Mass modification of itinerant carriers in RKKY oscillations induced by finite range exchange interactions

TL;DR

This paper analytically studies how finite-range exchange interactions modify RKKY oscillations in a one-dimensional quantum wire with a magnetic impurity, revealing effects on long-range behavior and carrier mass.

Contribution

It introduces an analytical model for RKKY oscillations considering finite-range exchange interactions, highlighting their impact on oscillation behavior and carrier mass in a 1D system.

Findings

Long-range RKKY oscillations are similar to zero-radius case when interaction radius is small.

Exchange interaction radius significantly modifies the effective mass of itinerant carriers.

Surface RKKY interaction anisotropy may stem from atomic orbital anisotropy, not just Fermi surface.

Abstract

We investigate the Ruderman-Kittel-Kasuya-Yosida oscillations of the itinerant carrier spin density in a system where those oscillations appear only due to a finite distribution of a localized spin. The system represents a half-infinite one-dimensional quantum wire with a magnetic impurity located at its edge. In contrast to the conventional model of a point-like exchange interaction the itinerant carrier spin density oscillations in this system exist. We {\it analytically} demonstrate that when the radius of the exchange interaction is less than the wave length of the itinerant carriers living on the Fermi surface, the long range behavior of the oscillations is identical to the one taking place in the zero radius limit of the same exchange interaction but for an infinite one-dimensional quantum wire where, in comparison with the original half-infinite system, the mass of the itinerant carriers is {\it strongly} modified by the exchange interaction radius. On the basis of our analysis we make a suggestion on directionality of surface Ruderman-Kittel-Kasuya-Yosida interaction shown in recent experiments: we believe that in general the anisotropy of the Ruderman-Kittel-Kasuya-Yosida interaction could result not only from the anisotropy of the {\it Fermi surface} of itinerant carriers but also from the anisotropy of the {\it spin carrying atomic orbitals} of magnetic impurities.