RKKI-exchange interaction

The RKKI-exchange interaction ( Ruderman - Kittel - Kasuya - Yosida interaction ) is an indirect exchange interaction between magnetic ions via collectivized conduction electrons .

This exchange interaction occurs in metals and semiconductors , where collectivized electrons mediate the exchange interaction of ions with localized oppositely directed spins , partially filled with d and f shells. Conduction electrons interact with the effective magnetic field of the ith site of the crystal lattice and acquire a certain spin polarization. When passing through the next lattice node, relaxation of the magnetic moments of the electron and the node will cause mutual changes in both the spin polarization and the spin of the lattice node.

It can be described using the notion that conduction electrons move in an effective field created by the localized magnetic moment of one node.

The interaction energy between the spins S at the ith and jth nodes of the magnetic sublattice is written as

E_{ij}={\frac {J^{2}}{\mu _{0}(g\mu _{B})^{2}}}\mathbf {S} _{i}\mathbf {S} _{j}\chi _{ij}

{\ displaystyle E_ {ij} = {\ frac {J ^ {2}} {\ mu _ {0} (g \ mu _ {B}) ^ {2}}} \ mathbf {S} _ {i} \ mathbf {S} _ {j} \ chi _ {ij}}

E _ {{ij}} = {\ frac {J ^ {2}} {\ mu _ {0} (g \ mu _ {B}) ^ {2}}} {\ mathbf S} _ {i} {\ mathbf S} _ {j} \ chi _ {{ij}}

,

where J is the exchange constant, g is the Landé factor , $\mu _{B}$ ${\ displaystyle \ mu _ {B}}$ $\ mu _ {B}$ - magneton of Bora , $\mu _{0}$ ${\ displaystyle \ mu _ {0}}$ $\ mu _ {0}$ - magnetic constant , $\chi _{ij}$ ${\ displaystyle \ chi _ {ij}}$ $\ chi _ {{ij}}$ - generalized magnetic susceptibility . For free electrons, the latter can be represented as

\chi _{ij}={\frac {(x\cos x-\sin x)}{x^{4}}}

{\ displaystyle \ chi _ {ij} = {\ frac {(x \ cos x- \ sin x)} {x ^ {4}}}}

\ chi _ {{ij}} = {\ frac {(x \ cos x- \ sin x)} {x ^ {4}}}

,

provided that $x=2\mathbf {k} _{F}\mathbf {R} _{ij}\gg 1$ ${\ displaystyle x = 2 \ mathbf {k} _ {F} \ mathbf {R} _ {ij} \ gg 1}$ $x = 2 {\ mathbf k} _ {F} {\ mathbf R} _ {{ij}} \ gg 1$ . Here $k_{F}$ ${\ displaystyle k_ {F}}$ $k_ {F}$ - wave vector at the Fermi level , $R_{ij}$ ${\ displaystyle R_ {ij}}$ $R_ {ij}$ - distance. Therefore, the interaction energy has an alternating oscillating character as a function of the distance between the interacting ions. The alternation of the interaction energy leads to the fact that, depending on the distance between the ions, the material will exhibit ferromagnetic properties if the energy minimizes the codirectionality of the spins, or antiferromagnetic in the opposite case. This is used in spin valves based on giant and tunnel magnetoresistance .

Literature

Stöhr, J. and Siegmann, HC Magnetism: From Fundamentals to Nanoscale Dynamics. - Springer-Verlag Berlin Heidelberg, 2006 .-- P. 290-293. - 821 p. - ISBN 978-3540302827 .
de Lacheisserie É., Gignoux D., Schlenker M. Magnetism: Fundamentals. - Springer, 2005. - Vol. 1. - P. 315-317. - 507 p. - (Magnetism). - ISBN 9780387229676 .

RKKI-exchange interaction

Literature

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