Random anisotropy axis

RAM random anisotropy-axis model i magnetic correlation length... 

In order to describe the magnetic order behavior of amorphous intermetallic compounds containing rare-earth atoms with nonzero orbital momentum, such as a-TbFe2, Harris et al. (1973) have introduced the random anisotropy-axis ... 

It is evident that the dipolar interaction increases the activation energy and slows the relaxation time of moment reversal. To explain the dependence quantitatively a simple model was proposed [26], inspired by the references contained in [22], where the relaxation time considered is for independent clusters and the dipolar interaction modifies Ueff. In the model, a test cluster of uniaxial anisotropy is surrounded by clusters with their anisotropy axis randomly oriented. The susceptibility is dominated by the largest particles in a sample since it is proportional... 

Fig. 9. Relative magnetisation curves for an array of magnetic ions with random easy axis anisotropy at T = 0 K.

Fig. 4.3-27 Schematic representation of the random anisotropy model for grains embedded in an ideally soft ferromagnetic matrix. The double arrows indicate the randomly fluctuating anisotropy axis the dark area represents the ferromagnetic correlation volume determined by the exchange length Lex = A/(K)) I [3.23]...

Fert and Levy (1980,1981) propose this DM interaction to be responsible for observed anisotropy effects in metallic spin glasses. The anisotropy field D is randomly distributed (like the T atoms), i.e. there is no global anisotropy axis, but with eq. 4 one gets a macroscopic anisotropy energy of unidirectional character... 

This relation is only valid for a crystal with isotropic /-factor. The effect of crystal anisotropy will be treated in Sect. 4.6.2. The function h(6) describes the probability of finding an angle 6 between the direction of the z-axis and the y-ray propagation. In a powder sample, there is a random distribution of the principal axes system of the EFG, and with h 6) = 1, we expect the intensity ratio to be I2J li = I, that is, an asymmetric Mossbauer spectrum. In this case, it is not possible to determine the sign of the quadmpole coupling constant eQV. For a single crystal, where h ) = — 6o) 5 delta-function), the intensity ratio takes the form... 

Figure 4.9 illustrates time-gated imaging of rotational correlation time. Briefly, excitation by linearly polarized radiation will excite fluorophores with dipole components parallel to the excitation polarization axis and so the fluorescence emission will be anisotropically polarized immediately after excitation, with more emission polarized parallel than perpendicular to the polarization axis (r0). Subsequently, however, collisions with solvent molecules will tend to randomize the fluorophore orientations and the emission anistropy will decrease with time (r(t)). The characteristic timescale over which the fluorescence anisotropy decreases can be described (in the simplest case of a spherical molecule) by an exponential decay with a time constant, 6, which is the rotational correlation time and is approximately proportional to the local solvent viscosity and to the size of the fluorophore. Provided that... 

Let us consider a population of N molecules randomly oriented and excited at time 0 by an infinitely short pulse of light polarized along Oz. At time t, the emission transition moments ME of the excited molecules have a certain angular distribution. The orientation of these transition moments is characterized by 0E, the angle with respect to the Oz axis, and by (azimuth), the angle with respect to the Oz axis (Figure 5.5). The final expression of emission anisotropy should be independent of

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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. 

Since the dipoles of chromophore molecules are randomly distributed in an inert organic matrix in amorphous PR materials, the material is centrosymmet-ric and no second-order optical nonlinearity can be observed. However, in the presence of a dc external field, the dipole molecules tend to be aligned along the direction of the field and the bulk properties become asymmetric. Under the assumption that the interaction between the molecular dipoles is negligible compared to the interaction between the dipoles and the external poling field (oriented gas model), the linear anisotropy induced by the external field along Z axis at weak poling field limit (pE/ksT <[Pg.276]

The same effect is produced if, instead of physical rotation of the chromophore, energy transfer takes place among them. A randomization of the emitting dipoles in a three-dimensional space results to a limiting value of r equal to zero. If the transport process involves transition dipoles orthogonal to an axis, the limiting value of r is equal to 0.137. The loss of anisotropy... 

To summarize this part of the chapter, we have constructed a consistent theory of linear and cubic dynamic susceptibilities of a noninteracting superparamagnetic system with uniaxial particle anisotropy. The scheme developed was specified for consideration of the assemblies with random axis distribution but may be easily extended for any other type of the orientational order imposed on the particle anisotropy axes. A proposed simple approximation is shown to be capable of successful replacement of the results of numerical calculations. 

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