S-f exchange

Liu (1961) noted that the wave functions of the 4f electrons on different rare earth (R) atoms in the solid state do not usually overlap. This is because the radius of the 4f shell is almost 0.35 A and the wave functions are therefore zero on the Wigner-Seitz sphere. There can therefore be no direct exchange, and exchange interactions between different R-magnetic moments must be mediated by the conduction electrons. Liu points out that there are two possible interaction types. In the first type the 4f magnetic moment on the R-atom polarizes the sp conduction bands of the compound via a direct s-f exchange interaction given by... 

In turn J q) is described in terms of a bare s-f exchange function j f between conduction and 4f electrons and the generalized susceptibility Xst which represents the conduction electron response to the local exchange field and which is calculable from the band structure. The expression for J(q) for N spins is then... 

Inelastic neutron scattering from both y- and a-Ce under pressure was investigated by Rainford et al. (1977). Their results indicate that the s-f exchange interaction, J, in y-Ce increases with increasing pressure as predicted by Coqblin. Also they find no experimental evidence for a magnetic contribution to the inelastic neutron scattering intensity of a-Ce. They conclude that if there is some residual 4f electronic character in a-Ce its dynamical response is too weak or diffuse to be observed in their experiment. 

The electrical and thermoelectric properties were determined over a large range of temperatures and for several compositions, and the conduction mechanisms were analyzed (see for instance Daunov et al., 1975 Beckenbaugh et al., 1975 Vasilev et al., 1975). ParaUel to this, optical properties were studied (Guntherodt et al., 1974 Eastman et al., 1974). The s-f exchange interactions were evaluated from the electronic resonance spectra (Urban et al., 1974). 

The conduction electrons are representable by the wave functions l/t(r)e =

conduction electrons with wave vector k are scattered by a magnetic 4f ion at position J /. The wave vector after scattering is k. Due to s-f exchange this scattering is spin dependent, resulting in a spin polarization around the scattering centre. The s-f exchange matrix element can be shown to be... 

The departure of the proportionality of the Op values to the de Gennes factor can be used as a measure of the variation of the s-f exchange energy G within a... 

NMR work on the magnetically ordered state of other intermetallic compounds is summarized in table 18.11. Many of these compounds have the CsCl structure, and in general a major objective has been to understand the dependence of the s-f exchange interaction on conduction electron concentration. 

Nuclear magnetic resonance of A1 in the paramagnetic state of R-Al intermetallic compounds. Values of the s-f exchange interaction parameter /sf are based on the uniform polarization model [Jaccarino et al. (I960)]. 

Nuclear magnetic resonance results for non-rare earth nuclei in the paramagnetic state of the cubic rare earth monopnictides. The s-f exchange parameter... 

Concerning the transport properties, more than twenty years ago van Daal and Buschow (1969) published the temperature dependence of the electrical resistivity of the RAI2 compounds. The results have been analyzed with respect to the spin-disorder scattering contribution to the total resistivity. For the analysis of the resistivity data the authors used eq. (50) for p p. This expression has been used to determine the effeetive mass ( i ) and the effective s-f exchange coupling constant The values thus obtained are compared to the values from Knight-shift and susceptibility measurements. The authors noted that CeAlj and YbAlj behave exceptionally. They suspected already, at that time, that the minimum in p versus T of CeAlj is caused by the Kondo effect. The unusual behaviour of the resistivity in YbAlj was attributed to the intermediate valence state of the Yb ion. 

Fermi surface structure, the energy spectrum of the conduction electrons and the s-f exchange interaction parameter which in turn will affect Tc and the characteristics of the helical structure ((p, fcr)- A more thorough discussion of this question will be presented in the next section. 

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