In the

physical theory Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict natural phenomena. This is in contrast to experimental physics, which uses experi ...

of spin glass

magnetization In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Accordingly, physicists and engineers usually define magnetization as the quanti ...

, 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 The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

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 In chemistry and physics, the exchange interaction is a quantum mechanical constraint on the states of indistinguishable particles. While sometimes called an exchange force, or, in the case of fermions, Pauli repulsion, its consequences cannot alw ...

. The simplest treatment assumes a Bloch wavefunction basis and therefore only applies to crystalline systems; the resulting correlation energy, computed with

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 middle ...

, takes the following form:

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

where 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 ...

, 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. Intuitively, we may picture this as when one magnetic atom scatters an electron wave, which then scatters off another magnetic atom many atoms away, thus coupling the two atoms' spins. Tadao Kasuya from

Nagoya University , abbreviated to or NU, is a Japanese national research university located in Chikusa-ku, Nagoya. It was established in 1939 as the last of the nine Imperial Universities in the then Empire of Japan, and is now a Designated National Universit ...

later proposed that a similar indirect exchange coupling could occur with localized inner d-electron spins instead of nuclei. This theory was expanded more completely by Kei Yosida of 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.

References

Further reading