Itinerant Ferromagnetism from One-Dimensional Mobility

TL;DR

This paper introduces a universal kinetic mechanism for half-metallic ferromagnetism driven by constrained 1D electron dynamics and strong Coulomb interactions, applicable across various models and doping levels.

Contribution

It reveals a new ferromagnetism mechanism based on 1D mobility and multi-spin exchanges, extending beyond the Nagaoka limit and applicable to different microscopic systems.

Findings

Induces ferromagnetism via multi-spin ring exchanges of even parity.

Establishes equivalence between bosonic and fermionic models, suggesting a Bose metallic phase.

Demonstrates the mechanism in solvable Lieb lattice models and other physical systems.

Abstract

We propose a universal kinetic mechanism for a half-metallic ferromagnet -- a metallic state with full spin polarization -- arising from strong on-site Coulomb repulsions between particles that exhibit constrained one-dimensional (1D) dynamics. We illustrate the mechanism in the context of a solvable model on a Lieb lattice in which doped electrons have 1D mobility. Such 1D motion is shown to induce only multi-spin ring exchanges of even parity, which mediate ferromagnetism and result in a unique half-metallic ground state. In contrast to the Nagaoka mechanism of ferromagnetism, this result pertains to any doped electron density in the {\it thermodynamic} limit. We explore various microscopic routes to such (approximate) 1D dynamics, highlighting two examples: doped holes in the strong-coupling limit of the Emery model and vacancies in a two-dimensional Wigner crystal. Finally, we demonstrate an intriguing exact equivalence between the bosonic and fermionic versions of these models, which implies a novel mechanism for the conjectured Bose metallic phase.