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We investigate the indirect exchange interaction between localized moments via conduction bands. The origin of the exchange is assumed to be the Anderson s-f mixing mechanism appropriate to anomalous rare earth and light actinide systems. The conduction states originate from s-orbitals in a CsCl structure. Hubbard correlation in Hartree-Fock approximation is included. We perform calculations of the coupling constants between localised moments and obtain a characteristic relationship between the conduction electrons density of states and the magnetic transition temperature.

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The conditions necessary in metals for the presence or absence of localized moments on solute ions containing inner shell electrons are analyzed. A self-consistent Hartree-Fock treatment shows that there is a sharp transition between the magnetic state and the nonmagnetic state, depending on the density of states of free electrons, the $s$-${}d$ admixture matrix elements, and the Coulomb correlation integral in the $d$ shell; that in the magnetic state the $d$ polarization can be reduced rather severely to nonintegral values, without appreciable free electron polarization because of a compensation effect; and that in the nonmagnetic state the virtual localized $d$ level tends to lie near the Fermi surface. It is emphasized that the condition for the magnetic state depends on the Coulomb (i.e., exchange self-energy) integral, and that the usual type of exchange alone is not large enough in $d$-shell ions to allow magnetic moments to be present. We show that the susceptibility and specific heat due to the inner shell electrons show strongly contrasting behavior even in the nonmagnetic state. A calculation including degenerate $d$ orbitals and $d$-${}d$ exchange shows that the orbital angular momentum can be quenched, even when localized spin moments exist, and even on an isolated magnetic atom, by kinetic energy effects.
We study the effect of the conduction-electron density of states on magnetic transition temperatures in metallic systems with localized magnetic moments. We assume the indirect-exchange interaction to originate from s-f mixing of the Anderson type and we perform calculations of the coupling parameters, up to fourth-nearest neighbors, in the formalism of da Silva and Falicov. The density-of-states models are obtained from a two-component band in tight-binding scheme and we include on-site Coulomb correlation. We find that the magnetic energy has a modulated Ruderman-Kittel-Kasuya-Yoshida-like behavior as a function of the number of conduction electrons n. This is, however, dominated by two strong maxima when n is such that the Fermi level lies on a peak of the density of states. In this condition the transition temperature is enhanced by at least 1 order of magnitude with respect to the weaker background. This behavior is found for different values of the virtual excitation energy of the s-f mixing mechanism.