Effective dimensionality approach to the RKKY interaction in multilayer systems

Abstract

We consider RKKY interaction in a quasi 2D system with nonparabolic dispersion. In our paper we calculate the I~KY range function assuming the in-layer confinement via effective dimensionality approach. We show, that indirect magnetic exchange in our system can be modelled by the effective spectral dimension which equals one. PACS: 75.70Key words: RKKY interaction, magnetic multilayer.The semimagnetic semiconductors/SSCs/form a model diluted magnetic system with metallic electrical properties. High concentration of the free charge carriers causes the indirect (RKKY) spin-spin exchange interaction to be responsible for their magnetic properties [1]. Due to the applications in information storage devices the planar SSC superstructures rather than bulk systems attract tile most attention. Recent advances in nanoteclmology allow, via planar doping, fabrication of superstructures in which the 2D electron-gas/2DEG/with nonparabolic dispersion can be observed.Ahnost all theoretical studies of the indirect magnetic interaction in SSC m'e based on the restrictive assumption that the doping is uniform and the free electron dispersion is parabolic [2], [3] . Since the spatial dependence of the exchange integrals is determined by the spectra of mobile charge carriers that mediate this interaction, the problem of RKKY exchange must be considered anew. In the following, using the method of effective dimension by He [4], [5] we will derive formulae for RKKY exchange integral in a 2DEG of nouparabolic dispersion. Let us consider a semiconductor with planm" doping, often used for forming V-shaped potential wells with quasi 2DEG. When the deposition of impurities can be represented by the Dirac (i-function, it is called 5 doping [6]. The enhanced mobility of the 2D electron gas in V-shaped, (f-doped semiconducting multilayers can be described by the following Hamiltonian [7] H = --oL1V 4 --O~2V 2 q-V,where h4 (1.

The spin 1 Blume Capel model with RKKY interactions

“…Clearly, for example, in the case of RKKY interactions, the spherical approximation is not appropriate for thin films and more valid forms of the interactions have to be derived (see for example, Refs. [33,34]). …”

Asymmetric Andreev Reflection and Spin Hall Resonance at the Josephson Junctions

“…of the condensate density can be found in [10]. In some nano-systems, the electron/condensate confinement causes a special form of particle dynamics to be taken into account [15][16][17]. Frequencies of condensate oscillations ω C and JJ frequency ω J = 4πeV o / in general do not coincide.…”

Magnetic and Magnetoelectric Effects within a Sandwich Structure with the Parabolic Quantum Well

“…However, in the case of PQW structure the confinement within quantum well makes invalid. Therefore, there is only limited progress in description of magnetic interactions in the nonsquare-QW superlattices [4][5][6][7]. Due to the doping (by the transition metal (TM) or rare-earth (RE) metal ions) the semimagnetic semiconductors form a model diluted magnetic system with metallic electrical properties.…”