Susceptibility van Vleck

Finally, Al (/= 5/2) and Co NMR spectroscopy have been used to probe AP+ in Al-doped lithium cobalt oxides and lithium nickel oxides. A Al chemical shift of 62.5 ppm was observed for the environment Al(OCo)e for an AP+ ion in the transition-metal layers, surrounded by six Co + ions. Somewhat surprisingly, this is in the typical chemical shift range expected for tetrahedral environments (ca. 60—80 ppm), but no evidence for occupancy of the tetrahedral site was obtained from X-ray diffraction and IR studies on the same materials. Substitution of the Co + by AF+ in the first cation coordination shell leads to an additive chemical shift decrease of ca. 7 ppm, and the shift of the environment A1(0A1)6 (20 ppm) seen in spectra of materials with higher A1 content is closer to that expected for octahedral Al. The spectra are consistent with a continuous solid solution involving octahedral sites randomly occupied by Al and Co. It is possible that the unusual Al shifts seen for this compound are related to the Van-Vleck susceptibility of this compound. 

Its constant paramagnetism is well explained by a Van Vleck susceptibility, the ground state being the non-magnetic J = 0 due to the 5f configuration this interpretation is well confirmed by the very low electronic specific heat. Accordingly, band calcula-... 

Crystal field levels in rare earth metals have been determined by measurements of properties such as (i) specific heat, (ii) Van Vleck susceptibility, (iii) magnetization in high magnetic fields, (iv) paramagnetic resonance, (v) Mossbauer effect, (vi) inelastic neutron scattering and (vii) miscellaneous methods. 

Some information on crystal electric field levels can be obtained from the measurement of temperature-dependent Van Vleck susceptibility which can be described by the relationship... 

As for the spin susceptibility, the partial Van Vleck susceptibility x v °f P is found... 

Here A% and Aorb are the hyperfme field due to spin and orbital angular momentum, Xs and Xvv are the spin and Van Vleck susceptibility, respectively, and pe is the Bohr magneton. In a heavy fermion system, where 4/ or 5/ electrons play principal roles, the state is specified by j = l +. 7, so that Ks is associated with the ground state (not purely due to spin and temperature dependent in general). AVv is induced from the transition between the ground state and the excited state, and is temperature independent. Each of As and Aorb includes the spin and orbital hyperfme fields. 

The hole numbers thus obtained are shown in Table 2.60 The plausibility of these results is confirmed by the Van Vleck susceptibility which is given by... 

Limited information about the CEF-levels can also be obtained from a measurement of the temperature dependent Van Vleck susceptibility (Hirst et al. 1968, Williams and Hirst 1970), which is given by... 

Here, x% and Xd are the s and d spin susceptibilities, which can be related to the fractional densities of states mentioned above, xy/ is the field-induced orbital paramagnetic susceptibility (Van Vleck susceptibility) arising from the orbital... 

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