Spin-orbit crystal field

Spin-orbital Crystal field coupling (Stark sublevels) (sublevels)... 

Table 2. Comparison of Coulomb, spin-orbit, crystal field and exchange interactions for actinides and lanthanide ions, (U Coulomb spin-orbit Hef crystal field, H,jch. = exchange)...

Central Coulomb Spin-Orbit Crystal Field... 

Ep = 2 edcv /wto is approximately 21 meV for most of the III-V and II-VI semiconductors, no is the linear refractive index, and Kpi, is a material independent constant (1940 cm (eV) for a two-parabolic-band model). It should be mentioned that the above model does not correctly account for the degeneracy of the valence band (heavy hole, light hole, and spin-orbit/crystal-field split-off bands) and assumes single parabolic conduction and valence bands. Using the Kane band structure with three valence bands and including excitonic effects have been shown to produce larger TPA coefficients [227]. 

SCCF spin-correlated crystal field spin-orbit coupling constant... 

The direction of the alignment of magnetic moments within a magnetic domain is related to the axes of the crystal lattice by crystalline electric fields and spin-orbit interaction of transition-metal t5 -ions (24). The dependency is given by the magnetocrystalline anisotropy energy expression for a cubic lattice (33) ... 

Mixing of LS-states by spin orbit coupling will be stronger with an increasing number of f-electrons. As a consequence, intermediate values of Lande g factor and reduced crystal field matrix elements must be used. 

The electrostatic and spin-orbit parameters for Pu + which we have deduced are similar to those proposed by Conway some years ago (32). However, inclusion of the crystal-field interaction in the computation of the energy level structure, which was not done earlier, significantly modifies previous predictions. As an approximation, we have chosen to use the crystal-field parameters derived for CS2UCI6 (33), Table VII, which together with the free-ion parameters lead to the prediction of a distinct group of levels near 1100 cm-. Of course a weaker field would lead to crystal-field levels intermediate between 0 and 1000 cm-1. Similar model calculations have been indicated in Fig. 8 for Nplt+, Pu1 "1 and Amlt+ compared to the solution spectra of the ions. For Am t+ the reference is Am4" in 15 M NHhF solution (34). 

In an octahedral crystal field, for example, these electron densities acquire different energies in exactly the same way as do those of the J-orbital densities. We find, therefore, that a free-ion D term splits into T2, and Eg terms in an octahedral environment. The symbols T2, and Eg have the same meanings as t2g and eg, discussed in Section 3.2, except that we use upper-case letters to indicate that, like their parent free-ion D term, they are generally many-electron wavefunctions. Of course we must remember that a term is properly described by both orbital- and spin-quantum numbers. So we more properly conclude that a free-ion term splits into -I- T 2gin octahedral symmetry. Notice that the crystal-field splitting has no effect upon the spin-degeneracy. This is because the crystal field is defined completely by its ordinary (x, y, z) spatial functionality the crystal field has no spin properties. 

The mixing coefficients a and b in (4.10) depend upon the efficiency of the spin-orbit coupling process, parameterized by the so-called spin-orbit coupling coefficient A (or for a single electron). As A O, so also do a or b. Spin-orbit coupling effects, especially for the first period transition elements, are rather small compared with either Coulomb or crystal-field effects, so the mixing coefficients a ox b are small. However, insofar that they are non-zero, we might write a transition moment as in Eq. (4.11). 

Again, however, this is strictly applicable only for free ions. Even though spin-orbit coupling is much less important for the first row of the d block, this formula provides a far less good approximation for d -block complexes than Eq. (5.6) does for lanthanide complexes. The reason is that the ground, and other, terms in these d complexes differ grossly from those of the corresponding free ion. These differences are one result of the crystal field. 

In octahedral symmetry, the F term splits into Aig + T2g + Tig crystal-field terms. Suppose we take the case for an octahedral nickel(ii) complex. The ground term is 2g. The total degeneracy of this term is 3 from the spin-multiplicity. Since an A term is orbitally (spatially) non-degenerate, we can assign a fictitious Leff value for this of 0 because 2Leff+l = 1. We might employ Van Vleck s formula now in the form... 

Theoretical analyses (75-77) of the matrix-induced changes in the optical spectra of isolated, noble-metal atoms have also been made. The spectra were studied in Ar, Kr, and Xe, and showed a pronounced, reversible-energy shift of the peaks with temperature. The authors discussed the matrix influence in terms of level shift-differences, as well as spin-orbit coupling and crystal-field effects. They concluded that an increase in the matrix temperature enhances the electronic perturbation of the entrapped atom, in contrast to earlier prejudices that the temperature dilation of the surrounding cage moves the properties of the atomic guest towards those of the free atom. 

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