Pauli susceptibility

Although it is required to refine the above condition I in actuality, this rather simple but impressive prediction seems to have much stimulated the experiments on the electrical-conductivity measurement and the related solid-state properties in spite of technological difficulties in purification of the CNT sample and in direct measurement of its electrical conductivity (see Chap. 10). For instance, for MWCNT, a direct conductivity measurement has proved the existence of metallic sample [7]. The electron spin resonance (ESR) (see Chap. 8) [8] and the C nuclear magnetic resonance (NMR) [9] measurements have also proved that MWCNT can show metallic property based on the Pauli susceptibility and Korringa-like relation, respectively. On the other hand, existence of semiconductive MWCNT sample has also been shown by the ESR measurement [ 10], For SWCNT, a combination of direct electrical conductivity and the ESR measurements has confirmed the metallic property of the sample employed therein [11]. More recently, bandgap values of several SWCNT... 

ESR can detect unpaired electrons. Therefore, the measurement has been often used for the studies of radicals. It is also useful to study metallic or semiconducting materials since unpaired electrons play an important role in electric conduction. The information from ESR measurements is the spin susceptibility, the spin relaxation time and other electronic states of a sample. It has been well known that the spin susceptibility of the conduction electrons in metallic or semimetallic samples does not depend on temperature (so called Pauli susceptibility), while that of the localised electrons is dependent on temperature as described by Curie law. 

As future outlook, it would be of great relevance to be able to eventually enhanee the intrinsic conductivity of CNTs. In this respect, the latest development in alkali metal intercalated CNTs looks rather promising. In faet, Chauvet et al. recently sueeeeded to dope aligned CNT by potassium and found that the Pauli susceptibility increases a factor of 3 upon doping, indicating that K-doped tubes are still good eonductors [23]. 

This kind of enhancement, which occurs for a half-full band near the point where an antiferromagnetic lattice forms, is quite different from the Stoner enhancement for nearly ferromagnetic metals described in Chapter 3, Section 11. The latter occurs for non-integral occupation of a d-band, and enhances the Pauli susceptibility only, not the specific heat, apart from probably small paramagnon effects. 

Fig. 10.5 Pauli susceptibility xP of Tei 2T1X liquid alloys plotted against

So, as regards the Knight shift, only this fraction of the nuclei will feel the resultant field. Those that do will be acted on by a strong field that is independent of H but increase as a increases. Thus the NMR line should show a splitting AH independent of Hy but increasing rapidly as c0—c increases. The two lines will be of comparable intensity when (1) approaches unity. Since 2N(E)fi2 is the Pauli susceptibility x, this occurs when... 

Fig. 2.11. Room temperature conductivity and temperature independent Pauli susceptibility versus dopant concentration Y for [Na CH) -] [8].

In the weak-coupling limit (t U, V), the effect of electron-electron interactions measured in terms of an effective, /eff, lead to a Stoner-type enhancement factor, which can slightly reduce the deviation from the expected Pauli susceptibility [5] ... 

The susceptibility data are normalized to the Pauli susceptibility of undimerized (CH). This correspond to a one-dimensional metal with a 10-eV-wide half-filled conduction band. Tight-binding calculations with no coulombic interactions give xP = 3.9 x 10 6 emu/mol. The nature of the conducting state in highly doped (CH)X (i.e., for y > 5 to 6%), as noted... 

The presence of a Pauli-like term is associated with a nonzero density of states at the Fermi level it has been presented by different authors as evidence for metallic behavior. Before mentioning other possible interpretations, we would point out that the decomposition x = Xc + XP s not unambiguous. Indeed, in the case of poly acetylene in the heavily doped regime (y > 6%), the existence of Pauli susceptibility is well established [83], since in all the temperature range x is almost constant (Xp Xc)-But this is generally not the case in other compounds in which a significant Curie term remains present. 

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