RKKY model

RKKY-type analysis of the conduction electron polarization Each time when the hyperfine fields at different sites in the same intermetallic compound were available-as for the Al sites in RjAlu in an NMR analysis by van Diepen et al. (1969)-or when the hyperfine fields and asymptotic paramagnetic Curie temperatures 0p could be correlated, or when the conduction electron concentration could be varied in pseudobinary intermetallic compounds, the RKKY model [as introduced by Jaccarino (1961) for the discussion of A1 NMR in RAI2] was the favourite framework for the NMR spectroscopists. For eq. (10b), is calculated as... 

The eqs. (lid) and (lie) can thus be generalized, not implying anymore the special distance dependence of the RKKY model [eq. (Ilf)] and allowing the experimental distinction between the influence of 6s-(6p-) and 5d-like conduction electrons to be made ... 

Amorphous Gd, , Al films prepared by sputtering were investigated by Jamet and Malozemoff (1978). In the paramagnetic regime the alloys of the concentrations X = 0.19, 0.44 and 0.63 were found to have a small positive g shift (Ag = 0.006 + 0.004). This is in contrast with the negative value of Ag observed earlier in crystalline Gd-Al compounds (see for instance Davidov et al., 1973). Jamet and Malozemoff analysed their data in terms of the RKKY model and conclude that the... 

The absence of coupling for a-axis and Zt-axis superlattices can be understood within the RKKY model. The rapid rise and relatively flat-topped peak of the susceptibility fY( z)> as shown in fig. 1, give rise to long tails in the real space response. Figure 46a shows the exchange energy J q) in the a -c plane, assuming that the sharp peak in the... 

In an isotropic RKKY model with a spherical Fermi surface, the Fermi vector is strongly dependent on the da ratio and on the number of free electrons Z per magnetic ion ... 

We shall give here a brief outline of the RKKY model without dwelling on the details. For this the reader is referred to de Gennes (1962), Mattis (1965) to mention only two of the numerous works available on this subject, also see ch. 3, subsection 4.1. The essential form of the indirect interaction between localized moments was introduced by Ruderman and Kittel (1954) to describe the hyperfine interactions between nuclear moments. This was then applied to the exchange interaction between localized electronic moments (Kasuya, 1956 Yosida, 1957). 

Generally the application of the RKKY model to the compounds with the CsCl structure is not too successful. It always needs a shift of kp from the free electron value kp before agreement is achieved. The cause of any discrepancies is usually ascribed to the presence of d-electrons (Morin et al., 1973), which can be present in the bands to a considerable extent. Many attempts at applying the RKKY model have involved pseudobinary series, such as Tb(Cu, Zn) in which case kpikp was found to be 0.85 (Pierre, 1969). The characteristic temperatures are shown in fig. 14.11 for this series. Buschow et al. (1975c) have concluded that the RKKY model fails for divalent B-elements, whereas better agreement is found for monovalent metals such as Ag and Cu. 

Band structure calculations are needed in order to determine the shape of the Fermi surface in intermetallics. The RKKY model would then have a more respectable foundation if applied to a compound whose Fermi surface is known to be approximately spherical and if the model could be explicitly avoided for the cases where the Fermi surface is distinctly nonspherical. As already mentioned in subsection 2.1 modifications of the RKKY model for general Fermi surface shapes are extremely difficult to apply. Band structure calculations up till now have been confined to the more symmetrical lattices. As a consequence, a very large fraction of such calculations involves the CsCl structure. As a first approximation the objects of the investigations contain no magnetic components, in order to find the undisturbed state of the Fermi surface. When... 

The RKKY model has been applied to GdZn2 and GdCu2 by Debray et al. (1970), Debray and Ryba (1971), Poldy and Kirchmayr (1974), and Buschow et... 

Summarizing, it seems that the RKKY model, though surprisingly successful within one system, cannot account on a broad basis for the magnetic properties of the compounds with the CeCu2 structure. In these compounds the failure of this model may be due to an increasing d-character of the conduction electrons... 

The RKKY model was applied to the RAg2 compounds by Miura et al. (1974) in connection with magnetic measurements and by Ohashi et al. (1975) in... 

Robinson et al. (1971) proposed the modified RKKY model in which the space extent of the 4f wave function was taken into account, and F q), in contrast to eq. (6), was written in the form... 

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