New model for the mixed-valence phenomenon in rare-earth materials

A model of a single rare-earth atom in a transition metal is derived, and terms describing screening of charge fluctuations in the resonant $l=3\mathrm{}$ scattering channels by the $l=2\mathrm{}$ channels are included. Using the Tomonaga approximation, in which charge fluctuations are represented by bosons, the screening channels are replaced by a boson field, and the model takes on a particularly simple form, the Anderson model of a magnetic impurity, now coupled to the boson field. The mean-field theory of this model suggests that, unlike in the original Anderson model, the impurity can be in a state of slowly fluctuating valence, which we identify with the mixed-valence phenomenon in certain rare-earth materials. These results suggest that the mixed-valence effect may be purely electronic in origin.