# Spin coupling in zigzag Wigner crystals

## TL;DR

This paper investigates the spin properties of electrons in a zigzag Wigner crystal within a quantum wire, revealing complex magnetic phases influenced by various exchange interactions.

## Contribution

It introduces a detailed analysis of the phase diagram of a zigzag Wigner crystal, highlighting the role of multi-particle exchange processes in determining spin order.

## Key findings

- Identification of regions with complete and partial spin polarization
- Discovery of a novel phase driven by four-particle ring exchange
- Mapping of the phase diagram including antiferromagnetic and dimer phases

## Abstract

We consider interacting electrons in a quantum wire in the case of a shallow confining potential and low electron density. In a certain range of densities, the electrons form a two-row (zigzag) Wigner crystal whose spin properties are determined by nearest and next-nearest neighbor exchange as well as by three- and four-particle ring exchange processes. The phase diagram of the resulting zigzag spin chain has regions of complete spin polarization and partial spin polarization in addition to a number of unpolarized phases, including antiferromagnetism and dimer order as well as a novel phase generated by the four-particle ring exchange.