A novel nonlinear spin wave theory for the spin 1/2 antiferromagnetic Heisenberg model on a triangular lattice

TL;DR

This paper introduces a new nonlinear spin wave theory for the spin 1/2 antiferromagnetic Heisenberg model on a triangular lattice, improving accuracy over linear theories by including higher-order corrections and analyzing phase stability.

Contribution

It extends the nonlinear spin wave theory to include higher-order 1/S corrections and provides a detailed phase diagram with stability analysis for magnetic orders.

Findings

Incommensurate configuration is unstable.

New phase transition point matches previous studies.

Negative energy excitations can be renormalized to positive.

Abstract

We extend the nonlinear spin wave theory (NLSWT) for the spin 1/2 antiferromagnetic Heisenberg model on a triangular lattice (TAFHM). This novel NLSWT considers the corrections one order higher in 1/S than the linear spin wave theory (LSWT). It also distinguishes in which circumstance the negative energy excitation, the sign of the breakdown of LSWT, shall be renormalized to be positive both by a boson normal ordering and a self-consistent iteration. We draw a phase diagram by testing the stability of various magnetic orders for different parameters. In particular, the incommensurate configuration is found unstable by our study. The new phase transition point (PTP) of the collinear configuration agrees well with various previous studies.