RKKY stands for ''Ruderman–Kittel–Kasuya–Yosida.'' It refers to a coupling mechanism of nuclear magnetic moments or localized inner d- or f-shell electron spins in a metal by means of an interaction through the conduction electrons. The RKKY interaction was originally proposed by Malvin Ruderman and Charles Kittel of the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

, as a means of explaining unusually broad nuclear spin resonance lines that had been observed in natural metallic silver. The theory uses second-order

perturbation theory In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middl ...

to describe an

indirect exchange coupling Indirect, the opposite of direct, may refer to: *Indirect approach, a battle strategy *Indirect DNA damage, caused by UV-photons *Indirect agonist or indirect-acting agonist, a substance that enhances the release or action of an endogenous neurotra ...

whereby the nuclear spin of one atom interacts with a conduction electron through the hyperfine interaction, and this conduction electron then interacts with another nuclear spin, thus creating a correlation energy between the two nuclear spins. (Alternatively, instead of nuclear spins coupling to conduction spins through the hyperfine interaction, another scenario is for inner electron spins to couple to conduction spins through the

exchange interaction In chemistry and physics, the exchange interaction (with an exchange energy and exchange term) is a quantum mechanical effect that only occurs between identical particles. Despite sometimes being called an exchange force in an analogy to classi ...

.) The theory is based on Bloch wavefunctions and is therefore only applicable to crystalline systems. The derived exchange interaction takes the following form: :

H(\mathbf_) = \frac \frac \left 2 k_m R_ \cos( 2 k_m R_ ) - \sin( 2 k_m R_ ) \right

where ''H'' represents the Hamiltonian,

R_

is the distance between the nuclei ''i'' and ''j'',

\mathbf_i

is the nuclear spin of atom ''i'',

\Delta_

is a matrix element that represents the strength of the hyperfine interaction,

m^*

is the effective mass of the electrons in the crystal, and

k_m

is the Fermi momentum. Tadao Kasuya from

Nagoya University , abbreviated to or NU, is a Japanese national research university located in Chikusa-ku, Nagoya. It was the seventh Imperial University in Japan, one of the first five Designated National University and selected as a Top Type university of ...

later proposed that a similar indirect exchange coupling could be applied to localized inner d-electron spins interacting through conduction electrons. This theory was expanded more completely by Kei Yosida of the UC Berkeley, to give a Hamiltonian that describes (d-electron spin)–(d-electron spin), (nuclear spin)–(nuclear spin), and (d-electron spin)–(nuclear spin) interactions. J.H. Van Vleck clarified some subtleties of the theory, particularly the relationship between the first- and second-order perturbative contributions. Perhaps the most significant application of the RKKY theory has been to the theory of giant magnetoresistance (GMR). GMR was discovered when the coupling between thin layers of magnetic materials separated by a non-magnetic spacer material was found to oscillate between ferromagnetic and antiferromagnetic as a function of the distance between the layers. This ferromagnetic/antiferromagnetic oscillation is one prediction of the RKKY theory.

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Further reading