Hund's coupling-assisted ferromagnetic percolation transition in a multiorbital flat band

TL;DR

This paper links Hund's coupling with flat band physics to demonstrate a ferromagnetic transition in a multiorbital system, using a percolation model and Monte Carlo simulations to analyze the transition near half filling.

Contribution

It establishes an exact connection between Hund's physics and flat band ferromagnetism in a multiorbital lattice model, introducing a percolation framework for ground state analysis.

Findings

Ferromagnetic transition occurs near half filling.

Ground states are dominated by maximum-spin clusters.

Monte Carlo simulations confirm the transition.

Abstract

By connecting Hund's physics with flat band physics, we establish an exact result for studying ferromagnetism in a multiorbital system. We consider a two-layer model consisting of a $p_x$, $p_y$-orbital honeycomb lattice layer and an $f$-orbital triangular lattice layer with sites aligned with the centers of the honeycomb plaquettes. The system features a flat band that admits a percolation representation for an appropriate chemical potential difference between the two layers. In this representation, the ground state space is spanned by maximum-spin clusters of localized single-particle states, and averaging over the ground states yields a correlated percolation problem with weights due to the spin degeneracy of the clusters. A paramagnetic-ferromagnetic transition occurs as the band approaches half filling and the ground states become dominated by states with a large maximum-spin cluster, as shown by Monte Carlo simulation.