RKKY stands for ''Ruderman–Kittel–Kasuya–Yosida.'' It refers to a

coupling A coupling is a device used to connect two shafts together at their ends for the purpose of transmitting power. The primary purpose of couplings is to join two pieces of rotating equipment while permitting some degree of misalignment or end mov ...

mechanism of

nuclear magnetic moment The nuclear magnetic moment is the magnetic moment of an atomic nucleus and arises from the spin of the protons and neutrons. It is mainly a magnetic dipole moment; the quadrupole moment does cause some small shifts in the hyperfine structure as ...

s or localized inner d- or f-shell electron spins in a metal by means of an interaction through the

conduction electron In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies i ...

s. The RKKY interaction was originally proposed by Malvin Ruderman and

Charles Kittel Charles Kittel (July 18, 1916 – May 15, 2019) was an American physicist. He was a professor at University of California, Berkeley from 1951 and was professor emeritus from 1978 until his death. Life and work Charles Kittel was born in New Yo ...

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 whereby the nuclear spin of one atom interacts with a

through the hyperfine interaction, and this

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 classic ...

.) 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 Hamiltonian may refer to: * Hamiltonian mechanics, a function that represents the total energy of a system * Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system ** Dyall Hamiltonian, a modified 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 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 Giant magnetoresistance (GMR) is a quantum mechanical magnetoresistance effect observed in multilayers composed of alternating ferromagnetic and non-magnetic conductive layers. The 2007 Nobel Prize in Physics was awarded to Albert Fert and Peter G ...

(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.

References

Further reading