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 ... 

If the Ln3+ centre is a Kramers ion, the spectra can be interpreted in terms of a doublet with largely anisotropic effective -values. If one neglects the admixture of higher lying/ multiplets and considers an axial symmetry, the effective g values will be... 

ADVANCED TOPIC THE APPLICATION TO OPTICAL TRANSITIONS OP KRAMERS IONS... 

Kramers Ions The High-Spin Fe(III) S = 5/2 Case The effects of the ZFS and Zeeman terms in Equation 1.8 on an S 5/2 ground state are shown in Figure 1.10 for a rhombic Fe(III) site with D> 0. First, note that the sixfold degenerate Ms values of... 

FIGURE 1.10 Panel (a) shows the effect of ZFS (left side) and application of a magnetic field in three molecular directions on the spin states giving rise to the observed saturation magnetization behavior (VTVH MCD) plotted in panel (b) for a S = 5/2, D> 0, and EID = 1/3 Kramers ion. 

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. 

Sm + /3-diketonates show intense luminescence of orange color . Sm + has an odd-electron configuration (4f ) and it is labeled, therefore, as a Kramer ion due to its electronic... 

For this reason, ESR is much more easily done in Kramers ions which have an odd number of electrons and at least a two fold degeneracy in the absence of an applied magnetic field (Kramers theorem). This restricts one to those paramagnetic iron materials which have half integer spin (1/2, 3/2, 5/2) and eliminates those iron materials with spins of 0, 1, 2 unless special efforts are made which we won t discuss here. 

There are six (6) Stark States evident here, each having a half-width of about 7 to 9 A. These have arisen because of the crystal field splitting, but more importantly represent transitioiis between Stark states of the Il5/2 and Ss/2 multiplets. This ion belongs to the so-called "Kramers Ions which consist of atoms having an "odd", i.e.- uneven ("u") number of electrons. 

Prior to the second order, the first-order perturbation theory requires a diagonalisation of the 2 x 2 submatrix having degenerate diagonal elements (Kramers ions, M = 1/2)... 

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