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Isotropic spin models

The Lines approximation is expected to be quite accurate for the description of the exchange interaction between a strongly axial doublet and an arbitrary isotropic spin. For all other cases, the Lines model [84] is a reasonable approximation. Efficient implementation of the Lines model was done in the program POLY ANISO. [Pg.170]

If b = 0, a = 1 the Ising model, if b = 1, a = 1 the isotropic Heisenberg model, and if b = 1, a = 0, the planar Heisenberg model or X-Y model is valid. In the following, the values of the exchange constants were calculated, or recalculated assuming a spin Hamiltonian of this form, instead of = - J 2 SjSi, occasionally used by certain au-... [Pg.91]

Due to the nature of the magnetic ions involved, both having a 6At fundamental term, the magnetic chains of Ba7MnFe6F34 are likely to be well described by an isotropic classical spin model, similar in principle to the one developed by Fisher [7] for the simple chain. This later uses however the recurrence relation (written here with trivial notations) ... [Pg.288]

The isotropic classical spin model for chains of rings already used for Ba7MnFe6F34 could be applied successfully to Ba2CaMnFe2F]4 [18,25] considering now the basic magnetic unit drawn in Fig. 23. The special role devoted to the nodal... [Pg.308]

The correlation time of spin label tumbling relative to the protein (tsl evaluated in terms of simple isotropic rotation model by... [Pg.245]

Carper and co-workers have performed a detailed analysis of the relaxation times of both [C4mim] [25] and [Cgmim]" [26] with [PF0]", which was later extended with more detail to deconvolute the relative contributions of the various relaxation mechanisms [27]. They found that the contribution of CSA to the experimentally observed relaxation time was about half of the contribution from dipolar relaxation. This work raises doubts about the applicability of isotropic relaxation models to ionic liquids. It is important to note that the and measurements of ionic liquids in the literature show different behaviour when attached to the same ion. The random Brownian motion that occurs in most liquids leads to rapid spin diffusion between nuclei bonded to a common ion or molecule, causing them to all exhibit the same T. The lack of such behaviour is a clear indication that the dynamics of ionic liquids are... [Pg.73]

The nuclear modulation effect was first observed by Rowan, Hahn, and Mims [16], and the theory was later developed by Mims in 1972 [17]. The origin of the nuclear modulation effect can be understood with a semi-quantitative discussion using a two-spin model system consisting of one electron spin (S = Vz) and one nuclear spin (/ = Vi). Assuming an isotropic g-matrix and an anisotropic hyperfme interaction, the spin Hamiltonian in the rotating frame can be written as... [Pg.20]

Fig. 1. Theoretical values of the spin-lattice relaxation rate (a l/T, —), off-resonance nonselective nuclear Overhauser effect (NOE b), rotating (fame spin - lattice relaxation rate (a l/ n )t linewidth (a,—), and off-resonance intensity ratio (R c) for P at 40.5 MHz. The random, isotropic motion model vtras utilized, as described in the text. The computed curves assume relaxation only from three protons that are 2.6 A way from the phosphorus. The and R curves were calculated assuming an off-resonance field of 0.47 G applied 8 kHz off-resonance. From Bolton and James (1980a). Copyright 1980 American Chemical Society. Fig. 1. Theoretical values of the spin-lattice relaxation rate (a l/T, —), off-resonance nonselective nuclear Overhauser effect (NOE b), rotating (fame spin - lattice relaxation rate (a l/ n )t linewidth (a,—), and off-resonance intensity ratio (R c) for P at 40.5 MHz. The random, isotropic motion model vtras utilized, as described in the text. The computed curves assume relaxation only from three protons that are 2.6 A way from the phosphorus. The and R curves were calculated assuming an off-resonance field of 0.47 G applied 8 kHz off-resonance. From Bolton and James (1980a). Copyright 1980 American Chemical Society.
For both alloy systems the theoretical results for p obtained in a fully relativistic are found in very satisfying agreement with the corresponding experimental data. In addition to these calculations a second set of calculations has been done making use of the two-current model. This means the partial resistivities p have been calculated by performing scalar relativistic calculations for every spin subsystem separately. As can be seen, the resulting total isotropic resistivity p is reasonably close to the fully relativistic result. Furthermore, one notes that the relative deviation of both sets of theoretical data is more pronounced for Co2,Pdi 2, than for Co2,Pti 2,. This has to be... [Pg.285]

From the selection rules of the 6j coefficients (.89), it follows that the biquadratic terms cannot mix the S = I levels with higher spin states. By contrast, the anisotropic symmetric and antisymmetric terms, whose magnitude is related to that of the isotropic component (89), can give rise to a substantial mixing. However, a detailed quantitative model is needed to verify whether the peculiar magnetic properties of [3Fe-4S] + centers can be explained by this mixing. [Pg.440]

Given the specific, internuclear dipole-dipole contribution terms, p,y, or the cross-relaxation terms, determined by the methods just described, internuclear distances, r , can be calculated according to Eq. 30, assuming isotropic motion in the extreme narrowing region. The values for T<.(y) can be readily estimated from carbon-13 or deuterium spin-lattice relaxation-times. For most organic molecules in solution, carbon-13 / , values conveniently provide the motional information necessary, and, hence, the type of relaxation model to be used, for a pertinent description of molecular reorientations. A prerequisite to this treatment is the assumption that interproton vectors and C- H vectors are characterized by the same rotational correlation-time. For rotational isotropic motion, internuclear distances can be compared according to... [Pg.137]

Now we consider thermodynamic properties of the system described by the Hamiltonian (2.4.5) it is a generalized Hamiltonian of the isotropic Ashkin-Teller model100,101 expressed in terms of interactions between pairs of spins lattice site nm of a square lattice. Hamiltonian (2.4.5) differs from the known one in that it includes not only the contribution from the four-spin interaction (the term with the coefficient J3), but also the anisotropic contribution (the term with the coefficient J2) which accounts for cross interactions of spins a m and s m between neighboring lattice sites. This term is so structured that it vanishes if there are no fluctuation interactions between cr- and s-subsystems. As a result, with sufficiently small coefficients J2, we arrive at a typical phase diagram of the isotropic Ashkin-Teller model,101 102 limited by the plausible values of coefficients in Eq. (2.4.6). At J, > J3, the phase transition line... [Pg.44]

The value of the Ising model lies therein that it is the only model of disorder to have produced valid theoretical predictions of spontaneous phase changes. To understand the role of symmetry it is noted that spontaneous magnetization, starting from a random distribution of spins, amounts to a process of ordering that destroys an existing isotropic arrangement. [Pg.502]


See other pages where Isotropic spin models is mentioned: [Pg.182]    [Pg.182]    [Pg.170]    [Pg.178]    [Pg.45]    [Pg.34]    [Pg.602]    [Pg.611]    [Pg.89]    [Pg.131]    [Pg.290]    [Pg.581]    [Pg.225]    [Pg.35]    [Pg.269]    [Pg.284]    [Pg.139]    [Pg.30]    [Pg.220]    [Pg.262]    [Pg.176]    [Pg.1511]    [Pg.285]    [Pg.54]    [Pg.71]    [Pg.443]    [Pg.179]    [Pg.229]    [Pg.194]    [Pg.92]    [Pg.194]    [Pg.334]    [Pg.105]    [Pg.201]    [Pg.592]    [Pg.602]   
See also in sourсe #XX -- [ Pg.182 ]




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