Nagaoka Ferromagnetism of 3x3 Dopant Arrays in Silicon

Nagaoka ferromagnetism (NF) is a long-predicted example of ferromagnetism in the Hubbard model and has been studied theoretically for many years. Recently, NF was realized experimentally in quantum-dots systems for 2x2 plaquettes. NF occurs when there is one fewer electron than half-filling and a large on-site Coulomb repulsion which does not arise naturally in materials. Due to the atomically precise fabrication of dopant arrays in Si, it is possible to engineer complex geometries and make highly controllable systems. These properties make them good candidates to study NF in different array geometries. Here we describe theoretical simulations done for 3x3 arrays of dopants in Si, such as the dopant arrays studied at NIST, and look for the emergence of NF. Unlike 2x2 plaquettes, we find no evidence for Nagaoka ferromagnetism in perfect 3x3 arrays. We show that the antiferromagnetic state is always the ground state in perfect 3x3 arrays because the energy cost to separate opposite spin electrons in suppressed in arrays larger 2x2. Theoretical simulations are done for arrays more constrained either by special geometries or disorder to see if additional localization induces NF. Our results define possible experiments to hunt for Nagaoka ferromagnetism.