Conduction electrons localisation

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. 

In this sense, atomic multiplet theory provides complementary information about the valence state. One can take the view that this information should be used, and then blended in some way with the conceptual framework of the Anderson single-impurity model, so that the matrix elements coupling the / electrons to the conduction band can continue to play the decisive role in determining the extent of / electron localisation. 

As pointed out above, there are two extreme situations involving localised and delocalised valence electrons in cluster physics at one end of the scale, the noble gases possess valence electrons which remain localised on individual atomic sites, while, at the other, the alkalis possess delocalised valence electrons which can wander over the cluster and resemble the conduction electrons of a metallic solid. 

Particular interest has been expressed in the Co/copper system because of the existence of a bound state formed between the localised magnetic impurity moments and the conduction-electron spins below a critical temperature [88]. The impurity moment is significantly quenched by spin compensation from the conduction electrons below the critical temperature, but this bound state can be perturbed by application of large external magnetic fields. 

More detailed measurements on the Pt/Fe system have covered compositions in the range 3-50 at. % Pt [81]. The 3 at. % alloy gave Hm = —1260 kG at 4-2 K and (99 keV) = -0-60(15) n.m. The value of the field is almost independent of composition within the range specified. Neutronscattering data have shown that there is no localised magnetic moment on the Pt atoms, so that the field is generated entirely by conduction-electron polarisation, approximately 0-07 unpaired conduction electrons being required per Pt atom. A similar mechanism is believed to act in the cobalt and nickel alloys [84]. 

The discrepancy between small AF moment in URu2Si2 and large thermodynamic anomalies has led to the postulation of a hidden (non-dipolar) order parameter. The cmcial questions about its nature are (i) Is the order primarily involving the localised 5f-CEF split states or the heavy itinerant conduction electrons, (ii) Does the hidden order parameter break time reversal invariance or not. In the former case it may induce AF as secondary order parameter, in the latter the two order parameters are umelated and their appearance at the same temperatnre Tm = To has to be considered as accidental. 

A natural objection to such an approach is the problem of whether conduction electrons in the given compounds can be considered to be quasi-free. As is known, the conductivity of refractory compounds is comparable to that of the corresponding transition metals and is considerably less than the conductivity of typical nontransition metals. In the case of high densities of states at the Fermi level this indicates a partial localisation of electrons, which appears when the crystal contains impurities, vacancies and other types of translational symmetry disturbances. There are indications, however, that partial localization of conduction electrons does not lead to qualitatively different relationships between the... 

So, despite the very small diameter of the MWCNT with respeet to the de Broglie wavelengths of the charge carriers, the cylindrical structure of the honeycomb lattice gives rise to a 2D electron gas for both weak localisation and UCF effects. Indeed, both the amplitude and the temperature dependence of the conductance fluctuations were found to be consistent with the universal conductance fluctuations models for mesoscopic 2D systems applied to the particular cylindrical structure of MWCNTs [10]. 

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