RKKY
Encyclopedia
RKKY stands for Ruderman-Kittel-Kasuya-Yosida and 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 M.A. Ruderman and Charles Kittel
of the University of California, Berkeley
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
to describe an indirect exchange coupling whereby the nuclear spin of one atom interacts with a conduction electron via 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 via the hyperfine interaction, another scenario is for inner electron spins to couple to conduction spins via the exchange interaction
.) The theory is based on Bloch wave
functions, and is therefore only applicable to crystalline systems. The derived exchange interaction takes the following form:
where H represents the Hamiltonian
,
is the distance between the nuclei i and j, 
is the nuclear spin of atom i, 
is a term that represents the strength of the hyperfine interaction, 
is the effective mass of the electrons in the crystal, and 
is the wave vector of the conduction electrons. In crystalline materials, the wave vectors of conduction electrons are very close to the Fermi surface
.
Tadao Kasuya of Nagoya University
later proposed that a similar indirect exchange coupling could be applied to localized inner d-electron spins interacting via conduction electrons. This theory was expanded more completely by Kei Yosida of the University of California, Berkeley
to give a Hamiltonian that describes (d-electron spin)-(d-electron spin), (nuclear spin)-(nuclear spin) as well as (d-electron spin)-(nuclear spin) interactions. 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 .
The RKKY interaction was originally proposed by M.A. Ruderman and Charles Kittel
Charles Kittel
Charles Kittel is an American physicist. He was a Professor at University of California, Berkeley from 1951 and has been Professor Emeritus since 1978.- Life and work :...
of the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
as a means of explaining unusually broad nuclear spin resonance
Nuclear magnetic resonance
Nuclear magnetic resonance is a physical phenomenon in which magnetic nuclei in a magnetic field absorb and re-emit electromagnetic radiation...
lines that had been observed in natural metallic silver. The theory uses second-order perturbation theory
Perturbation theory
Perturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem...
to describe an indirect exchange coupling whereby the nuclear spin of one atom interacts with a conduction electron via the hyperfine interaction
Hyperfine structure
The term hyperfine structure refers to a collection of different effects leading to small shifts and splittings in the energy levels of atoms, molecules and ions. The name is a reference to the fine structure which results from the interaction between the magnetic moments associated with electron...
, 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 via the hyperfine interaction, another scenario is for inner electron spins to couple to conduction spins via the exchange interaction
Exchange interaction
In physics, the exchange interaction is a quantum mechanical effect without classical analog which increases or decreases the expectation value of the energy or distance between two or more identical particles when their wave functions overlap...
.) The theory is based on Bloch wave
Bloch wave
A Bloch wave or Bloch state, named after Felix Bloch, is the wavefunction of a particle placed in a periodic potential...
functions, and is therefore only applicable to crystalline systems. The derived exchange interaction takes the following form:
where H represents the Hamiltonian
Molecular Hamiltonian
In atomic, molecular, and optical physics as well as in quantum chemistry, molecular Hamiltonian is the name given to the Hamiltonian representing the energy of the electrons and nuclei in a molecule...
,
is the distance between the nuclei i and j, is the nuclear spin of atom i, is a term that represents the strength of the hyperfine interaction, is the effective mass of the electrons in the crystal, and is the wave vector of the conduction electrons. In crystalline materials, the wave vectors of conduction electrons are very close to the Fermi surfaceFermi surface
In condensed matter physics, the Fermi surface is an abstract boundary useful for predicting the thermal, electrical, magnetic, and optical properties of metals, semimetals, and doped semiconductors. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline...
.
Tadao Kasuya of Nagoya University
Nagoya University
Nagoya University is one of the most prestigious universities in Japan. It can be seen in the several rankings such as shown below.-General Rankings:...
later proposed that a similar indirect exchange coupling could be applied to localized inner d-electron spins interacting via conduction electrons. This theory was expanded more completely by Kei Yosida of the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
to give a Hamiltonian that describes (d-electron spin)-(d-electron spin), (nuclear spin)-(nuclear spin) as well as (d-electron spin)-(nuclear spin) interactions. Van Vleck
John Hasbrouck van Vleck
John Hasbrouck Van Vleck was an American physicist and mathematician, co-awarded the 1977 Nobel Prize in Physics, for his contributions to the understanding of the behavior of electrons in magnetic solids....
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 .