure of merit R 0- where R is the reflectivity and the Kerr angle (T) a Curie temperature between 400 and 600 K, the lower limit to enable stable domains at room temperature and the upper limit because of the limited laser power for writing. 

Oriented In-Plane Texture. In this kind of film the properties (H and in the various in-plane directions (texture and nontexture directions) are different. The texture of the film can be supported by the texture of the substrate and the crystal lattice can be smaller in the texture direction than in the transverse direction. This can be the source for strain-induced magnetic anisotropy (magnetostriction). It is also found that the crystal is aligned in the texture direction (92). 

Magnetic Anisotropy Energy. There are several kinds of magnetic anisotropy energy and perhaps the most weU known is the magnetocrystaUine anisotropy. Only a crystalline soHd has this property because the energy is dictated by the symmetry of the crystal lattice. For example, in bcc Fe, the easy axis is in a (100) direction and in fee Ni, it is in a (111) direction. 

Hot pressing to produce substantial texture and magnetic anisotropy via plastic deformation is accompHshed by a process referred to as... 

Tellurium also improves the properties of electrical steels by aiding in the magnetic anisotropy, malleable cast iron (77), and spheroidal (graphitic) cast irons (see also Metal surface TiiEATiffiNTs). 

Figure 1 The principal sources of structural data are the NOEs, which give information on the spatial proximity d of protons coupling constants, which give information on dihedral angles < i and residual dipolar couplings, which give information on the relative orientation 0 of a bond vector with respect to the molecule (to the magnetic anisotropy tensor or an alignment tensor). Protons are shown as spheres. The dashed line indicates a coordinate system rigidly attached to the molecule.

The barium ferrite was found to have an increase in magnetic anisotropy, as in the nickel ferrite, but its overall effect on magnetization was less because of greater magnetocrystalline anisotropy. The shock modification caused reduced crystallite size and local damage that resulted in increased microwave absorption. 

The SH, SCHs, and weakly directing halogens cause small shifts, which to a large extent are determined by magnetic anisotropy effects, especially in the case of the halogens. Attempts have been made to estimate these effects for the other thiophenes. Except for orthohydrogens, these effects are usually very small. 

B. Heinrich and J.F. Cochran, Ultrathin metallic magnetic films magnetic anisotropies and exchange interactions. Advances in Physics 42, 523 (1993). 

The calculation of the magnetic anisotropy of non-cubic materials requires an expansion up to 1 /c . Except in the case of fully relativistic calculations, the expansion is never carried out consistently and only the spin-orbit perturbation is calculated to second order (or to infinite order), without taking account of the other terms of the expansion. In this section, we shall follow Gesztesy et al. (1984) and Grigore et al. (1989) to calculate the terms H3 and H. Hz will be found zero and H4 will give us terms that must be added to the second order spin-orbit calculation to obtain a consistent semi-relativistic expansion. 

I thank P. Bruno for his explanation of the calculation of magnetic anisotropy, and Ph. Sainctavit, L. Varga and D. Cabaret for their thorough readings of the manuscript. 

Chemical applications of magnetic anisotropy studies on transition metal complexes. S. Mitra, Prog. Inorg. Chem., 1977, 22, 310-408 (160). 

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