Ruderman-Kittel interaction

There are also cases in which the unpaired localized electrons of the lattice interact with the conduction electrons. The information of the spin state of a given ion is transmitted to another one, via the conduction electrons. Since the Pauli exclusion principle cannot be violated, the spins, feeling the interaction, will comply. This is called the Ruderman-Kittel interaction. 

This description ha.s given us a moment on an isolated ion. If there are other ions with moments, there will be coupling through the free electrons, just as the ions were coupled through the free-electrons producing the indirect interaction between ions of Eq. (17-9). This interaction between moments, the Ruderman-Kittel interaction di.scussed in Section 19-A (Ruderman and Kittel, 1954), also shows the Fricdel oscillations that were illustrated in Fig. 17-2. Thus, at low temperatures the moments will order themselves to minimize the interaction... 

Furthermore in order to understand the dynamics of the coupled RE-ion system it is often not sufficient to work with the effective ion-ion interaction model. Instead it is important not to eliminate the particles (or excitations) from the dynamical treatment which are mediating the interaction from ion to ion. For example if the conduction electrons are mediating the RE-ion interactions via (generalized) Ruderman-Kittel interaction then the dynamics of the electronic excitations will enter into the dynamics of the coupled RE-ion system. But if the conduction electrons are eliminated from the considerations by replacing their effect by an effective RE ion-ion interaction this dynamical influence is lost and the resulting excitation spectrum may be over-simplified in certain regions in q-space. The same holds true if the phonons are mediating the ion-ion interaction. We will pay special attention to this problem as we proceed. 

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... 

We shall treat indirect exchange interaction using Ruderman-Kittel s method, which is concerning the hyperfine interaction between s electrons and nuclei in metals. The result obtained by this method will be the same as that of Yosida s method. 

ODR ODS OEIC oxygen dissolution reaction oxide dispersion-strengthened optoelectronic integrated circuit RIM RKKY rigid-ion model Ruderman-Kittel-Kasuya-Yoshida (electron interactions)... 

---