Magnetism of the Bilayer Wigner Crystal

TL;DR

This paper investigates the magnetic properties of the bilayer Wigner crystal using semiclassical methods, revealing a complex phase diagram with ferromagnetic, antiferromagnetic, and exotic phases, and suggesting experimental accessibility in transition-metal dichalcogenides.

Contribution

It provides the first detailed analysis of the exchange interactions and magnetic phases of the bilayer Wigner crystal across different densities and structures.

Findings

Identification of multiple magnetic phases including ferromagnetic and antiferromagnetic.

Prediction of a rich phase diagram with potential spin-nematic and valence-bond solid phases.

Estimation that magnetic phases are experimentally accessible in bilayer transition-metal dichalcogenides.

Abstract

The multiple-spin exchange frequencies of the bilayer Wigner crystal are determined by the semiclassical method, which is asymptotically exact in the limit of dilute electron densities. The evolution of the exchange frequencies with interlayer distance -- as the crystal undergoes a sequence of structural transitions -- leads to both ferromagnetic and multi-sublattice antiferromagnetic phases. Extrapolation of the results to higher density suggests a rich magnetic phase diagram of the bilayer Wigner crystal, including the possibility of spin-nematic and valence-bond solid phases. The bilayer crystal is stable to higher electron densities than the monolayer, leading to enhanced magnetic energy scales. Our estimates of the exchange energies suggest some of the magnetic phases may be accessible in recently discovered bilayer Wigner crystals in a transition-metal dichalcogenide system.