Non-Kramers ions

The application of a magnetic field to the wavefunctions obtained by the procedure described in the previous sections results in the complete removal of the degeneracy of the / multiplet, either pertaining to Kramers or non-Kramers ions, and yields a temperature-dependent population of the different 2/ + 1 components (Figure 1.2) Thus, at low temperatures, large deviations from the Curie law are observed. The effect of the magnetic field is described by the Zeeman Hamiltonian ... 

Non-Kramers Ions High-Spin Fe(II) S = 2 Non-Kramers ions have a very different ZFS behavior.29 For a 5 = 2 ground state with a rhombic ligand field (Figure 1.11, where E / 0), ZFS can eliminate all the Ms degeneracy even in the absence of a magnetic field. 

VTVH MCD data for non-Kramers ions allowing the measurement of spin Hamiltonian parameters of EPR inactive centers.29,34... 

Thus, for non-Kramers ions, VTVH MCD uses an excited state to obtain ground-state EPR parameters of EPR inactive, but paramagnetic, metal sites. 

The first equation refers to non-Kramer ions the second refers to Kramer ions where the energy between doublets is sufficiently large compared with ksT the third refers to Kramer ions doublets where the energy gap is small compared with ksT. The term in the equations with the coefficient A is the direct process part the terms with coefficients B and C refer to Raman and Orbach process, respectively. 

The excitations in systems composed of non-Kramers ions were studied by Fert and Campbell (1978) and Bieri et al. (1982). Here the ground state doublet is split to various degrees, corresponding to a wide distribution of crystal field excitations down to zero energy. This leads to a specific heat contribution at low temperatures which is nearly independent of temperature. 

The primary effect of the crystal field on any manifold of levels of a 4f ion is to raise the 2J + I degeneracy, giving a set of levels with an overall splitting of a few hundred wave-numbers. If the ion has an odd number of electrons, then by Kramers theorem a two-fold degeneracy must remain in each level, but for a non-Kramers ion there is no such restriction. All the degeneracy may be lifted by a field of low... 

It was pointed out independently by Williams (1967) and Culvahouse et al. (1967) that for a non-Kramers ion at a site lacking in full inversion symmetry, terms linear in an electric held may exist for a doublet state. Thus for Cj, symmetry (but not for C y) the system may have a permanent electric dipole moment, and its interaction with an electric held may be represented by additional terms of the form -I- SyEy). Transitions then occur with an RF electric held normal to the z-axis, even in the absence of a distortion from axial symmetry. As before, random distortions again produce an asymmetrical line shape, but with a maximum corresponding to the point for zero distortion, unlike the magnetic transitions referred to above. The asymmetry is present because in each case the distortions move the transitions to higher frequency at constant applied held, or to lower held at constant frequency. Such electric dipole moments also give rise to electric interactions between the ions (see section 5.6). 

For a system with octahedral or tetrahedral symmetry, saturation data collected at different temperatures superimpose for all spin systems. For low-symmetry sites (e.g., protein-active sites) only isotherms for 5=1/2 systems superimpose in general. The spread or nesting behavior observed in VTVH MCD for systems with Sf j2 is ascribed to the zero-field splitting (ZFS) of the Ms sublevels of the ground state, and is discussed in the next sections, first for Kramers-type systems (half-integer spin) and then for non-Kramers ions (integer spin), as exemplified by Fe . 

As discussed in [22], the spherical symmetry of is destroyed when these ions are situated in solids, so that a multiplet term level can be split up to 2/ + 1 crystal field levels for a non-Kramers ion. Due to the parity selection mle for pure electronic transitions in solids, the 41 (i) 4 (f) transition between states i and f is ED forbidden to first order. Parity describes the inversion behavior of the wavefunction of an electronic orbital, so that s,d... orbitals have even parity whereas p,f... orbitals are odd. The spectral feature representing the pure electronic transition is termed the electronic origin or the zero phonon line. An ED transition requires a change in orbital parity because the transition dipole operator (pe) is odd, and the overall parity for the nonzero integral involving the Einstein coefficient of spontaneous emission, A(ED) ... 

Although the above equations have been oversimplified for the real relaxation process, it can stiU be concluded that the spin lattice relaxation time is temperature dependent. The first equation refers to non-Kramers ions the second refers to Kramers ions with the energy between doublets being small compared with T the third refers to Kramers ions doublets... 

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