---
abstract: 'Iron chalcogenides display a rich variety of electronic orders in their phase diagram. A particularly enigmatic case is FeTe, a metal which possesses co-existing hole and electron Fermi surfaces as in the iron pnictides but has a distinct ($\pi$/2,$\pi/2$) bicollinear antiferromagnetic order in the Fe square lattice. While local-moment physics has been recognized as essential for understanding the electronic order, it has been a long-standing challenge to understand how the bicollinear antiferromagnetic ground state emerges in a proper quantum spin model. We show here that a bilinear-biquadratic spin-$1$ model on a square lattice with nonzero ring-exchange interactions exhibits the bicollinear antiferromagnetic order over an extended parameter space in its phase diagram. Our work shows that frustrated magnetism in the quantum spin model provides a unified description of the electronic orders in the iron chalcogenides and iron pnictides.'
author:
- 'Hsin-Hua Lai'
- 'Shou-Shu Gong'
- 'Wen-Jun Hu'
- Qimiao Si
bibliography:
- 'bib4FeTeBC.bib'
title: Frustrated magnetism and bicollinear antiferromagnetic order in FeTe
---

*Introduction.*— Iron-based superconductors (FeSCs) have been of extensive interest during the past eight years [@Kamihara2008; @Johnston2010; @PCDai2015; @Si2016]. Early work in the field focused on the iron pncitides, such as BaFe$_2$As$_2$ with various chemical substitutions. 