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'''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.  
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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 magnetic resonance|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 structure|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:
 
<math>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 ] </math>
 
where H represents the [[Molecular Hamiltonian|Hamiltonian]], <math>R_{ij}</math> is the distance between the nuclei i and j, <math>\mathbf{I}_i </math> is the nuclear spin of atom i, <math>\Delta k_m k_m</math> is a term that represents the strength of the hyperfine interaction, <math>m^*</math> is the [[effective mass (solid-state physics)|effective mass]] of the electrons in the crystal, and <math>k_m</math> 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. [[John Hasbrouck Van Vleck|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.<ref>S.S.P. Parkin and D. Mauri, Physical Review B Vol. 44 7131-7134 (1991)</ref><ref>Y. Yafet, Physical Review B Vol. 36 3948-3949 (1987)</ref>
 
==References==
# M.A. Ruderman and C. Kittel, Phys. Rev. 96, 99 (1954).
# T. Kasuya, Prog. Theor. Phys. 16, 45 (1956).
# K. Yosida, Phys. Rev. 106, 893 (1957).
# J. H. Van Vleck. Reviews of Modern Physics 34, 681-686 (1962).
# A. Blandin and J. Friedel, J. phys. rad. 20, page 160-168 (1959)
# Quantum Theory of Solids, 2ed. pp 360–366, C. Kittel, Wiley 1987
<references/>
 
[[Category:Magnetism]]
 
[[es:Interacción RKKY]]

Latest revision as of 23:36, 10 May 2014

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