Ruderman, Kittel, Kasuya, Yosida interaction

Here we have in mind such materials as EuS with a comparatively high concentration of Gd atoms to give a degenerate electron gas, and a large number of metallic transitional-metal compounds where ions of mixed valence exist (in the latter there may be uncertainty about whether the electrons are in a conduction (4s) band or the upper Hubbard band described in Chapter 4). In such a case a new interaction term arises between the moments which is via the conduction electrons. This is the so-called RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction, which is an oscillating function of distance (Ruderman and Kittel 1954, Kasuya 1956, Yosida 1957 for a detailed description see Elliott 1965). This derives from the formulae of Chapter 1, Section 5. Consider an atom with magnetic moment in a given direction then the wave functions of conduction electrons with spin up and with spin down will vary with distance in different ways, so that... 

RKKY (Ruderman, Kittel, Kasuya, Yosida) exchange interaction... 

Zener gave rise to appear two main approaches. The first is double exchange (DE) mechanism in the sense of Anderson and Hasegawa [6]. The second is the mechanism of indirect interaction by Ruderman-Kittel-Kasuya-Yosida (RKKY) [25-27]. 

The canonical spin glass consists of a noble metal (Au, Ag, Cu, or Pt) diluted with a transition metal ion, such as Fe or Mn. The magnetic interaction in such systems is mediated by the conduction electrons, leading to an indirect exchange interaction—the RKKY (Ruderman and Kittel [70], Kasuya [71], and Yosida [72]) interaction, whose coupling constant J R) oscillates strongly with distance r between the spins as... 

In metallic systems with 4f atoms the most prominent source of long-range interaction between magnetic moments is the mechanism first described by Ruderman and Kittel (1954), Kasuya (1956) and Yosida (1957), which involves the conduction-electron sea as mediator of the interaction. Distinctive features of the RKKY-interactions are its long range and oscillatory nature ... 

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). 

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