Kinetic Energy Driven Ferromagnetic Insulator

TL;DR

This paper introduces a minimal fermionic model on a trimerized triangular lattice demonstrating a ferromagnetic insulator driven by kinetic energy, with a detailed analysis of competing superexchange interactions.

Contribution

It constructs and analyzes a Hubbard model on a trimerized triangular lattice revealing a kinetic energy driven ferromagnetic insulating phase, highlighting the role of ferromagnetic superexchange.

Findings

Ferromagnetic insulator occurs at 1/3 filling with strong interactions.

Ferromagnetic superexchange is derived as proportional to -t'^2/t.

Competing antiferromagnetic interactions lead to frustrated phases.

Abstract

We construct a minimal model of interacting fermions establishing a ferromagnetic insulating phase. It is based on the Hubbard model on a trimerized triangular lattice in the regime of $t\gg |t^\prime|>0$ with $t$ and $t^\prime$ the intra- and inter-trimer hopping amplitudes, respectively. At the $\frac{1}{3}$-filling, each trimer becomes a triplet spin-1 moment, and the inter-trimer superexchange is ferromagnetic with $J =- \frac{2}{27}\frac{t^{\prime 2}}{t}$ in the limit of $U/t=+\infty$. As $U/t$ becomes finite, the antiferromagnetic superexchange competes with the ferromagnetic one. The system enters into a frustrated antiferromagnetic insulator when $\lambda >U/t\gg 1$ where $\lambda$ is a constant at the order of 10. In contrast, a similar analysis to the trimerized Kagome lattice shows that only the antiferromagnetic superexchange exists at $\frac{1}{3}$-filling.