# Broken mirror symmetry, incommensurate spin correlations, and $B_{2g}$ nematic order in iron pnictides

## TL;DR

This paper investigates the origin of $B_{2g}$ nematic order in hole-doped iron pnictides, linking it to incommensurate magnetic fluctuations and proposing a microscopic mechanism supported by theoretical modeling.

## Contribution

It introduces a classification of nematic orders by mirror symmetries, constructs a Ginzburg-Landau theory connecting magnetic fluctuations to nematicity, and identifies incommensurate $(q,q)$ fluctuations as the driver of $B_{2g}$ nematic order.

## Key findings

- Incommensurate $(q,q)$ magnetic fluctuations underlie $B_{2g}$ nematic order.
- Microscopic calculations support the link between spin correlations and nematicity.
- The proposed mechanism aligns with existing experimental evidence and suggests new experimental tests.

## Abstract

Motivated by growing indications for a distinct form of nematic correlations in the extremely hole doped iron pnictide compounds $A$Fe$_2$As$_2$ ($A$=K,Rb,Cs), we consider spin-driven nematic order in the general case of incommensurate magnetic fluctuations. We classify the nematic order parameters by broken mirror symmetries of the tetragonal $D_{4h}$ point group, and use this scheme to construct a general Ginzburg-Landau theory that links the nematic order to spatial pattern of magnetic fluctuations. Our analysis points to incommensurate magnetic fluctuations of wavevector $(q,q)$ as underlying a $B_{2g}$ nematic order in $A$Fe$_2$As$_2$. We substantiate this idea by microscopic calculations of the nematic order based on 3-sublattice $(2\pi/3,2\pi/3)$ spin correlations in an extended bilinear-biquadratic Heisenberg model. We summarize the existing evidence in support of the proposed mechanism, suggest ways to further test it in future experiments, and discuss the implications of our results for iron-based high temperature superconductivity.