Possible chiral phase transition in two-dimensional solid $^3$He

TL;DR

This paper investigates a two-dimensional spin model for solid helium-3, revealing a chiral phase transition driven by four-spin interactions, with analysis through spin-wave theory and Monte Carlo simulations.

Contribution

It introduces a novel chiral order phase in a 2D spin system with four-spin interactions, analyzed using spin-wave approximation and Monte Carlo methods.

Findings

Scalar chiral order appears when four-spin interactions dominate.

A finite-temperature phase transition in scalar chirality is observed.

Critical properties of the transition are characterized through simulations.

Abstract

We study a spin system with two- and four-spin exchange interactions on the triangular lattice, which is a possible model for the nuclear magnetism of solid $^3$He layers. It is found that a novel spin structure with scalar chiral order appears if the four-spin interaction is dominant. Ground-state properties are studied using the spin-wave approximation. A phase transition concerning the scalar chirality occurs at a finite temperature, even though the dimensionality of the system is two and the interaction has isotropic spin symmetry. Critical properties of this transition are studied with Monte Carlo simulations in the classical limit.