Spin of conduction electrons

Tk (single ion) Kondo temperature Oc, spin of conduction electron... 

Recently it was pointed out by Zener7 that the atomic moments, in parallel orientation, might react with the electrons in the conduction band in such a way as to uncouple some of the pairs, producing a set of conduction electrons occupying individual orbitals, and with spins parallel to the spins of the atomic electrons. Zener assumed that the conduction band for the transition metals is formed by the 4.s orbitals of the atoms, and that there is somewhat less than one conduction electron per atom in iron, cobalt, and nickel. Like Slater, he attributed the atomic magnetic moments to the partially filled 3d subshell. 

Here we have in mind such materials as EuS with a comparatively high concentration of Gd atoms to give a degenerate electron gas, and a large number of metallic transitional-metal compounds where ions of mixed valence exist (in the latter there may be uncertainty about whether the electrons are in a conduction (4s) band or the upper Hubbard band described in Chapter 4). In such a case a new interaction term arises between the moments which is via the conduction electrons. This is the so-called RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction, which is an oscillating function of distance (Ruderman and Kittel 1954, Kasuya 1956, Yosida 1957 for a detailed description see Elliott 1965). This derives from the formulae of Chapter 1, Section 5. Consider an atom with magnetic moment in a given direction then the wave functions of conduction electrons with spin up and with spin down will vary with distance in different ways, so that... 

Electron spin resonance measurements at room temperature on poly(thienylpyrrole) showed an asymmetric line characteristic of conduction electrons, with a g value near that of the free electron indicating that the spin resonance is not due to the sulfur and/or nitrogen moieties. 

In the meantime some new routes towards high temperature and possibly exotic superconductivity have been investigated. This is the case for the heavy fermion compounds in which the close interplay between local magnetic moments and the spin of delocalized electrons has led to the possibility of a nonphonon mediated mechanism for electron pairing [4]. A very successful route towards high-T, s has been followed with conducting layered cuprates after the discovery of superconductivity in (La, Sr)2Cu04 [5]. 

The minimum energy gap is also the important factor for other properties of a solid which depend on the electrons in the conduction band. These include the Pauli spin paramagnetism, and the (small) contribution of the electrons to thermal conductivity. All of these properties are due to extremely small concentrations of free electrons. Thus for silicon, where El = 1.1 eV, the number of conduction electrons is only 2 x 10 /cm, compared with an atom concentration of 5 X 10 /cm. This is for a sample where impurity concentrations have been reduced to 1 part in 10 by zone refining. 

Measurements of the nuclear spin-lattice (or longitudinal) relaxation rate Rj are most commonly used to obtain information on the hydrogen jump rates. In favorable cases such measurements allow one to trace the changes in the hydrogen jump rate over the range of four decades. However, the measured values of normally also contain additive contributions not related to hydrogen motion, for example, the contribution due to the hyperfine interaction between nuclear spins and conduction electrons. The motional contribution to the spin-lattice relaxation rate, can be extracted using the difference in the temperature and frequency... 

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