# Ground-State Phase Diagram of the Multiple-Spin Exchange Model with up to the Six-Spin Exchange Interactions on the Triangular Lattice

## TL;DR

This study maps the ground-state phase diagram of a triangular lattice multiple-spin exchange model including up to six-spin interactions, revealing new phases and the effects of higher-order interactions on magnetic phases.

## Contribution

It introduces the first analysis of the six-spin exchange interactions' impact on the phase diagram, identifying new phases and modifications to existing magnetic states.

## Key findings

- Five- and six-spin interactions expand the ferromagnetic phase.
- Antiferromagnetic-like phases are contracted by higher-order interactions.
- A new 1/6 magnetization plateau with a twelve-sublattice structure appears.

## Abstract

The ground state of the multiple-spin exchange model with up to the six-spin exchange interactions on a triangular lattice in the magnetic field is investigated within the mean-field approximation. By comparing the phase diagrams of systems with and without the five- and six-spin interactions, we find that the five- and six-spin interactions expand the ferromagnetic phase. In contrast, the antiferromagnetic-like phases are contracted. A phase with a 1/2 plateau is also contracted by the five- and six-spin interactions. In addition to the results that have not yet been reported for systems with up to the four-spin interactions, we obtain new phases for systems with up to the six-spin interactions. In particular, a 1/6 plateau appears in the low magnetic field near the ferromagnetic phase in the magnetization process. This phase has a twelve-sublattice structure in which a unit cell consists of seven spins parallel to the magnetic field and five spins antiparallel to it.