Dynamic Ruderman–Kittel–Kasuya–Yosida indirect interaction (abstract)

Abstract

The spin polarization of a degenerate electron gas has been used to describe the coupling [Ruderman–Kittel–Kasuya–Yosida (RKKY) indirect interaction] between two spins in metals. Nowadays such the RKKY interaction is investigated very much in particular with the problems of coupling in magnetic superlattices. However, in well-known RKKY interaction between two spins it is supposed that the spins are not subject to the external alternating magnetic field (static case). We consider the RKKY interaction between two spins, when they are subject to the external alternating magnetic field. We shown, that the RKKY indirect interaction in free-electron gas for transversal component of the spins (value of the coupling, its spatial dependence, the periods of spatial oscillations) depends on a frequency of the alternating magnetic field. This behavior is caused by the frequency dependence of the dynamic magnetic susceptibility of an electron, which determines the indirect coupling. The largest value of the coupling is in the frequency region hω∼εF, where εF is the energy Fermi. For high frequency region hω⩽εF: In contrast to the static case, where there is only one period 2kF for free-electron, in high frequency hω∼εF dynamical case the spatial dependence of the RKKY interaction have complicated form and there are three main uncommensurable periods of oscillations kF, (1+2)kF, (2−1)kF; the spatial dependence of coupling for large kFr contains terms r−1 and r−2; value of coupling is (kFr)2 as much then in a static case. For the frequency region hω≪εF: the dynamic RKKY interaction contains terms, value of which is determined by the frequency of the magnetic field; there are the oscillations of coupling with a period 2kF, which are amplitude-modulated by a oscillation with a large spatial period; these oscillations have amplitude, which is determined also by a frequency.