Magnetic interlayer coupling in multilayers of fractional dimensionality

Fracton Excitations in the Magnetic "Net Fractal" Systems

“…It is natural to assume that the self-similarity of the fractal is reflected also in the symmetry of exchange interactions. We assume therefore that also the exchange integrals exhibit the power law scaling with the separation, we take it in the form I(λr ij ) = λ −σ I(r ij ) (for the Ruderman-Kittel-Kasuya-Yosida (RKKY)-like interactions the σ can be approximated by the spectral dimension of the system [3,4]). Let us now recall the (log-scale) isomorphism of "net fractals" and some crystal lattices.…”

RKKY Interaction in Coupled Quantum Dots

“…Therefore, it is evident that the indirect magnetic interactions due to the confined electrons are governed by the values of the effective spectral dimension as shown in [4]. The analytical expression for the RKKY-like exchange integral in the case of an arbitrary spectral di-mension α is given by the following expression [4]:…”

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

“…Perturbative calculations of the RKKY exchange integral in the PQW system which account for this spectrum give us [6]:…”

“…with Y ν (x) being the Neumann function [6] and d = 4 is the effective spectral dimension of the PQW system. It is worthwhile to mention here that in general in the case of quasi-2D electron gas systems the effective spectral dimension can take any value from the 1 ≤ d ≤ 4 range [8].…”

“…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.…”