# Intertwined spin-orbital coupled orders in the iron-based superconductors

## TL;DR

This paper presents a unifying theoretical framework for understanding the complex intertwined spin and orbital orders in the underdoped phase of iron-based superconductors, revealing novel phenomena and experimental implications.

## Contribution

It introduces a symmetry-respecting model that unifies various magnetic and vestigial phases, including exotic orbital orders and emergent spin-orbit interactions, in iron-based superconductors.

## Key findings

- Identification of vestigial phases with Ising-like order parameters
- Prediction of electro-nematic and ferro-Néel effects
- Explanation of complex ordered states within a symmetry-based framework

## Abstract

The underdoped phase diagram of the iron-based superconductors exemplifies the complexity common to many correlated materials. Indeed, multiple ordered states that break different symmetries but display comparable transition temperatures are present. Here, we argue that such a complexity can be understood within a simple unifying framework. This framework, built to respect the symmetries of the non-symmorphic space group of the FeAs/Se layer, consists of primary magnetically-ordered states and their vestigial phases that intertwine spin and orbital degrees of freedom. All vestigial phases have Ising-like and zero wave-vector order parameters, described in terms of composite spin order and exotic orbital-order patterns such as spin-orbital loop-currents, staggered atomic spin-orbit coupling, and emergent Rashba- and Dresselhaus-type spin-orbit interactions. Moreover, they host unusual phenomena, such as the electro-nematic effect, by which electric fields acts as transverse fields to the nematic order parameter, and the ferro-N\'eel effect, by which a uniform magnetic field induces N\'eel order. We discuss the experimental implications of our findings to iron-based superconductors and possible extensions to other correlated compounds with similar space groups.