Magnetic impurities in metals: the s d exchange model

Impurity magnetism in metals can be investigated essentially under two aspects: One can explore the criteria for the formation and stabilization of localized magnetic moments; and one can attempt to explain the change in the various physical properties which arise from localized moments. The investigation of the existence of localized magnetic moments of impurities in metals starts with the pioneer work of Friedel [1], Anderson [2], and Wolff [3]. By means of the concept of a ''virtual bound state" (resonance state) Friedel was able to explain why local magnetic moments are generally more stable in monovalent metals than in polyvalent metals. According to this concept, for the existence of such a moment the balance between the (screened) Coulomb interaction between the electrons of an incomplete d- or f-shell of the impurity and the coupling between the impurity electrons and the conduction band of the matrix is wssential. This coupling depends (besides the properties of the impurity) on the density of states N($\epsilon$) of the conduction electrons: A large density of states N($\epsilon$) at the impurity levels invokes a strong interaction between the d- or f-electronsand the conduction electrons and therefore a large broadening of the impurity levels. An impurity keeps its magnetic moment if this broadening is small compared to the spin splitting of its levels due to the interatomic interaction, or if the exchange energy gained by this interaction is larger than the loss in kinetic energy. The position of the impurity levels with respect to the Fermi level of the matrix is determined by the charge neutrality. A magnetic moment can exist only, if at least part of the broadened levels of the electrons of one spin direction are below the Fermi level and part of the levels of the electrons with opposite spin direction above. For a quantitative [...