Formation of Localized Magnetic States and Kondo Effect in Metals

Abstract

On the localized magnetic states on an impurity in metals, there are two questions: one is how the localized magnetic moments are formed in metals and the other is what effects it gives rise to on conduction electrons. The first problem has been discussed by Friedel,!) Anderson,2 > Wolff3> and others.4>,s> While' the second problem is the so-called Kondo problem and, after the epochal work of Kondo,6> it has been investigated using various methods. 7> Despite many efforts, however, this problem has not been settled. Traditionally, one has independently studied these two questions by a tacit consent. However, we emphasize that, taking account of the Kondo effect, 7l we cannot essentially treat two problems separately and then must simultaneously examine them at the same stage. First of all, it is . convenient to define that the . localized states in metals are in a magnetic. regime, if the localized part of the magnetic susceptibility exhibits a Curie-like behavior and in a non-magnetic regime otherwise. Now, to describe qualitatively the properties of the· localized magnetic state in metals, we adopt the non-degenerate Anderson's model with the ordinary potential: