Related Experiment Video
Updated: May 12, 2026

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices
Published on: July 11, 2025
Indirect RKKY interaction between localized magnetic moments in armchair graphene nanoribbons
1Department of Solid State Physics, Faculty of Physics and Applied Informatics, University of Łódź, Łódź, Poland. kszalowski@uni.lodz.pl
Abstract:
A form of indirect Ruderman-Kittel-Kasuya-Yosida (RKKY)-like coupling between magnetic on-site impurities in armchair graphene nanoribbons is studied theoretically. The calculations are based on a tight-binding model for a finite nanoribbon system with periodic boundary conditions. A pronounced Friedel-oscillation-like dependence of the coupling magnitude on the impurity position within the nanoribbon resulting from quantum size effects is found and investigated. In particular, the distance dependence of coupling is analysed. For semiconducting nanoribbons, this dependence is exponential-like, resembling the Bloembergen-Rowland interaction. For metallic nanoribbons, interesting behaviour is found for finite length systems, in which zero-energy states make an important contribution to the interaction. In such situations, the coupling decay with distance can then be substantially slower.
Related Concept Videos
π Electron Effects on Chemical Shift: Overview
¹H NMR: Long-Range Coupling
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
NMR Spectroscopy: Spin–Spin Coupling
Atomic Nuclei: Nuclear Relaxation Processes

