# Spin-Wave Theory for the Scalar Chiral Phase in the Multiple-Spin Exchange Model on a Triangular Lattice

## TL;DR

This paper investigates quantum fluctuations in a scalar chiral phase of a multiple-spin exchange model on a triangular lattice, showing the phase's stability and correcting previous scalar chirality estimates.

## Contribution

It provides a linear spin-wave analysis demonstrating the robustness of the tetrahedral structure against quantum fluctuations and corrects earlier scalar chirality values.

## Key findings

- Tetrahedral structure remains stable under quantum fluctuations.
- Quantum corrections are small for certain interactions.
- Previous scalar chirality values are corrected.

## Abstract

We study the effects of quantum fluctuations on a non-coplanar tetrahedral spin structure, which has a scalar chiral order, in the spin-1/2 multiple-spin exchange model with up to the six-spin exchange interactions on a triangular lattice. We find that, in the linear spin-wave approximation, the tetrahedral structure survives the quantum fluctuations because spin waves do not soften in the whole parameter region of the tetrahedral-structure phase evaluated for the classical system. In the quantum corrections to the ground-state energy, sublattice magnetization, and scalar chirality, the effects of the quantum fluctuations are small for the ferromagnetic nearest-neighbor interactions and for the strong five-spin interactions. The six-spin interactions have little effect on the quantum corrections in the tetrahedral-structure phase. This calculation also corrects an error in the previously reported value of scalar chirality for the spin-1/2 multiple-spin exchange model with up to the four-spin exchange interactions.