Spin direct process

In the oxidized form, the weak coupling of the high-spin Fe(III) ion to its surroundings amd the very large ligand-field energy of about 10,000 cm (12) are not liable to give rise to very efficient relaxation processes (see Appendix). However, the S = 5/2 manifold provides a set of transitions for multiple direct processes that may be efficient... 

Several types of spin-lattice relaxation processes have been described in the literature [31]. Here a brief overview of some of the most important ones is given. The simplest spin-lattice process is the direct process in which a spin transition is accompanied by the creation or annihilation of a single phonon such that the electronic spin transition energy, A, is exchanged by the phonon energy, hcoq. Using the Debye model for the phonon spectrum, one finds for k T A that... 

If the Zeeman splitting is large compared to the crystal field splitting, this leads to cx B T. Usually, the direct process is important only compared to other spin-lattice processes at low temperatures, because only low-energy phonons with hojq = A contribute to the direct process. 

I2H2O as a function of the reciprocal temperature. The points are data obtained from fits of the Mdssbauer spectra (Fig. 6.6). The broken curve is a fit to the Einstein model for a Raman process. The dotted curve corresponds to a contribution from a direct process due to interactions between the electronic spins and low-energy phonons associated with critical fluctuations near the phase transition temperature. (Reprinted with permission from [32] copyright 1979 by the Institute of Physics)... 

As already observed for some isotropic polynuclear clusters [30 - 32], slow relaxation of the magnetization in an external magnetic field can occur because of the inefficient transfer of energy to the environment, for example, the helium bath, and consequent reabsorption of the emitted phonon by the spin system. The phenomenon, also known as phonon bottleneck (PB), was first introduced by Van Vleck [33]. It is characteristic of low temperatures, where relaxation is dominated by the direct process between closely spaced levels, and results from the low density of phonons with such a long wavelength to match the small energy separation... 

The special feature of the spin crossover process in all bpym-bridged dinuclear compounds studied so far is the occurrence of a plateau in the spin transition curve. A reasonable assumption to account for this observation is that a thermal spin transition takes place successively in the two metal centres. However, it cannot be excluded that spin transition takes place simultaneously in the dinuclear units leading directly from [HS—HS] pairs to [LS-LS] pairs with decreasing temperature. Therefore, two possible conversion pathways for [HS—HS] pairs with decreasing temperature may be proposed [HS—HS]<->[HS—LS]<->[LS—LS] or [HS-HS] [LS-LS]. The differentiation of the existence of the [LS—LS], [HS—LS], and [HS—HS] spin pairs is not trivial and has recently been solved experimentally by utilisation of magnetisation versus magnetic field measurements as a macroscopic tool [9], and by Mossbauer spectroscopy in an applied magnetic field as a microscopic tool [11]. 

Such localized states as under discussion here may arise in a system with local permutational symmetries [Aa] and [AB], If [Aa] + [S] and [Ab] = [5], the outer direct product [Aa] 0 [AB] gives rise to a number of different Pauli-allowed [A], If the A and B subsystems interact only weakly, these different spin-free [A] levels will be closely spaced in energy. The extent of mixing of these closely spaced spin-free states under the full Hamiltonian, H = HSF + f2, may then be large. Thus, systems which admit a description in terms of local permutational symmetries may in some cases readily undergo spin-forbidden processes, such as intersystem crossing. 

Besides the spin-forbidden processes of Sections VII-XII, there are a number of other spin-forbidden processes of interest. Intersystem crossing may occur in certain predissociation phenomena and in P-type delayed fluorescence.198 Also of interest are the heavy atom effect and the direct interaction of radiation with spin. 

Fig. 3.3. Lattice and spin transitions are coupled by (A) direct processes, (B) Raman processes, (C) Orbach processes. The proximity of the excited electronic state favors both Orbach and Raman processes. The electronic states are labeled with n, the lattice vibrational states are labeled with V. A and 8 indicate energy separations with excited states coupled to the ground state by spin-orbit coupling.

The interpretation of carbon T p data is complicated by the fact that spin-spin (cross-relaxation) processes as well as rotating frame spin-lattice processes may contribute to the relaxation (40). Only the latter process provides direct information on molecular motion. For the CH and CH2 carbons of PP, the Tip s do not change greatly over the temperature interval -110°C to ambient and, as opposed to the T behavior, the CH2 carbon has a shorter T p than the CH carbon. These results suggest that spin-spin processes dominate the Tip (46). However, below ca. -115°C, the Tip s for both carbons shorten and tend toward equality. McBrierty et al. (45) report a proton Ti minimum (which reflects methyl group reorientation at KHz frequencies) at -180°C. No clear minimum is observed in the data, perhaps due to an interplay of spin-spin and spin-lattice processes. Nonetheless, it is apparent that the methyl protons are responsible for the spin-lattice portion of the Tip relaxation for CH and CH2 carbons. 

Direct process the spin center transfer to another energy level by absorption or emission of one phonon. 

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