Magnetism from multiparticle ring exchange in moir\'e Wigner crystals

TL;DR

This paper studies how multiparticle ring exchange interactions influence magnetism in two-dimensional Wigner crystals within moiré superlattices, revealing potential magnetic phase transitions driven by external potentials.

Contribution

It introduces a semiclassical approach to analyze multiparticle ring exchange couplings in Wigner crystals under external potentials, highlighting potential magnetic phase transitions.

Findings

Transition from ferromagnet to 120° Nél antiferromagnet with increasing potential

Transition occurs at weaker potentials for triangular lattices

Transition occurs at much larger potentials for honeycomb lattices

Abstract

We investigate the multiparticle ring exchange couplings of the two-dimensional triangular Wigner crystal in external commensurate triangular and honeycomb potentials, using a semiclassical approach valid in the regime where Coulomb interactions dominate over electronic kinetic energy. In this limit, increasing the strength of the potential drives a transition from a ferromagnet to a $120^\circ$ N\'eel antiferromagnet for both external potential types. In the triangular case, we find that the transition occurs already for a weak potential, whereas in the honeycomb case, it occurs when the potential is nearly two orders of magnitude larger. Our results are relevant to the magnetism of generalized Wigner crystal phases observed at certain rational fillings of the moir\'e superlattice in transition-metal dichalcogenide heterobilayers.