Eur. Phys. J. B 64, 95-103 (2008)
https://doi.org/10.1140/epjb/e2008-00285-7

Magnetism of quantum dot clusters: a Hubbard model study

¹ NanoScience Center, Department of Physics, 40014 University of Jyväskylä, Jyväskylä, Finland
² Inspecta LTD, 02151 Espoo, Finland

Corresponding author: ^a Matti.Manninen@phys.jyu.fi

Received: 29 April 2008
Published online: 16 July 2008

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.