thumb|The RKKY interaction is a long-range interaction between magnetic moments in a metal. The energy oscillates with distance, decaying as <math>r^{-3}</math>. The oscillations are caused by the interaction of the magnetic moments with the conduction electrons in the metal.
thumb|A schematic diagram of 4 electrons scattered by 4 magnetic atoms far apart. Each atom is at the center of decaying electron waves. The electrons mediate the interactions among the atoms, whose poles can flip because of the influence of other atoms and the surrounding electrons. Reproduced from and .
In the physical theory of spin glass magnetization, the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction models the coupling of nuclear magnetic moments or localized inner d- or f-shell electron spins through conduction electrons. It is named after Malvin Ruderman, Charles Kittel, Tadao Kasuya, and Kei Yosida, the physicists who first proposed and developed the model.
Malvin Ruderman and Charles Kittel of the University of California, Berkeley first proposed the model to explain unusually broad nuclear spin resonance lines in natural metallic silver. The theory is an indirect exchange coupling: the hyperfine interaction couples the nuclear spin of one atom to a conduction electron also coupled to the spin of a different nucleus. The assumption of hyperfine interaction turns out to be unnecessary, and can be replaced equally well with the exchange interaction.
The simplest treatment assumes a Bloch wavefunction basis and therefore only applies to crystalline systems; the resulting correlation energy, computed with perturbation theory, takes the following form: <math display=block>H(\mathbf{R}_{ij}) = \frac{\mathbf{I}_i \cdot \mathbf{I}_j}{4} \frac{\left| \Delta_{k_m k_m} \right|^2 m^*}{(2 \pi )^3 R_{ij}^4 \hbar^2} \left[ 2 k_m R_{ij} \cos( 2 k_m R_{ij} ) - \sin( 2 k_m R_{ij} ) \right]\text{,}</math> where represents the Hamiltonian, is the distance between the nuclei and , is the nuclear spin of atom , is a matrix element that represents the strength of the hyperfine interaction, is the effective mass of the electrons in the crystal, and is the Fermi momentum. J.H. Van Vleck clarified some subtleties of the theory, particularly the relationship between the first- and second-order perturbative contributions.
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