Coupling indirect RKKY

Here Xt is the static susceptibility of the f-electron system, E is the magnetic relaxation rate of the f-state and Kff denotes the coupling constant of the spin of the ESR probe to the f moment via the indirect RKKY exchange. A schematic representation of the interactions which are described in eq. (34) and are responsible for the linewidth broadening in HFS is shown in fig. 41. 

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... 

The behaviour pertinent to the opposite limit of the well localized f states is found in most rare-earth compounds. The 4f states are situated more than 5 eV below EF in most of them. The strength of the interaction of f and conduction-band electrons is considerable (= 0.1 eV), but contributes only indirectly to the magnetic coupling of f-moments via polarization of conduction electrons (RKKY), the 4f-moment magnitude remaining preserved. For f states closer to EF, as is the case of y-Ce or some Ce compounds (a situation comparable To some actinide compounds), the interactions between the f- and conduction-band states becomes stronger. The Kondo Hamiltonian can be written as... 

Within the RKKY theory, the polarization of the conduction electrons is also responsible for the long-range indirect coupling between the spins of the lanthanide ions. As shown by Oe Gennes (1962), in terms of molecular field theory, the paramagnetic Curie temperature is proportional to the average interaction of one lanthanide ion with all the other lanthanide ions. 

The most widely accepted form of magnetic interaction between the 4f moments is the RKKY interaction. Since there is virtually no overlap between the 4f wavefunctions on different 4f atoms, magnetic coupling proceeds indirectly via polarization of the conduction electrons. Due to the sharp discontinuity of filled and empty conduction electron states at the Fermi energy E, this conduction electron... 

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