Magnetism of quantum dot clusters: A Hubbard model study

TL;DR

This study investigates the magnetic properties of quantum dot clusters using a Hubbard model, revealing how electron filling influences magnetic coupling and spin states in these nanoscale systems.

Contribution

It provides a detailed analysis of magnetism in quantum dot clusters considering different electron fillings and harmonic oscillator shells using exact diagonalization.

Findings

Half-filled shells exhibit antiferromagnetic behavior modeled by the Heisenberg model.

Other fillings tend to favor large total spins, indicating ferromagnetic coupling.

Magnetic properties depend on the electron filling and shell structure within the quantum dots.

Abstract

Magnetic properties of two and three-dimensional clusters of quantum dots are studied with exact diagonalization of a generalized Hubbard model. We study the weak coupling limit, where the electrons interact only within a quantum dot and consider cases where the second or third harmonic oscillator shell is partially filled. The results show that in the case of half-filled shell the magnetism is determined by the antiferromagnetic Heisenberg model with spin 1/2, 1 or 3/2, depending on the number of electrons in the open shell. For other fillings the system in most cases favors a large total spin, indicating a ferromagnetic coupling between the dots.