Easy direction

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This approximation is strictly valid only for systems of uniaxial symmetry, i.e, having two equivalent magnetic easy directions. For systems with more equivalent directions (magnetite for example... 

The fluctuations of the magnetization direction around an easy axis, known as collective magnetic excitations, can be considered fast compared to the time scale of Mossbauer spectroscopy because there are no energy barriers between magnetization directions close to an easy direction, and the magnetic splitting in the... 

Cation dehydration connected with the standard hydration energy of the cation multiplied by —1, —ACj j+ this quantity is experimentally attainable under certain conditions and it is especially easy directly to determine the difference in this quantity for a number of cations. 

In spm crystals, the aligned spins are not allowed to point arbitrarily towards any direction regarding the crystal structure, which favors some axes against others aligning onto directions called easy directions is less energy consuming than aligning onto other directions. 

Another process responsible for a fluctuation of the local magnetic field is Neel relaxation. It corresponds to the flip of the crystal magnetization vector from one easy direction of anisotropy to another. The correlation time of this... 

When the anisotropy energy is large enough it prevents any precession of the magnetic moment of super-paramagnetic crystals. The magnetic fluctuations then arise from the jumps of the moment between different easy directions. The precession prohibition is introduced into the Freed equations in order to meet that requirement every time the electron Larmor precession frequency appears in the equations, it is set to zero 12). 

Arylmercury chlorides are valuable reagents for the preparation of aryltellurium trichlorides because they are used when the aromatic substrate is not sufficiently reactive for an easy direct condensation with tellurium tetrachloride. ... 

The first type is the crystal anisotropy which is responsible for the dependence of the magnetization curves on the orientation of the crystal in the magnetic field. The energy E, which is necessary to deflect the magnetic moment in a single crystal from the easy direction into less easy ones is given for cubic crystals by ... 

We used in (9.17) the subtracted electron factor. However, it is easy to see that the one-loop anomalous magnetic moment term in the electron factor generates a correction of order a Za)Ep in the diagrams in Fig, and also should be taken into account. An easy direct calculation of the anomalous magnetic moment contribution leads to the correction... 

This critical field called coercivity ff. or switching field Ff., is also equal to FF. If a field is applied in between 0 and 90° the coercivity varies from maximum to zero. In the case of this special example the applied field Ha = Hs = Hc = Hk. Based on the classical theory, Stoner-Wohlfarth (33) considered the rotation unison for noninteracted, randomly oriented, elongated particles. The anisotropic axis can be due to the shape anisotropy (depending on the size and shape of the particle) or to the crystalline anisotropy. In the prolate ellipsoids b is the short axis and a the longest axis. The demagnetizing factors are IV (in the easy direction) and The demagnetizing fields can then be calculated by Hda = — Na Ms, and Hdb = — Nb Ms. The shape anisotropy field is Hd = (Na — Nb)Ms. Then the switching field Hs = Hd = (Na — Nb)Ms. 

Magnetization of a material. Initially, magnetization increases by growth of favorably oriented domains. At high fields, the direction of magnetization rotates out of the easy direction. 

The approximate expression for K (Eq. (9.28)) leaves out all but two of the terms of an infinite power series, and even the term involving K2 can often be safely neglected. If it is assumed that K2 is negligible and Aj is positive, then K has a minimum value of zero if any two of the direction cosines are zero, i.e. the anisotropy energy is a minimum along all three crystal axes and these are therefore the easy directions. If Kx is negative, the minimum occurs for ai = a2 = a3 = 1/ /3, i.e. the body diagonal is the easy direction. 

The anisotropy constants listed in Table 9.1, which anticipate the discussion of ferrites (Section 9.2 et seq.), indicate that the easy directions for cubic crystals are [111] except for those containing cobalt, in which case they are [100]. For... 

The energy minimum occurs for 9 = 0, making the c axis the easy direction. 

Magnetic anisotropy yields easy magnetization directions corresponding to local energy minima and energy barriers that separate the easy directions. On an atomic scale, the barriers are easily overcome by thermal fluctuations, but... 

Generally, isotropic permanent magnets with a remanence ration JJJS > 0.5 are referred as remanence enhanced materials. However, the theoretical limit for the remanence of noninteracting grains depends on the crystal symmetry, the crystallographic orientation of the easy directions, and the volume fraction and the saturation polarization of the phases. The remanence ratio a two-phase nanocomposite magnet is... 

Given values of the constants appearing in the expressions for the matrix elements listed in (8.238), we can calculate the energies of the hyperfine levels for N = 1 and hence calculate the transition frequencies. This we shall now do, but note that this is the easy direction in which to proceed Brooks, Lichten and Reno [42] had the more difficult problem of determining the constants from the experimental data. Their values [42] are as follows (MHz) ... 

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