# Odd-Parity Magnetism in Fe-Based Superconductors

## TL;DR

This paper demonstrates that Fe-based superconductors with coplanar magnetic order realize an odd-parity magnetic state, revealing new magnetic properties and responses related to inversion symmetry breaking and spin-orbit effects.

## Contribution

The study combines modeling and density-functional theory to identify odd-parity magnetism in Fe-based superconductors and explores its electronic and magnetic responses.

## Key findings

- Electronic spins polarized along the $k_z$-direction without spin-orbit coupling.
- Splitting of up and down states exhibits an $h$-wave form-factor.
- Inversion symmetry breaking leads to finite out-of-plane Berry curvature and non-linear anomalous Hall effect.

## Abstract

Odd-parity magnetism constitutes an intriguing phase of matter which breaks inversion symmetry while preserving time-reversal symmetry. Here we demonstrate that the Fe-based superconductors exhibiting coplanar magnetic order realize an odd-parity magnetic state by combining low-energy modeling with density-functional theory. In the absence of spin-orbit coupling, the electronic spins are polarized along the $k_z$-direction and the splitting of the up and down states exhibits an $h$-wave form-factor. The magnitude of the splitting depends sensitively on specific parameters of the low-energy model, including specific out-of-plane hopping parameters and the Fermi energies of the hole- and electron-pockets. Interestingly, despite this state breaking inversion symmetry and exhibiting a finite out-of-plane Berry curvature and non-linear anomalous Hall effect, the Edelstein effect vanishes. Incorporating spin-orbit coupling tilts the momentum-space electronic spins into the ($k_x,k_y$)-plane and imparts finite in-plane components to the Edelstein response. Our findings highlight the Fe-based superconductors as platforms for exploring odd-parity magnetism both on its own and coexisting with unconventional superconductivity.